watermarking, compression, and their combination for 3-d

Numéro d’ordre : 2007-ISAL-0099 Année 2007

THÈSE

présentée devant

L’Institut National des Sciences Appliquées de Lyon et

Yeungnam University

pour obtenir

LE GRADE DE DOCTEUR

ÉCOLE DOCTORALE : ÉLECTRONIQUE, ÉLECTROTECHNIQUE, AUTOMATIQUE FORMATION DOCTORALE : IMAGES ET SYSTÈMES

par

Jae-Won CHO

Watermarking, Compression, and Their Combination

for 3-D Triangular Meshes

Soutenue le 7 décembre 2007

Jury :

M. Marc ANTONINI DR CNRS Rapporteur externe M. Ki-Ryong KWON Professeur Rapporteur externe Mme. Françoise PRETEUX Professeur Examinatrice M. Hyun-Soo KANG Professeur Examinateur M. Kook-Yeol YOO Professeur Examinateur Mme. Isabelle MAGNIN DR Inserm Président du jury M. Ho-Youl JUNG Professeur Co-directeur de thèse M. Rémy PROST Professeur Co-directeur de thèse

INSA Direction de la Recherche - Ecoles Doctorales 2007 SIGLE ECOLE DOCTORALE NOM ET COORDONNEES DU RESPONSABLE

CHIMIE

CHIMIE DE LYON http://sakura.cpe.fr/ED206 M. Jean Marc LANCELIN

Insa : R. GOURDON

M. Jean Marc LANCELIN Université Claude Bernard Lyon 1 Bât CPE 43 bd du 11 novembre 1918 69622 VILLEURBANNE Cedex Tél : 04.72.43 13 95 Fax : [email protected]

E.E.A.

ELECTRONIQUE, ELECTROTECHNIQUE, AUTOMATIQUEhttp://www.insa-lyon.fr/eea M. Alain NICOLAS Insa : D. BARBIER [email protected] Secrétariat : M. LABOUNE AM. 64.43 – Fax : 64.54

M. Alain NICOLAS Ecole Centrale de Lyon Bâtiment H9 36 avenue Guy de Collongue 69134 ECULLY Tél : 04.72.18 60 97 Fax : 04 78 43 37 17 [email protected] Secrétariat : M.C. HAVGOUDOUKIAN

E2M2

EVOLUTION, ECOSYSTEME, MICROBIOLOGIE, MODELISATION http://biomserv.univ-lyon1.fr/E2M2 M. Jean-Pierre FLANDROIS Insa : S. GRENIER

M. Jean-Pierre FLANDROIS CNRS UMR 5558 Université Claude Bernard Lyon 1 Bât G. Mendel 43 bd du 11 novembre 1918 69622 VILLEURBANNE Cédex Tél : 04.26 23 59 50 Fax 04 26 23 59 49 06 07 53 89 13 [email protected]

EDIIS

INFORMATIQUE ET INFORMATION POUR LA SOCIETE http://ediis.univ-lyon1.fr M. Alain MILLE Secrétariat : I. BUISSON

M. Alain MILLE Université Claude Bernard Lyon 1 LIRIS - EDIIS Bâtiment Nautibus 43 bd du 11 novembre 1918 69622 VILLEURBANNE Cedex Tél : 04.72. 44 82 94 Fax 04 72 44 80 53 [email protected] - [email protected]

EDISS

INTERDISCIPLINAIRE SCIENCES-SANTE M. Didier REVEL Insa : M. LAGARDE

M. Didier REVEL Hôpital Cardiologique de Lyon Bâtiment Central 28 Avenue Doyen Lépine 69500 BRON Tél : 04.72.35 72 32 Fax : [email protected]

MATERIAUX DE LYON M. Jean Marc PELLETIER Secrétariat : C. BERNAVON 83.85

M. Jean Marc PELLETIER INSA de Lyon MATEIS Bâtiment Blaise Pascal 7 avenue Jean Capelle 69621 VILLEURBANNE Cédex Tél : 04.72.43 83 18 Fax 04 72 43 85 28 [email protected]

Math IF

MATHEMATIQUES ET INFORMATIQUE FONDAMENTALE M. Pascal KOIRAN Insa : G. BAYADA

M.Pascal KOIRAN Ecole Normale Supérieure de Lyon 46 allée d’Italie 69364 LYON Cédex 07 Tél : 04.72.72 84 81 Fax : 04 72 72 89 69 [email protected] Secrétariat : Fatine Latif - [email protected]

MEGA

MECANIQUE, ENERGETIQUE, GENIE CIVIL, ACOUSTIQUE M. Jean Louis GUYADER Secrétariat : M. LABOUNE PM : 71.70 –Fax : 87.12

M. Jean Louis GUYADER INSA de Lyon Laboratoire de Vibrations et Acoustique Bâtiment Antoine de Saint Exupéry 25 bis avenue Jean Capelle 69621 VILLEURBANNE Cedex Tél :04.72.18.71.70 Fax : 04 72 18 87 12 [email protected]

SSED

SCIENCES DES SOCIETES, DE L’ENVIRONNEMENT ET DU DROIT Mme Claude-Isabelle BRELOT Insa : J.Y. TOUSSAINT

Mme Claude-Isabelle BRELOT Université Lyon 2 86 rue Pasteur 69365 LYON Cedex 07 Tél : 04.78.69.72.76 Fax : 04.37.28.04.48 [email protected]

Abstract

This dissertation deals with watermarking, compression, and their combination for three-

dimensional (3-D) triangular meshes. We first propose algorithms individually in order to

watermark static meshes and to compress mesh sequences. Finally we derive a combined

system for joint compression and watermarking.

Firstly, we propose two oblivious (or blind) watermarking techniques for 3-D static

meshes. They mainly use statistical features of vertex norms to embed watermark; the

first proposed method shifts the mean value of the distribution and the second proposed

method changes its variance. Histogram mapping functions are introduced to modify

the distribution. These mapping functions are devised in order to reduce the visibility

of watermark as much as possible. Since the statistical features of vertex norms are

less sensitive to signal alterations, the proposed methods can be robust against general

attacks. In addition, our methods employ a blind watermark detection scheme, which can

extract the watermark without referring to the original mesh model. Through simulations,

we demonstrate that the proposed approaches are robust against several attacks such as

adding binary noise, smoothing, uniform quantization, simplification, sub-division, vertex

re-ordering, and similarity transform.

Next, we present two compression methods for 3-D mesh sequences with constant

connectivity. The proposed methods mainly use an exact integer spatial wavelet analy-

sis (SWA) technique to efficiently decorrelate the spatial coherence of each mesh frame

and also to promptly transmit mesh frames with various spatial resolutions under differ-

ent bandwidth conditions (spatial scalability). To reduce the temporal redundancy, the

first proposed method applies multi-order differential coding (MDC) to the 1-D temporal

sequences after SWA of each mesh frame. MDC determines the optimal order of the dif-

ferential coder by analyzing the variance of prediction errors. Compared to the first-order

differential coding (FDC) scheme, the method can improve the compression performance.

The second proposed method applies temporal wavelet analysis (TWA) to the 1-D tem-

poral sequences. In particular, this method offers spatiotemporal multi-resolution coding.

Through simulations, we prove that our approaches enable efficient lossy-to-lossless com-

pression for 3-D mesh sequences.

Finally, we present a joint watermarking and compression method for 3-D mesh se-

quences. Our approach is based on the proposed compression method using SWA and

TWA. For robust and invisible watermark, a new watermarking technique derived from our

second watermarking scheme is applied to the intermediate step of the compression process.

Watermark embedding is carried out by the histogram mapping function which modifies

the variance of spatiotemporal wavelet coefficients belonging to specific sub-bands. The

hidden watermark is robust against several attacks such as additive binary noise, smooth-

ing, and frame dropping, because the employed watermark carrier is a statistical feature

of spatiotemporal wavelet coefficients. Through simulations, we prove that our approach

enables to efficiently compress 3-D mesh sequences and to strictly protect its ownership

in a single framework.

Keywords

Watermarking, compression, joint compression and watermarking, 3-D static meshes, 3-D

mesh sequences, and constant connectivity

Resume

Cette these contribue au tatouage, a la compression et a la combinaison de ces deux

techniques pour des objets 3-D representes par leur maillage surfacique. Dans un premier

temps, nous traitons individuellement ces deux problemes, puis, dans un deuxieme temps

nous les combinons.

Dans une premiere partie, nous proposons deux methodes de tatouage aveugle pour des

maillages statiques 3-D. Ces propositions utilisent les proprietes statistiques, de la norme

des vecteurs associes aux coordonnees des sommets, pour incorporer le tatouage. Une

premiere methode modifie la moyenne de la distribution de la norme des sommets et une

deuxieme methode change sa variance. Ces operations sont effectuees par transformations

non lineaires de la distribution de la norme des sommets (transformations d’histogramme).

Ces transformations sont concues dans le but de reduire la visibilite du tatouage. Comme

les proprietes statistiques des normes des sommets sont peu sensibles a des modifications

geometriques ou topologiques du maillage, nos propositions sont robustes aux attaques.

De plus, nos methodes emploient une extraction aveugle du tatouage, c’est a dire sans le

maillage original. Nous demontrons, par des simulations, que nos approches sont robustes

aux attaques telles que: l’addition de bruit binaire, le lissage, la quantification uniforme,

la simplification, la subdivision, le reordonnancement des sommets, et des transformations

affines.

Dans une deuxieme partie, nous proposons des algorithmes de compression des sequenc-

es de maillages 3-D a connectivite constante. Ces propositions utilisent une analyse

en ondelettes spatiales pour decorreler la geometrie des trames et pour les transmettre

progressivement, avec une resolution croissante (echelonnage spatial) afin de permettre

une adaptation a la bande passante disponible. A chaque niveau de resolution du mail-

lage des trames on considere que les coordonnees d’un sommet sont trois signaux (1D)

temporels independants. Dans une premiere methode nous appliquons a ces signaux un

codage differentiel, avec un ordre multiple, afin de reduire la redondance temporelle. Nous

determinons l’ordre optimal de prediction par celui qui conduit a la variance de l’erreur de

prediction la plus faible. En effet, nous montrons que l’entropie de l’erreur de prediction

decroıt lorsque sa variance decroıt. Dans une deuxieme methode nous appliquons une

analyse en ondelettes temporelles a ces signaux 1-D. Cette methode permet un codage

multi-resolution dans l’espace et le temps. Nous montrons, experimentalement, que nos

approches permettent, non seulement la compression avec pertes, mais aussi la compres-

sion sans pertes des sequences de maillages 3-D.

Finalement, nous presentons une methode combinant la compression et de tatouage

des sequences de maillages 3-D. Cette proposition s’appuie sur notre deuxieme methode de

compression qui utilise les analyses en ondelettes spatiales et temporelles. Afin d’obtenir un

tatouage robuste et invisible, une nouvelle approche, qui decoule de la deuxieme methode

de tatouage, est appliquee a l’etape intermediaire de la methode de compression. La vari-

ance des coefficients d’ondelettes spatio-temporelles qui appartiennent a certaines sous

bandes est modifiee par transformation d’histogramme. Le tatouage est robuste aux at-

taques telles que: l’addition de bruit binaire, le lissage, la suppression de trames. Ces

performances sont dues aux proprietes statistiques des coefficients d’ondelettes spatio-

temporelles employees comme porteur du tatouage. Par les simulations, nous montrons

que notre approche permet de compresser efficacement les sequences de maillages 3-D,

tout en protegeant leur proprietaire de copies frauduleuses, avec une methode combinant

compression et tatouage.

Mots cles

Tatouage, compression, compression et tatouage combines, maillages statiques 3-D, seque-

nces de maillages 3-D et connectivite constante

요약문 본 학위 논문은 3차원 삼각 메쉬 데이터(3-D triangular meshes)를 위한 워터마킹(watermarking), 압축(compression), 그리고 이들간의 통합 시스템을 다룬다. 워터마킹 및

압축 통합 시스템을 본 학위 논문의 최종 목표로 하여 각각의 연구 주제를 고찰한 뒤,

두 연구 주제로부터 하나의 통합된 시스템을 도출해 내기로 한다.

먼저, 3차원 정지 메쉬(3-D static mesh)를 위한 두 가지 블라인드(blind) 워터마킹 기법을 제안한다. 제안하는 방법은 워터마크(watermark)를 삽입하기 위해 통계적 특성(statistical feature)을 이용한다. 즉, 제안하는 첫 번째 방법은 확률 분포(probability

distribution)의 평균 값(mean value)을, 두 번째 방법은 확률 분포의 분산(variance)을 수정함으로써 워터마크를 삽입한다. 이를 위해 히스토그램 대응 함수(histogram mapping

function)가 워터마크의 비지각성(invisibility)을 극대화하기 위해 고안되었다. 일반적으로 좌표 벡터(vertex norm)의 통계적 특성은 신호 변형에 둔감하기 때문에 제안하는 방법은 다양한 신호처리 공격에 강인하다. 게다가 제안하는 방법은 원본 신호의 참조 없이 삽입된 워터마크 검출(watermark extraction)이 가능한 블라인드 기법이다. 모의 실험을 통하여 제안하는 방법이 이진 잡음 첨가(adding binary noise), 스무딩(smoothing), 균일 양자화(uniform quantization), 간략화(simplification), 세분화(subdivision), 좌표 재배열(vertex re-ordering), 유사 변환(similarity transform)과 같은 다양한 공격에 강인함을 증명한다.

다음으로 고정된 연결 정보(constant connectivity)를 가지는 3차원 메쉬 시퀀스(3-D

mesh sequence)를 위한 두 가지 압축 기법을 제안한다. 제안하는 방법은 효율적으로 각각의 메쉬 프레임의 공간 중복성(spatial redundancy)을 제거할 수 있을 뿐만 아니라 시시각각 변화하는 네트워크 환경에 대비하여 최고 해상도(highest resolution)로부터 최저

해상도(lowest resolution)까지 다양한 공간 해상도(spatial multi-resolutions)를 가지는 메쉬

프레임(mesh frame)을 전송하는 것이 가능한 정수형 공간 웨이블릿 분해 기법(exact

integer spatial wavelet analysis)을 주로 사용한다. 시간 중복성(temporal redundancy)을 제거하기 위한 방법으로서 제안하는 첫 번째 방법은 공간 웨이블릿 분해 후 얻어지는 1차원 신호 열(1-D temporal sequence)에 다차 차분 부호화 기법(multi-order differential coding

scheme)을 적용한다. 이 다차 차분 부호화 기법은 예측 오차(prediction error)의 분산을

분석함으로써 차분 부호화기의 최적 차수(optimal order)를 구할 수 있으며, 1차 차분 부호화기(first-order differential coder)와 비교 했을 때 압축 효율을 높일 수 있다. 제안하는

두 번째 방법은 공간 웨이블릿 분해 후 얻어지는 1차원 신호 열에 시간 축 웨이블릿

분해 기법(temporal wavelet analysis scheme)을 적용한다. 특히 이 방법은 시/공간 다 해상도(spatiotemporal multi-resolutions) 전송을 가능하게 한다. 모의 실험을 통하여 제안된

두 가지 방법이 손실 및 무손실 압축(lossy-to-lossless)이 하나의 단일 프레임워크에서

이루어질 수 있음을 증명한다.

마지막으로 3차원 메쉬 시퀀스를 위한 워터마킹 및 압축 통합 시스템을 제안한다.

제안하는 방법은 앞서 제안된 시/공간 웨이블릿 변환을 이용한 압축 기법에 기반한다.

삽입될 워터마크의 강인성 및 비지각성을 위해서 앞서 제안된 3차원 정지 메쉬 워터마킹 기법으로부터 확장된 새로운 방법이 압축의 중간 과정에 적용된다. 이 때, 워터마크 정보는 히스토그램 대응 함수를 이용하여 특정 부대역(sub-band)에 속하는 시/공간 웨이블릿 계수의 분산을 수정함으로써 삽입된다. 제안된 방법은 시/공간 웨이블릿

계수의 통계적 특성을 이용하기 때문에 삽입된 워터마크는 이진 잡음 첨가, 스무딩,

프레임 제거(frame dropping) 등과 같은 다양한 공격에 강인하다. 모의 실험을 통하여

제안된 방법이 하나의 통합된 시스템에서 3차원 메쉬 시퀀스를 위한 효율적인 압축

및 저작권 보호가 가능함을 입증한다.

핵심어 워터마킹, 압축, 압축 및 워터마킹의 통합 시스템, 3차원 정지 메쉬, 3차원 메쉬 시퀀스, 고

정 연결 정보

Contents

1 Introduction 1

1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Main Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.3 Organization of the Dissertation . . . . . . . . . . . . . . . . . . . . . . . . 4

2 Watermarking for 3-D Static Meshes 5

2.1 Introduction and State of the Arts . . . . . . . . . . . . . . . . . . . . . . . 6

2.2 Proposed Watermarking Methods . . . . . . . . . . . . . . . . . . . . . . . . 9

2.2.1 The Proposed Watermarkig Method Using Mean Modification . . . 12

2.2.2 The Proposed Watermarking Method Using Variance Modification . 17

2.3 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.3.1 Attack Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.3.2 Parameters for Robustness . . . . . . . . . . . . . . . . . . . . . . . 37

2.3.3 ROC Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

2.4 Summaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

3 Compression for 3-D Mesh Sequences 43


3.2 Wavelet-based Multi-resolution Analysis . . . . . . . . . . . . . . . . . . . . 47

3.2.1 SWA (Spatial Wavelet Analysis) and Its Synthesis . . . . . . . . . . 47

3.2.2 TWA (Temporal Wavelet Analysis) and Its Synthesis . . . . . . . . . 50

3.3 Proposed Compression Methods . . . . . . . . . . . . . . . . . . . . . . . . . 52

3.3.1 The Proposed Compression Method Using SWA and MDC . . . . . 52

ii CONTENTS

3.3.2 The Proposed Compression Method Using SWA and TWA . . . . . 58


3.4.1 SWA+MDC Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

3.4.2 SWA+TWA Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

3.5 Summaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

4 Joint Watermarking and Compression 73


4.2 Proposed Joint Watermarking and Compression Method . . . . . . . . . . . 78

4.2.1 Encoding Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

4.2.2 Decoding Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86


4.3.1 Attack Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

4.3.2 Parameters for Robustness . . . . . . . . . . . . . . . . . . . . . . . 98

4.4 Summaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

5 Conclusions and Perspectives 103

A Histogram Mapping Function 107

A.1 For Shifting Mean Value of Uniform Distribution . . . . . . . . . . . . . . . 107

A.2 For Changing Variance of Uniform Distribution . . . . . . . . . . . . . . . . 109

A.3 For Changing Variance of Laplacian Distribution . . . . . . . . . . . . . . . 110

B Estimation of Entropy 113

C Finding the Optimal Order 115

Bibliography 117

List of Figures

2.1 Proposed watermarking method by shifting the mean of the distribution . . 10

2.2 Proposed watermarking method by changing the variance of the distribution 10

2.3 Distribution of vertex norms obtained from the bunny model, where dashed

vertical lines indicate the border of each bin. . . . . . . . . . . . . . . . . . 12

2.4 (a) Block diagrams of the watermark embedding for the proposed water-

marking method shifting the mean value of vertex norms (continued on next

page) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.4 (b) Block diagrams of the watermark extraction for the proposed water-

marking method shifting the mean value of vertex norms (continued from

previous page) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.5 (a) Block diagrams of the watermark embedding for the proposed water-

marking method changing the variance of vertex norms (continued on next

page) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.5 (b) Block diagrams of the watermark extraction for the proposed water-

marking method changing the variance of vertex norms (continued from

previous page) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.6 Original mesh models (a) buddha, (b) bunny, (c) dragon (continued on next

page) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.6 (d) cow, (e) face, and (f) fandisk (continued from previous page) . . . . . . 25

2.7 Watermarked mesh models, where (a)-(f) are watermarked by mean mod-

ification method and (g)-(l) by variance modification method. (continued

on next page) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

iv LIST OF FIGURES



from previous page and contined on next page) . . . . . . . . . . . . . . . . 27



from previous page and contined on next page) . . . . . . . . . . . . . . . . 28



from previous page) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

2.8 Bunny model watermarked by mean modification method and attacked by

(a) multiplicative binary noise with error ratio of 0.5%, (b) 7bits/coordinate

quantization, (c) smoothing with iteration of 50 and relaxation of 0.03 and

(d) simplification with reducing 90.65% of vertices . . . . . . . . . . . . . . 30

2.9 (a) Relationship between the strength factor and the correlation. As an

example, a smoothing attack with iteration 30 and relaxation 0.03 is applied.

(continued on next page) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

2.9 (b) Relationship between the number of bins and the correlation. As an

example, a smoothing attack with iteration 30 and relaxation 0.03 is applied.

(continued from previous page) . . . . . . . . . . . . . . . . . . . . . . . . . 39

2.10 ROC curves of bunny model (a) watermarked by mean modification method

and attacked by multiplicative noise, (b) watermarked by mean modification

method and attacked by simplification (continued on next page) . . . . . . 41

2.10 (c) watermarked by variance modification method and attacked by multi-

plicative noise, and (d) watermarked by variance modification method and

attacked by simplification (continued from previous page) . . . . . . . . . . 42

3.1 (a) SWA (Spatial Wavelet Analysis) and (b) its synthesis processes . . . . . 48

3.2 2-channel (a) TWA (Temporal Wavelet Analysis) and (b) its synthesis pro-

cesses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

LIST OF FIGURES v

3.3 The encoding process of the proposed method using SWA and MDC tech-

niques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

3.4 Variances (σ2) of prediction errors of Face model according to different

orders (m) of MDC. The x-coordinate of the first base mesh vertex sequence

of this model is designated for a practical example. . . . . . . . . . . . . . . 56

3.5 Prediction error distributions of Face model in terms of (a) FDC and (b)

MDC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

3.6 The encoding process of the proposed method using SWA and TWA tech-

niques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

3.7 Distributions of wavelet coefficients of the x-axis of the first base mesh

sequence of Face model using (a) Haar (2/2 tap) filters, (b) Le Gall (5/3

tap) filters (continued on next page) . . . . . . . . . . . . . . . . . . . . . . 60

3.7 (c) Daubechies (9/7 tap) filters (continued from previous page) . . . . . . . 61

3.8 Original mesh sequences, (a)-(c) Cow models (continued on next page) . . . 63

3.8 (d)-(f) Face models (continued from previous page) . . . . . . . . . . . . . . 64

3.9 Distributions of practical optimal orders of the differential coder in SWA+MDC

for (a) Cow and (b) Face models . . . . . . . . . . . . . . . . . . . . . . . . 65

3.10 R-D curves of SWA, SWA+FDC and SWA+MDC methods for (a) Cow and

(b) Face models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

3.11 R-D curves of SWA+TWA method at different spatial resolutions where

three temporal wavelet filter-banks are used for (a) Cow and (b) Face models 70

3.12 R-D curves of SWA+TWA method at different spatiotemporal resolutions,

where the temporal sequences are decomposed into five levels using Daubechies

filter banks for (a) Cow and (b) Face models . . . . . . . . . . . . . . . . . 71

4.1 Proposed watermarking method by changing the variances of high frequency

sub-band signal: (a) distributions of two subsets, A and B, of high fre-

quency sub-band signal, the modified distributions of the two subsets for

embedding watermark (b) +1 and (c) −1, where, we assume that the initial

two subsets have the same Laplacian distributions for the simple illustration. 80

vi LIST OF FIGURES

4.2 The encoding process of the proposed joint watermarking and compression

scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

4.3 The watermark embedding process . . . . . . . . . . . . . . . . . . . . . . . 83

4.4 The decoding process of the proposed joint watermarking and compression

scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

4.5 The watermark extraction process . . . . . . . . . . . . . . . . . . . . . . . 88

4.6 Watermarked mesh sequences, (a)-(c) Cow models (continued on next page) 91

4.6 (d)-(f) Face models (continued from previous page) . . . . . . . . . . . . . . 92

4.7 Cow model attacked by (a)-(c) multiplicative binary noise with error ratio

of 1% (continued on next page) . . . . . . . . . . . . . . . . . . . . . . . . . 95

4.7 (d)-(f) 6bits/coordinate quantization (continued from previous page and

continued on next page) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

4.7 (g)-(i) smoothing with iteration of 120 and relaxation of 0.03 (continued

from previous page) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

A.1 Histogram mapping function, Y = Xk, for different parameters of k . . . . 108

A.2 Expectation of the output random variable via histogram mapping function

with different k, assuming that the input random variable is uniformly

distributed over unit range [0, 1]. . . . . . . . . . . . . . . . . . . . . . . . . 109

A.3 Histogram mapping function, sign (X) |X|k, for different parameter of k . . 110

A.4 Variance of the output random variable via histogram mapping function

with different k, assuming that the input random variable is uniformly

distributed over the normalized range [−1, 1]. . . . . . . . . . . . . . . . . . 111

A.5 Second moment (variance) of the output random variable via histogram

mapping function with different k, assuming that the input variable has

Laplacian distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

B.1 Relationship between the entropy and the variance according to different σ 114

List of Tables

2.1 Evaluation of watermarked meshes when no attack . . . . . . . . . . . . . . 23

2.2 Evaluation of robustness against multiplicative binary noise attacks . . . . . 32

2.3 Evaluation of robustness against uniform quantization attacks . . . . . . . . 33

2.4 Evaluation of robustness against smoothing attacks . . . . . . . . . . . . . . 34

2.5 Evaluation of robustness against simplification attacks (continued on next

page) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

2.5 (Continued from previous page) . . . . . . . . . . . . . . . . . . . . . . . . . 36

2.6 Evaluation of robustness against 1:4 sub-division attacks . . . . . . . . . . . 36

3.1 The lossless compression results of SWA+MDC method compared with

SWA and SWA+FDC methods . . . . . . . . . . . . . . . . . . . . . . . . . 62

3.2 The lossless compression results of SWA+TWA method compared with

TWA scheme according to temporal wavelet decomposition levels and three

temporal wavelet filter-banks: Haar (2/2 tap), Le Gall (5/3 tap) and Daubechies

(9/7 tap) filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

4.1 Parameters used in the simulations . . . . . . . . . . . . . . . . . . . . . . . 90

4.2 Evaluation of compression performance and watermark robustness when no

attack . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

4.3 Evaluation of robustness against intra-frame attacks . . . . . . . . . . . . . 98

4.4 Adjusted parameters to improve robustness (Face) . . . . . . . . . . . . . . 99

4.5 Evaluation of compression performance and watermark robustness in terms

of different threshold α and different β (When no attack) . . . . . . . . . . 99

viii LIST OF TABLES

4.6 Evaluation of robustness according to different threshold α and different β

(After intra-frame attacks applied to Face) . . . . . . . . . . . . . . . . . . . 100

Chapter 1

Introduction

1.1 Background

The information revolution has more and more led to convenient and interesting lives since

the end of the twentieth century. We are not unfamiliar with many digital devices, such as

laptop, PDA, MP3 player, and portable multimedia player, any longer. Wherever we are,

the Internet connected to the World Wide Web enables to know what happened on the

whole parts of the globe. DMB (Digital Multimedia Broadcasting) service providers, from

the last three or four years, have already offered live broadcasts with various channels via

digital personal devices such as mobile phone and PDA at every where and time that we

want. In the near future, human beings would live in the Ubiquitous environment as we

have seen in a new prospective life model such as Cool Town presented by the Hewlett-

Packard Corporation. All electronic and mechanical equipments would be linked together

by an integrated network, and therefore someone who lives in the city might access, control

and communicate with another terminal wherever and whenever he/she wants.

With these remarkable breakthroughs of the digital information and the network tech-

nologies, the requirements of high quality multimedia data have gradually become con-

spicuous and concurrently encouraged the investigation of data compression in order to

compactly store and to promptly transmit a huge source data. Several international stan-

dardization working groups such as JPEG (Joint Photographic Experts Group) 1 and

1JPEG is a collaboration between ISO (International Organization for Standardization) standard and

2 Introduction

MPEG (Moving Picture Experts Group) 2, since 1980’s, have devoted commendable en-

deavors to establish competent frameworks for compression and transmission of audios,

2-D still images, 2-D videos and 3-D meshes.

Such facilities of the information and communication technologies, however, have not

always done make salutary results acting up to the social morality, owing to the essen-

tial characteristics: digitalized data could be exactly copied, easily modified and illegally

distributed without any effort. Besides, the World Wide Web fundamentally offers infor-

mation sharing services to end users. For those reasons, over the last decade, illegal use of

copyrighted data has been posed a serious problem on digital industrial fields. Many peer

to peer systems such as Napster and eDonkey have instigated to share copyrighted digital

data, and caused great financial damages of ownership holders. As a part of exploring

ways toward copyright protection, very recently, watermarking has been highlighted as a

good way out. It supplies information hiding scheme, and also enables to trace routes

of illegal distribution. Some international standards and associations such as JPEG2000

part 8 - JPSEC 3 and SDMI (Secure Digital Music Initiative) 4, from the last few years,

have tried to provide systematic mechanisms for ownership protection.

Until now, most studies on watermarking and compression have proceeded with each

separate framework. It is caused by the fact that watermarking within compressed bit-

stream could seriously affect the auditory or visual quality of decompressed data and

conversely that lossy compression based on quantization might interfere with the ownership

assertion of watermarked data. Nevertheless, it is clear that these two research topics

CCITT (International Telegraph and Telephone Consultative Committee) recommendation. It is the first

international standard for 2-D still images represented as grayscale and color. The outline of the standard-

ization has been considerably summarized in [Wallace, 1992].2MPEG was established by the joint ISO and IEC (International Electrotechnical Commission) technical

committee in order to develop efficient coding standards of moving pictures, associated audio and their

combination. An overview of the principal issues has been substantially recapitulated in [Sikora, 1997].3JPEG2000 is a wavelet transform based image coding standard expanded from JPEG. The part 8,

so-called JPSEC, of the standard provides security maintenance methodologies including security of trans-

action, protection of contents and so on. An overview of JPSEC has been quite obviously summarized

in [F. Dufaux, 2004].4SDMI is an international forum formed in 1998 for the protection of digital music resources focused

on on-line delivering.

1.2 Main Contributions 3

should be simultaneously treated for prompt and also secure transmission of multimedia

data over network. Although some parts of international coding standards, which were

previously mentioned, have strived to develop a combined system of two technologies,

researches on joint watermarking and compression are still in its early stages. Therefore,

it should be expedited to investigate this undeveloped research area.

1.2 Main Contributions

This dissertation deals with watermarking, compression, and their combination for three

dimensional (3-D) data. 3-D data, a new type of multimedia data, has been more and more

widely used in many applications including on/off-line video games, animation movies,

medical images, and so on. Triangular meshes and their temporal sequences have been

regarded as very appropriate means for efficient representation of 3-D objects. However,

since they require enormous costs in order to be stored and to be transmitted as well

as to be created, they should be efficiently compressed and strictly protected. Pursuing

to design a joint watermarking and compression scheme for 3-D mesh sequences as the

final goal of this dissertation, we primarily discuss two individual research topics and then

derive a combined system from both of them.

Watermarking We propose two watermarking schemes for 3-D static meshes

using distribution of vertex norms. The probability distribution of vertex norms would

not be sensitive to intentional or non-intentional alterations. Therefore, the first and

second proposed methods embed copyright owner’s information, so-called watermark, by

means of modifying mean or variance of vertex norms, respectively. The mean or variance,

in our methods, is changed into desired values via histogram mapping functions which

are newly designed in this dissertation. Both methods could be robust against general

attacks. Besides, they employ oblivious schemes which do not require the original data at

the watermark extraction side.

Compression We propose two compression methods for 3-D mesh sequences.

Our approaches basically utilize a SWA (Spatial Wavelet Analysis) not only to efficiently

de-correlate spatial coherence but also to transmit 3-D mesh sequences with various spa-

4 Introduction

tial resolutions. The first and second methods reduce temporal redundancy by adopting

a MDC (Multi-order Differential Coding) and TWA (Temporal Wavelet Analysis) tech-

niques, respectively. The first proposed method can improve compression performance of

FDC (the First-order Differential Coding) technique. Note that we could easily determine

the optimal order via an estimation of entropy coding efficiency using variance of tempo-

ral sequence. The second compression method, for temporal geometry coding, employs

several lossless wavelet filter banks including Haar (2/2 taps), Le Gall (5/3 taps), and

Daubechies (9/7 taps) filters. Our schemes enable lossy-to-lossless compression for 3-D

mesh sequences.

Joint Watermarking and Compression The proposed joint watermarking and

compression technique is based on the proposed compression method using SWA and TWA

schemes. For robust and invisible watermark, a new watermarking technique derived from

our 3-D static mesh watermarking scheme which modifies the variance of vertex norms

to embed watermark is applied to the intermediate step of the compression process. The

variance of spatiotemporal wavelet coefficients belonging to specific sub-band, to embed

watermark, is modified by a histogram mapping function. The hidden watermark can be

quite robust against several possible attacks because a statistical feature is employed as the

watermark carrier in our proposed method. Our scheme realizes a combined compression

system towards copyright protection for 3-D mesh sequences in a single framework.

1.3 Organization of the Dissertation

This dissertation is organized as follows. Chapter 2, Chapter 3, and Chapter 4 respectively

treat of three main research topics: watermarking, compression, and their combination.

Each chapter firstly introduces the overview and the state of the arts of pertinent research

area, and describes the proposed methods in detail. After that, the proposed methods are

evaluated in terms of the criterions required for individual application. The summaries

of each proposed technique are provided in the end of each chapter. Finally, we conclude

this dissertation with final remarks and perspectives in Chapter 5.

Chapter 2

Watermarking for 3-D Static

Meshes

This chapter presents two oblivious (or blind) watermarking techniques for 3-D static

meshes. Although it has been known that oblivious watermarking schemes are less robust

than non-oblivious ones, they are more useful for various applications where a host sig-

nal is not available in the watermark detection procedure. From a viewpoint of oblivious

watermarking for a 3-D polygonal mesh model, distortion-less attacks, such as similarity

transforms and vertex re-ordering, might be more serious than distortion attacks including

multiplicative noise, smoothing, simplification, re-meshing, clipping and so on. Clearly,

it is required to develop an oblivious watermarking that is robust against distortion-less

as well as distortion attacks. In this chapter, we propose two oblivious watermarking

methods for 3-D polygonal mesh models, which modify the distribution of vertex norms

according to the watermark bit to be embedded. One method is to shift the mean value

of the distribution and another is to change its variance. Histogram mapping functions

are introduced to modify the distribution. These mapping functions are devised to reduce

the visibility of watermark as much as possible. Since the statistical features of vertex

norms are invariant to the distortion-less attacks, the proposed methods are robust against

such attacks. In addition, our methods employ an oblivious watermark detection scheme,

which can extract the watermark without referring to the original mesh model. Through

simulations we demonstrate that the proposed approaches are remarkably robust against

6 Watermarking for 3-D Static Meshes

distortion-less attacks. Besides, they are also fairly robust against various distortion at-

tacks.

2.1 Introduction and State of the Arts

With the remarkable growth of the network technology such as WWW (World Wide

Web), digital media enables us to copy, modify, store, and distribute digital data without

effort. As a result, it has become a new issue to research schemes for copyright protection.

Traditional data protection techniques such as encryption are not adequate for copyright

enforcement, because the protection cannot be ensured after the data is decrypted. Water-

marking provides a mechanism for copyright protection by embedding information, called

a watermark, into host data [Praun et al., 1999]. Unlike encryption, digital watermarking

does not restrict access to the host data but ensures the hidden data remain inviolate and

recoverable. Note that so-called fragile or semi-fragile watermarking techniques have also

been widely used for content authentication and tamper proofing [Cayre and Macq, 2003].

Here, we address only watermarking technique for copyright protection, namely robust

watermarking.

Most previous research has focused on general types of multimedia data including text

data, audio stream [Bender et al., 1996,Gruhl and Bender, 1996,Cho et al., 2004], still

images [Seo et al., 2003,Cox et al., 1997,Lin et al., 2000], and video stream [Hartung and

Girod, 1998]. Recently, with the interest and requirement of 3-D models such as VRML

(Virtual Reality Modeling Language), CAD (Computer Aided Design), polygonal mesh

models and medical objects, several watermarking techniques for 3-D mesh models have

been developed [Ohbuchi et al., 2001, Ohbuchi et al., 1998, Yu et al., 2003b, Yu et al.,

2003a,Benedens, 1999,Kanai et al., 1998,Yin et al., 2001,Praun et al., 1999,Cayre and

Macq, 2003,Wagner, 2000,Lee et al., 2003,Jian-qiu et al., 2004,Cho et al., 2005,Cho et al.,

2006a].

Since 3-D mesh watermarking techniques were introduced in [Ohbuchi et al., 1998],

there have been several attempts to improve the performance in terms of transparency

and robustness. R. Ohbuchi et al. [Ohbuchi et al., 1998] proposed three watermarking

2.1 Introduction and State of the Arts 7

schemes: TSQ (Triangle Similarity Quadruple), TVR (Tetrahedral Volume Ratio), and

a visible mesh watermarking method. These schemes can be regarded as oblivious tech-

niques that can extract the watermark without reference of original mesh model, but they

are not sufficiently robust against various attacks. For example, TVR is very vulnerable

to re-meshing, simplification and re-ordering attacks. Beneden [Benedens, 1999] proposed

a watermark embedding method that modifies the local distribution of vertex directions

from the center point of model. The method is robust against simplification attack, be-

cause the local distribution is not sensitive to such operations. An extended scheme was

also introduced in [Lee et al., 2003] to overcome a weakness to cropping attack. However,

the method still requires pre-processing for re-orientation during the process of watermark

detection, as the local distribution essentially varies with the degree of rotation. Z. Yu et

al. [Yu et al., 2003b,Yu et al., 2003a] proposed a vertex norm modification method that

perturbs the distance between the vertices to the center of model according to watermark

bit to be embedded. It employs, before the modification, scrambling of vertices for the

purpose of preserving the visual quality. Note that it is not an oblivious technique and

also requires pre-processing such as registration and re-sampling. Some multi-resolution

based methods have also been introduced [Ohbuchi et al., 2001, Kanai et al., 1998, Yin

et al., 2001]. S. Kanai et al. [Kanai et al., 1998] proposed a watermarking algorithm based

on wavelet transform. Similar approaches, using Burt-Adelson style pyramid and mesh

spectral analysis were also published in [Yin et al., 2001] and [Ohbuchi et al., 2001], respec-

tively. The multi-resolution techniques could achieve a highly transparency of watermark,

but have yet to overcome various attacks such as vertex re-ordering and simplification,

since the connectivity information of vertices must be exactly known for multi-resolution

analysis and reconstruction. In addition, they are categorized as non-oblivious schemes.

In this dissertation, our interests focus on developing an oblivious watermarking.

3-D polygonal mesh models have serious difficulties for watermark embedding. While

image data is represented by brightness (or amplitudes of RGB components in the case of

color images) of pixels sampled over a regular grid in two dimension, 3-D polygonal models

have no unique representation, i.e., no implicit order and connectivity of vertices [Yu et al.,

2003b, Yu et al., 2003a]. This creates synchronization problem during the watermark


extraction, which makes it difficult to develop robust watermarking techniques. For this

reason, most techniques developed for other types of multimedia are not effective for 3-D

meshes. Furthermore, a variety of complex geometrical and topological operations could

disturb the watermark extraction for assertion of ownership [Yu et al., 2003a].

The geometrical attacks include adding noise, smoothing and so on. Vertex re-ordering,

simplification and re-meshing fall into the category of topological attacks. These attacks

can be re-classified into two categories: distortion and distortion-less attacks [Cho et al.,

2005]. Distortion attacks include adding noise, simplification, smoothing, re-meshing,

clipping, and so on, which may cause visual deformation of the watermarked mesh model.

Most conventional watermarking techniques of 3-D polygonal mesh models have been de-

veloped to be robust mainly against the distortion attacks [Ohbuchi et al., 2001,Benedens,

1999,Kanai et al., 1998,Yin et al., 2001,Lee et al., 2003, Jian-qiu et al., 2004]. On the

other hand, distortion-less attacks include similarity transform and vertex re-ordering.

Note that the distortion-less attacks are more serious attacks on 3-D mesh watermarking

as they could fatally destroy the hidden watermark without any perceptual changes of

watermarked mesh model. Clearly, it is required to develop a watermarking technique

that is robust against distortion-less as well as distortion attacks.

In this chapter, we propose a statistical approach that modifies the distribution of

vertex norms to hide watermark information into host 3-D meshes. The distribution of

vertex norms is modified by two methods. One is to shift the mean value of the distribution

according to the watermark bit to be embedded and another to change its variance. A

similar approach has been used to shift the mean value in our previous work [Cho et al.,

2005], where a constant is added to vertex norms. Note that more sophisticated skills

are introduced in this chapter. In particular, histogram mapping functions are newly

introduced and used for the purpose of elaborate modification. Since the statistical features

are invariant to distortion-less attacks and less sensitive to various kinds of distortion ones,

robustness of watermark can be easily achieved. In addition, the proposed methods employ

a blind watermark detection scheme.

The rest of this chapter is organized as follows. In Section 2.2, the proposed water-

marking methods are described in detail, including the main idea behind the statistical

2.2 Proposed Watermarking Methods 9

approach, their embedding and extracting procedures. Here, histogram mapping functions

are also introduced to efficiently change the mean value and variance of the vector norm

distribution. Section 2.3 shows the simulation results of the proposed against various

distortion and distortion-less attacks. Finally, Section 2.4 summarizes this chapter.

2.2 Proposed Watermarking Methods

In order to achieve robustness of watermark against distortion-less attacks, it is very

important to find a watermark carrier, also called primitive in [Ohbuchi et al., 1998], that

can effectively preserve watermark from such attacks. For example, if vertices arranged in

a certain order are used as the watermark carrier, the hidden watermark bit stream cannot

be retrieved after vertex re-ordering. This is caused by the fact that 3-D polygonal meshes

do not have implicit order and connectivity of vertices. For the same reason, pre-processing

such as registration and re-sampling is required like as in [Yu et al., 2003b,Yu et al., 2003a]

or the robustness against distortion-less attacks cannot be guaranteed [Ohbuchi et al.,

2001,Ohbuchi et al., 1998,Kanai et al., 1998,Yin et al., 2001]. Clearly, statistical features

can be promising watermark carriers as they are generally less sensitive to these kinds

of attacks. Several features can be obtained directly from 3-D meshes, particularly, the

distribution of vertex directions and distribution of vector norms. Distribution of vertex

directions has been used as a watermark carrier in [Benedens, 1999, Lee et al., 2003],

where vertices are grouped into distinct sets according to their local direction and the

distribution of vertex direction is altered in each set separately. The distribution does not

change by vertex re-ordering operation, but it varies in essence with rotation operation.

Thus, it requires re-orientation processing before watermark detection [Benedens, 1999,Lee

et al., 2003]. On the other hand, the distribution of vertex norms does not change either

by vertex re-ordering or rotation operations. This is the reason why the distribution of

vertex norms is used as a watermark carrier in our methods.

We propose two watermarking methods that embed watermark into the 3-D mesh

model by modifying the distribution of vertex norms. Fig. 2.1 and 2.2 show the main

idea of each method, respectively. The first method is to make the mean value of vertex


Figure 2.1: Proposed watermarking method by shifting the mean of the distribution

Figure 2.2: Proposed watermarking method by changing the variance of the distribution


norms greater or smaller than a reference value according to watermark bit that we want to

insert. Assume that the vertex norms of original meshes are mapped into the interval [0, 1]

and have a uniform distribution over the interval as shown in Fig. 2.1(a). In this figure,

an arrow indicates the mean value of the vertex norms. To embed a watermark bit of

+1, the distribution is modified so that its mean value is greater than a reference value as

shown in Fig. 2.1(b). To embed −1, the distribution is modified so that it is concentrated

on the left side, and the mean value becomes smaller than a reference as shown in Fig.

2.1(c). The watermark extraction process is quite simple if the reference value is known.

The hidden watermark bit can be easily retrieved by simple comparison of the reference

with the mean value of vertex norms obtained from watermarked meshes. The second

proposed method is to change the variance of vertex norms to be greater or smaller than a

reference. Assume that the vertex norms are mapped into the interval [−1, 1] and have a

uniform distribution over the interval as shown in Fig. 2.2(a), where its standard deviation

is indicated by bi-directional arrow. To embed a watermark bit of +1, the distribution is

modified to concentrate on both margins. This leads to increase the standard deviation

as shown in Fig. 2.2(b). To embed −1, the distribution is altered to concentrate on the

center so that the standard deviation becomes smaller than a reference deviation as shown

in Fig. 2.2(c). Similar to the first proposed, the watermark can be extracted by comparing

the reference variance and variance taken from watermarked meshes.

Starting from the main idea of modifying the distribution of vertex norms, we introduce

some techniques to enhance watermark capacity and transparency. The distribution is

divided into distinct sections, hereafter referred to as bins, each of which is used as a

watermark embedding unit to embed one bit of watermark. The number of watermark

bits to be embedded can be properly selected by taking account the transparency. As an

example, Fig. 2.3 shows the distribution of a bunny model, which is divided into bins by

dashed vertical lines. It also shows that the distribution of each bin is close to uniform.

In addition, we introduce histogram mapping functions that can effectively modify the

distribution. The mapping functions are devised to reduce the visibility of the watermark

as much as possible.


Figure 2.3: Distribution of vertex norms obtained from the bunny model, where dashed

vertical lines indicate the border of each bin.

2.2.1 The Proposed Watermarkig Method Using Mean Modification

This method embeds watermark information into 3-D polygonal mesh model by shifting

the mean value of each bin according to assigned watermark bit. All of the vertex norms

in each bin are modified by a histogram mapping function. Fig. 2.4 depicts the watermark

embedding and extraction processes, which are described in detail in the followings.

Fig. 2.4(a) shows the watermark embedding process. First, Cartesian coordinates of a

vertex vi = (xi, yi, zi) on the original mesh model V (vi ∈ V) are converted into spherical

coordinates (ρi, θi, φi) by means of

ρi =√

(xi − xg)2 + (yi − yg)2 + (zi − zg)2

θi = tan−1 (yi − yg)(xi − xg)

for 0 ≤ i ≤ L− 1 (2.1)

φi = cos−1 (zi − zg)√(xi − xg)2 + (yi − yg)2 + (zi − zg)2

where L is the number of the vertex, (xg, yg, zg) is the center of gravity of the mesh

model, and ρi is the i-th vertex norm. The vertex norm represents the distance between


(a)

Fig

ure

2.4:

(a)

Blo

ckdi

agra

ms

ofth

ew

ater

mar

kem

bedd

ing

for

the

prop

osed

wat

erm

arki

ngm

etho

dsh

iftin

gth

em

ean

valu

eof

vert

ex

norm

s(c

onti

nued

onne

xtpa

ge)


(b)

Figure

2.4:(b)

Block

diagrams

ofthe

waterm

arkextraction

forthe

proposedw

atermarking

method

shiftingthe

mean

valueof

vertex

norms

(continuedfrom

previouspage)


each vertex and the center of gravity. The proposed method uses only vertex norms for

watermarking and keeps the other two components, θi and φi, intact. Note that the

distribution of vertex norms is invariant to vertex re-ordering and similarity transforms.

Second, vertex norms are divided into N distinct bins with equal range, according to

their magnitude. Each bin is used independently to hide one bit of watermark. If every bin

is processed for watermark embedding, we can insert at maximum N bits of watermark.

To classify the vertex norms into N bins, maximum and minimum vertex norms, ρmax

and ρmin, are calculated in advance. The n-th bin Bn is defined as follows.

Bn =ρn,j

∣∣∣∣ρmin +ρmax − ρmin

N· n < ρi

< ρmin +ρmax − ρmin

N· (n+ 1)

(2.2)

for 0 ≤ n ≤ N − 1, 0 ≤ i ≤ L− 1 and 0 ≤ j ≤Mn − 1

where Mn is the number of vertex norms belonging to the n-th bin and ρn,j is the j-th

vertex norm of the n-th bin.

Third, vertex norms belonging to the n-th bin are mapped into the normalized range

of [0, 1] by

ρn,j =ρn,j −minρn,j∈Bn ρn,j

maxρn,j∈Bn ρn,j −minρn,j∈Bn ρn,j(2.3)

where maxρn,j∈Bn ρn,j is the maximum vertex norm of the n-th bin and minρn,j∈Bn ρn,j

is the minimum vertex norm. ρn,j is the normalized, j-th vertex norm of the n-th bin.

Note that each bin now has a distribution very close to uniform over the unit interval as

mentioned in the previous section.

The fourth step of the proposed watermark embedding is to shift the mean value of

each bin via transforming vertex norms by the histogram mapping function as presented

in Appendix A.1. To embed a watermark bit of +1 (ωn = +1), vertex norms ρn,j are

transformed in order to shift the mean of the distribution by a factor, α (0 < α < 12).

Alternatively, to embed ωn = −1, vertex norms are transformed in order to shift the mean

by a factor −α. Then the mean of each bin, µ′n, is changed by

µ′n =

12 + α if ωn = +1

12 − α if ωn = −1

(2.4)


where α is the strength factor that can control the robustness and the transparency of

watermark. The exact parameter kn can be found directly from Eq. (A.3).

kn =

1−2α1+2α if ωn = +1

1+2α1−2α if ωn = −1

(2.5)

Note that kn exists in the range of ]0, 1[ when the watermark bit is +1, and kn does in

the range of ]1,∞[ when watermark bit is −1.

The real vertex norm distribution in each bin is neither continuous nor uniform. Then

the parameter kn cannot be calculated by Eq. (2.5). To overcome this difficulty we use

an iterative approach as follow.

For embedding ωn = +1 into the n-th bin:

1) Initialize the parameter kn as 1;

2) Transform normalized vertex norms by ρ′n,j = (ρn,j)kn ;

3) Calculate mean of transformed vertex norms through

µ′n = 1Mn

∑Mn−1j=0 ρ′n,j ;

4) If µ′n <12 + α, decrease kn (kn = kn −∆k) and go back to 2);

5) Replace normalized vertex norms with transformed norms using ρn,j = ρ′n,j ;

6) End.

For embedding ωn = −1 into the n-th bin:

4) If µ′n >12 − α, increase kn (kn = kn + ∆k) and go back to 2);

The fifth step is inverse processing of the third step. Transformed vertex norms of each

bin are mapped onto the original range by

ρ′n,j = ρ′n,j ·(

maxρn,j∈Bn

ρn,j − minρn,j∈Bn

ρn,j)

+ minρn,j∈Bn

ρn,j (2.6)

where maxρn,j∈Bn ρn,j and minρn,j∈Bn ρn,j are the same as those used in the step

three.

Finally, the watermark embedding process is completed by combining all of the bins

and converting the spherical coordinates to Cartesian coordinates. Let ρ′i be a vertex norm


in the combined bin. A watermarked mesh model V′ consisting of vertices v′i = (x′i, y′i, z

′i)

represented in Cartesian coordinate is obtained by

x′i = ρ′i cos θi sinφi + xg

y′i = ρ′i sin θi sinφi + yg for 0 ≤ n ≤ L− 1 (2.7)

z′i = ρ′i cosφi + zg

where θi, φi, and the center of gravity are the same as those calculated in the first step.

The watermark extraction process is quite simple as shown in Fig. 2.4(b). Similar

to embedding process, the watermarked mesh model is first converted to spherical coor-

dinates. After finding the maximum and minimum vertex norms, the vertex norms are

classified into N bins and mapped onto the normalized range of [0, 1]. Then, the mean of

each bin, µ′′n is calculated and compared to the reference value, 12 . The watermark hidden

in the n-th bin, ω′′n, is extracted by means of

ω′′n =

+1, if µ′′n >12

−1, if µ′′n <12

(2.8)

Note that the watermark detection process does not require the original meshes.

2.2.2 The Proposed Watermarking Method Using Variance Modifica-

tion

In this method, the variance of vertex norm distribution is changed to hide one bit of

watermark in each bin. Again, a histogram mapping function is introduced and applied.

Both the watermark embedding and extraction processes of the method are quite similar

to mean modification method, as introduced in previous section and shown in Fig. 2.5.

Fig. 2.5(a) shows the watermark embedding process. As the first two steps and the last

step of this watermark embedding process are identical to those mentioned in Sub-section

2.2.1, only the unique steps of this method are described in details. Note that notations

have not been changed from the previous section for the sake of simplicity.

In the first and second steps, vertices of original meshes are represented in spherical

coordinate, and vertex norms are divided into N bins such as ρn,j ∈ Bn for 0 ≤ n ≤ N −1

and 0 ≤ j ≤Mn − 1.


(a)

Figure

2.5:(a)

Block

diagrams

ofthe

waterm

arkem

beddingfor

theproposed

waterm

arkingm

ethodchanging

thevariance

ofvertex

norms

(continuedon

nextpage)


(b)

Fig

ure

2.5:

(b)B

lock

diag

ram

sof

the

wat

erm

ark

extr

acti

onfo

rth

epr

opos

edw

ater

mar

king

met

hod

chan

ging

the

vari

ance

ofve

rtex

norm

s

(con

tinu

edfr

ompr

evio

uspa

ge)


In the third step, vertex norms of each bin are mapped into a normalized range similar

to the mean modification method. However, the range [−1, 1] is now mapped by

ρn,j = 2 ·(ρn,j −minρn,j∈Bn ρn,j

)maxρn,j∈Bn ρn,j −minρn,j∈Bn ρn,j

− 1 (2.9)

where ρn,j is the j-th vertex norm of the n-th bin represented in the normalized range.

Note that each bin has a nearly uniform distribution over the interval [−1, 1].

The fourth step of the watermark embedding process is to change variance of each

bin via transforming vertex norms by the histogram mapping function as presented in

Appendix A.2. To embed ωn = +1, vertex norms ρn,j are transformed in order to change

the variance of the distribution by a strength factor, α (0 < α < 13). To embed ωn = −1,

vertex norms are transformed in order to change the variance by a factor −α. Then the

variance of each bin, σ2′n , is changed by

σ2′n =

13 + α if ωn = +1

13 − α if ωn = −1

(2.10)

The exact parameter can be found directly from Eq. (A.4).

kn =

1−3α1+3α if ωn = +1

1+3α1−3α if ωn = −1

(2.11)

Note that kn exists in the range of ]0, 1[ when the watermark bit is +1, and kn does in

the range of ]1,∞[ when watermark bit is −1.

As mentioned in Sub-section 2.2.1, Eq. (2.11) is not useful for the real vertex norm

distribution. Thus we use an iterative approach as follow.

For embedding ωn = +1 into the n-th bin:

1) Initialize the parameter kn as 1;

2) Transform normalized vertex norms by ρ′n,j = sign (ρn,j) |ρn,j |kn ;

3) Calculate the variance of transformed vertex norms through

σ2′n = 1

Mn

∑Mn−1j=0 ρ′2n,j ;

4) If σ2′n < 1

3 + α, decrease kn (kn = kn −∆k) and go back to 2);

5) Replace normalized vertex norms with transformed norms using ρn,j = ρ′n,j ;

2.3 Simulation Results 21

6) End.

For embedding ωn = −1 into the n-th bin:

4) If σ2′n > 1

3 − α, increase kn (kn = kn + ∆k) and go back to 2);

The fifth step is to map each bin onto the original range using

ρ′n,j =12·(ρ′n,j + 1

)·(

maxρn,j∈Bn

ρn,j − minρn,j∈Bn

ρn,j)

+ minρn,j∈Bn

ρn,j (2.12)

Finally, the watermark embedding process is completed by combining all of the bins

and converting the spherical coordinates to Cartesian coordinates using Eq. (2.7).

Watermark extraction process for this method is also quite simple as illustrated in Fig.

2.5(b). The variance of each bin, σ2′′n is calculated and compared with the reference value,

13 . The watermark hidden in n-th bin, ω′′n, is extracted by means of

ω′′n =

+1, if σ2′′n > 1

3

−1, if σ2′′n < 1

3

(2.13)

Note that this watermark extraction process is performed without the original mesh model.

2.3 Simulation Results

Simulations were carried out on six 3-D triangular mesh models, a buddha (with 543 652

vertices and 1 087 716 cells), a bunny (with 35 947 vertices and 69 451 cells), a dragon

(with 15 574 vertices and 29 999 cells), a cow (with 2 903 vertices and 5 804 cells), a face

(with 539 vertices and 1 042 cells) and a fandisk (with 6 475 vertices and 12 946 cells) as

shown in Fig. 2.6.

To measure the quality distortion between the original mesh model and watermarked

one, we use Metro [Cignoni et al., 1998] which provides the HD (Hausdorff Distance)

between two static surfaces modeled by triangular meshes. It first evaluates two one-sided

distances, e (V,V′) and e (V′,V) (V and V′ represent the original and deformed surfaces

of meshes, respectively). Note that there exist surfaces such that e (V,V′) 6= e (V′,V).


For that reason, the HD, E (V,V′), is obtained by taking the maximum value of two

one-sided distances:

E(V,V′) = max

e(V,V′) , e (

V′,V)

(2.14)

The robustness of the watermark is measured in terms of correlation between the

original watermark and the extracted one.

Corr =∑N−1

n=0 (ω′′n −$

′′)(ωn −$)√∑N−1

n=0 (ω′′n −$′′)2 ×

∑N−1n=0 (ωn −$)2

(2.15)

where $ indicates the average of the watermark and Corr is on the range of [−1, 1].

In the simulations, we embedded 64 bits of watermark into a mesh model considering

the trade-off between the robustness and the transparency of watermark. Then, vertex

norms were divided into 64 bins and one bit of watermark was hidden in each bin. For

comparison of the two proposed methods, the strength factor of watermark was determined

experimentally so that both methods have very similar quality for each model in terms of

HD. Fig. 2.7 shows the watermarked mesh models, of which the performance are listed

in Table 2.1 in terms of HD and Corr when no attack. Here, the strength factor of

each watermark is also listed. The table shows that the statistical approach employed in

the proposed methods cannot embed a watermark bit into every bin in the case of very

small size models such as face. This is mainly caused by the fact that some of the bins

are empty or do not contain enough number of vertices. For this reason, the proposed

methods are not recommended to be applied to such small size models (approximately

having under 2 000 vertices). However, the hidden watermark can be extracted perfectly

from all watermarked models except for the smallest size model. This means the proposed

methods guarantee to hide a watermark bit into every bin for models with a sufficient

number of vertices. From the viewpoint of watermark transparency, mean modification

method maintains better visual quality than variance modification method. Some artifacts

appear in smooth regions such as in the lower belly of buddha and the rump of bunny

as shown in Fig. 2.7(g) and Fig. 2.7(h). In particular, the artifacts are conspicuous in

flat regions of fandisk, even when small strength factor is applied. This is mainly due to

the fact that every vertex is modified without considering local curvature of models. It


Table 2.1: Evaluation of watermarked meshes when no attack

Method ModelStrength

factorHD Corr

Mean

Modification

buddha 0.03 0.38×10−4 1.00

bunny 0.03 0.40×10−4 1.00

dragon 0.04 0.45×10−4 1.00

cow 0.16 5.84×10−3 1.00

face 0.16 1.41×10−2 0.43

fandisk 0.01 7.32×10−4 1.00

Variance

Modification

buddha 0.06 0.35×10−4 1.00

bunny 0.07 0.41×10−4 1.00

dragon 0.11 0.48×10−4 1.00

cow 0.26 5.91×10−3 1.00

face 0.28 1.27×10−2 0.49

fandisk 0.05 7.85×10−4 1.00

is also caused by discontinuities in the boundaries of neighbor bins when the distribution

is modified. As results, the proposed methods are not applicable to CAD models with

flat region. Consequently, attack simulations have been performed with buddha, bunny,

dragon and cow.

2.3.1 Attack Simulations

To evaluate the robustness of the watermark, various distortion and distortion-less attacks

were performed on the watermarked meshes. Each attack was applied with varying at-

tack strengths. Distortion attacks including multiplicative binary random noise, uniform

quantization, smoothing, simplification and sub-division were carried out. As examples,

the watermarked bunny models deformed by various distortion attacks are shown in Fig.

2.8.

For evaluating the resistance to noise attack, binary random noise was added to each


(a)

(b)

(c)

Figure

2.6:O

riginalm

eshm

odels(a)

buddha,(b)

bunny,(c)

dragon(continued

onnext

page)


(d)

(e)

(f)

Fig

ure

2.6:

(d)

cow

,(e

)fa

ce,an

d(f

)fa

ndis

k(c

onti

nued

from

prev

ious

page

)


(a)

(b)

(c)

Figure

2.7:W

atermarked

mesh

models,w

here(a)-(f)

arew

atermarked

bym

eanm

odificationm

ethodand

(g)-(l)by

variancem

odification

method.

(continuedon

nextpage)


(d)

(e)

(f)

Fig

ure

2.7:

Wat

erm

arke

dm

esh

mod

els,

whe

re(a

)-(f

)ar

ew

ater

mar

ked

bym

ean

mod

ifica

tion

met

hod

and

(g)-

(l)

byva

rian

cem

odifi

cati

on

met

hod.

(con

tinu

edfr

ompr

evio

uspa

gean

dco

ntin

edon

next

page

)


(g)

(h)

(i)

Figure

2.7:W

atermarked

mesh

models,w

here(a)-(f)

arew

atermarked

bym

eanm

odificationm

ethodand

(g)-(l)by

variancem

odification

method.

(continuedfrom

previouspage

andcontined

onnext

page)


(j)

(k)

(l)

Fig

ure

2.7:

Wat

erm

arke

dm

esh

mod

els,

whe

re(a

)-(f

)ar

ew

ater

mar

ked

bym

ean

mod

ifica

tion

met

hod

and

(g)-

(l)

byva

rian

cem

odifi

cati

on

met

hod.

(con

tinu

edfr

ompr

evio

uspa

ge)


(a) (b)

(c) (d)

Figure 2.8: Bunny model watermarked by mean modification method and attacked by (a)

multiplicative binary noise with error ratio of 0.5%, (b) 7bits/coordinate quantization, (c)

smoothing with iteration of 50 and relaxation of 0.03 and (d) simplification with reducing

90.65% of vertices


vertex norm 1 in watermarked model with three different error rates: 0.1%, 0.3% and

0.5% [Yu et al., 2003b]. Here, the error rate represents the noise amplitude as a fraction

of the maximum vertex norm of the object. We perform each noise attack five times

using different random seeds and report the median as shown in Table 2.2. The effect

of the noise attack is shown in Fig. 2.8(a). The performance of variance modification

method decreases faster than that of mean modification method as increasing the error

rate. Both methods are fairly resistant to the noise attacks under an error rate of 0.3,

but good watermark detection cannot be expected for higher error rates. This is due to

the fact that the multiplicative noise essentially alters the distribution of vertex norms

in the divided bins. In addition, more vertex norms exceed the range of each bin as the

noise error rate increases. Similar tendency was observed in quantization and smoothing

attacks. For such reasons, the robustness cannot be enhanced beyond a certain level even

when the strength factor α increases. The robustness can also be improved by widening

the size (width) of bin, but the transparency of watermark and the number of bits to be

embedded should be considered.

To evaluate the robustness against uniform quantization attacks, three different quanti-

zation rates are applied to watermarked meshes. Each coordinate of vertices is represented

with 7bits, 8bits and 9bits. Table 2.3 shows the robustness against the quantization attack.

An example is shown in Fig. 2.8(b). Both methods are fairly robust up to 8bits quan-

tization. Similar to the case of noise attack, variance modification has relatively abrupt

diminution of the robustness as the quantization step size increases.

Table 2.4 shows the performance of the watermarking schemes after smoothing attacks

[Field, 1988]. Three different pairs of iteration and relaxation were applied. An example

of the attack is also shown in Fig. 2.8(c), where the effect can be seen in the rounded

edges. The robustness depends on the smoothness of the original meshes. Buddha and

bunny are relatively less sensitive to smoothing attacks.

To evaluate the robustness of our methods against simplification attacks, we utilized

a simplification method [Shroder et al., 1992]. Watermarked models were simplified by

various reduction ratios. Table 2.5 demonstrates that the proposed methods are robust

1It is multiplicative noise in the coordinates.


Table 2.2: Evaluation of robustness against multiplicative binary noise attacks

Method Model Error rate HD Corr

Mean

Modification

buddha

0.1% 0.54×10−4 0.94

0.3% 1.26×10−4 0.73

0.5% 1.96×10−4 0.41

bunny

0.1% 0.59×10−4 0.87

0.3% 1.47×10−4 0.51

0.5% 2.38×10−4 0.18

dragon

0.1% 0.68×10−4 1.00

0.3% 1.49×10−4 0.55

0.5% 2.37×10−4 0.21

cow

0.1% 6.27×10−3 0.97

0.3% 8.95×10−3 0.91

0.5% 1.27×10−2 0.41

Variance

Modification

buddha

0.1% 0.54×10−4 1.00

0.3% 1.26×10−4 0.81

0.5% 1.96×10−4 −0.29

bunny

0.1% 0.59×10−4 1.00

0.3% 1.47×10−4 0.53

0.5% 2.38×10−4 −0.39

dragon

0.1% 0.70×10−4 1.00

0.3% 1.49×10−4 0.65

0.5% 2.37×10−4 −0.34

cow

0.1% 6.30×10−3 1.00

0.3% 8.74×10−3 0.50

0.5% 1.29×10−2 0.22


Table 2.3: Evaluation of robustness against uniform quantization attacks

Method Model Quantization HD Corr

Mean

Modification

buddha

9bits 0.64×10−4 0.87

8bits 1.21×10−4 0.78

7bits 2.42×10−4 0.47

bunny

9bits 0.69×10−4 0.94

8bits 1.26×10−4 0.88

7bits 2.46×10−4 0.39

dragon

9bits 0.75×10−4 0.94

8bits 1.30×10−4 0.84

7bits 2.48×10−4 0.43

cow

9bits 6.43×10−3 0.91

8bits 7.81×10−3 0.94

7bits 1.22×10−2 0.51

Variance

Modification

buddha

9bits 0.64×10−4 1.00

8bits 1.21×10−4 0.97

7bits 2.42×10−4 0.19

bunny

9bits 0.73×10−4 1.00

8bits 1.28×10−4 0.97

7bits 2.46×10−4 −0.01

dragon

9bits 0.82×10−4 1.00

8bits 1.34×10−4 1.00

7bits 2.49×10−4 0.72

cow

9bits 6.56×10−3 1.00

8bits 8.07×10−3 0.72

7bits 1.23×10−2 0.11


Table 2.4: Evaluation of robustness against smoothing attacks

Method Model(# of iteration,

relaxation)HD Corr

Mean

Modification

buddha

(10,0.03) 0.32×10−4 1.00

(30,0.03) 0.33×10−4 1.00

(50,0.03) 0.36×10−4 0.94

bunny

(10,0.03) 0.41×10−4 0.75

(30,0.03) 0.80×10−4 0.57

(50,0.03) 1.21×10−4 0.46

dragon

(10,0.03) 0.76×10−4 0.62

(30,0.03) 1.85×10−4 0.39

(50,0.03) 2.88×10−4 0.24

cow

(10,0.03) 1.03×10−2 0.69

(30,0.03) 2.43×10−2 0.23

(50,0.03) 3.67×10−2 0.17

Variance

Modification

buddha

(10,0.03) 0.31×10−4 1.00

(30,0.03) 0.31×10−4 1.00

(50,0.03) 0.33×10−4 1.00

bunny

(10,0.03) 0.42×10−4 0.97

(30,0.03) 0.81×10−4 0.87

(50,0.03) 1.22×10−4 0.75

dragon

(10,0.03) 0.79×10−4 0.97

(30,0.03) 1.89×10−4 0.27

(50,0.03) 2.92×10−4 0.18

cow

(10,0.03) 1.00×10−2 0.42

(30,0.03) 2.40×10−2 0.11

(50,0.03) 3.64×10−2 0.11


Table 2.5: Evaluation of robustness against simplification attacks (continued on next page)

Method Model Reduction ratio HD Corr

Mean

Modification

buddha

30.02% 0.38×10−4 1.00

50.02% 0.39×10−4 0.94

70.03% 0.41×10−4 0.84

90.10% 1.05×10−4 0.75

bunny

32.11% 0.44×10−4 0.94

51.44% 0.52×10−4 0.77

70.79% 0.70×10−4 0.58

90.65% 3.44×10−4 0.38

dragon

30.36% 0.98×10−4 0.76

50.97% 1.91×10−4 0.75

63.74% 3.43×10−4 0.44

82.46% 7.47×10−4 0.22

cow

30.01% 1.02×10−2 0.46

44.54% 2.09×10−2 0.46

58.77% 4.31×10−2 0.46

75.41% 6.83×10−2 0.17

against simplification attacks. In addition, variance modification method is more robust

than mean modification method. In this table, the percentage represents the number of

vanished vertices as a fraction of total number of vertices. Fig. 2.8(d) shows an example

of the simplification attack. Sub-division attacks were also carried out. Each triangle

was uniformly divided into four cells. The performance is listed in Table 2.6. The results

show that the proposed methods are robust against sub-division attacks, similar to attacks

using simplification. The results demonstrate that the distribution of vertex norms is less

sensitive to changes in the number of vertices. Clearly, this is an additional advantage of

the statistical approach. However, clipping attack simulation shows that the proposed are

very vulnerable to such attacks that cause severe alteration to the center of gravity of the

model.


Table 2.5: (Continued from previous page)

Variance

Modification

buddha

30.02% 0.35×10−4 1.00

50.02% 0.35×10−4 1.00

70.46% 0.37×10−4 1.00

90.01% 0.92×10−4 0.97

bunny

32.10% 0.44×10−4 1.00

51.43% 0.52×10−4 0.97

70.78% 0.70×10−4 0.94

89.71% 3.35×10−4 0.79

dragon

30.42% 0.99×10−4 1.00

50.97% 1.96×10−4 1.00

63.81% 3.48×10−4 0.71

81.70% 8.52×10−4 0.53

cow

30.01% 1.08×10−2 1.00

43.62% 2.13×10−2 0.51

58.63% 2.13×10−2 0.37

76.34% 2.13×10−2 0.25

Table 2.6: Evaluation of robustness against 1:4 sub-division attacks

Method Model # of cells HD Corr

Mean

Modification

buddha 4,350,864 0.38×10−4 1.00

bunny 277,804 0.34×10−4 0.87

dragon 119,996 2.80×10−4 0.62

cow 11,609 5.78×10−3 0.58

Variance

Modification

buddha 4,350,864 0.35×10−4 1.00

bunny 277,804 0.41×10−4 0.94

dragon 119,996 2.82×10−4 1.00

cow 11,609 5.29×10−3 0.61


To evaluate the robustness of our methods against distortion-less attacks, vertex re-

ordering and similarity transforms were carried out. Vertex re-ordering attack was per-

formed iteratively 100 times, also changing the seed of random number generator for each

iteration. Similarity transforms were carried out with many combinations of rotation,

uniform scaling, and translation factors. It is not necessary to tabulate watermark detec-

tion performance because both proposed perfectly extracted the hidden watermark infor-

mation. As intended, the proposed watermarking methods are perfectly robust against

distortion-less attacks.

2.3.2 Parameters for Robustness

In this section, we analyze two parameters that can be adjusted to improve the robustness

of the proposed methods. One is the watermark strength factor α, another is the size of

bin. For these analyses, bunny model and mean modification method were used. Smooth-

ing operation with iteration of 30 and relaxation of 0.03 was applied as an example attack.

To analyze the effect of watermark strength factor, bunny model was watermarked with

varying the strength factor and underwent the smoothing attack. Here, 64 bits of wa-

termark were embedded. Fig. 2.9(a) shows the correlation of watermark detection along

different strength factors. Corresponding HD of watermarked meshes is also plotted. It

shows that the robustness can be improved to a certain limited level as the strength factor

increases. However, the watermark transparency should be carefully considered, as HD

increases linearly. Fig. 2.9(b) shows the relationship between the size of bin and the

correlation, where the strength factor is used as α = 0.03. Note that the size of bin is

inversely proportional to the number of bins. This shows that the robustness can also be

improved as the size of bin increases. In other words, this means that the use of larger

bins reduces the probability that vector norms exceed the corresponding bin when be-

ing attacked by smoothing operations. However, watermark transparency should be also

carefully considered. Note that the use of larger bins limits the number of watermark bits.


(a)

Figure 2.9: (a) Relationship between the strength factor and the correlation. As an

example, a smoothing attack with iteration 30 and relaxation 0.03 is applied. (continued

on next page)


(b)

Figure 2.9: (b) Relationship between the number of bins and the correlation. As an

example, a smoothing attack with iteration 30 and relaxation 0.03 is applied. (continued

from previous page)


2.3.3 ROC Analysis

The proposed methods were analyzed by ROC (Receiver Operating Characteristic) curve

that represents the relation between probability of false positives Pfp and probability of

false negatives Pfn by varying the decision threshold TCorr for declaring the watermark

present [Praun et al., 1999]. The probability density functions for Pfp and Pfn were mea-

sured experimentally with 100 correct and 100 wrong keys, and approximated to Gaussian

distribution. In these simulations, we used the same watermarked model of bunny as used

in Sub-section 2.3.1. Fig. 2.10 shows the ROC curves when multiplicative binary noise and

simplification attacks are respectively applied into the watermarked model of bunny. EER

(Equal Error Rate) is also indicated in this figure. As shown in the figure, the proposed

methods have fairly good performance in terms of watermark detection for both attacks.

2.4 Summaries

In this chapter, we proposed two statistical watermarking methods for 3-D polygonal mesh

models that modify the distribution of vertex norms via changing respectively the mean

and the variance of each bin by histogram mapping function. Through the simulations,

we proved that both proposed methods are perfectly robust against distortion-less attack

such as vertex re-ordering and similarity transforms. Moreover, they are fairly robust

against various kinds of distortion attacks, in particular, simplification and sub-division

operations. However, there are some drawbacks. Our proposals are not applicable to very

small size models and CAD models with flat regions, and are very vulnerable to clipping

attacks that cause severe alteration to the center of gravity of the model. Nevertheless,

the simulation results demonstrate a possible, oblivious watermarking method based on

statistical approach for 3-D polygonal mesh model.

2.4 Summaries 41

(a)

(b)

Fig

ure

2.10

:R

OC

curv

esof

bunn

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odel

(a)

wat

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(c)(d

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2.10:(c)

waterm

arkedby

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odificationm

ethodand

attackedby

multiplicative

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(d)w

atermarked

byvariance

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andattacked

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plification(continued

fromprevious

page)

Chapter 3

Compression for 3-D Mesh

Sequences

In this chapter, we present two compression methods for irregular three-dimensional (3-

D) mesh sequences with constant connectivity. The proposed methods mainly use an

exact integer spatial wavelet analysis (SWA) technique to efficiently decorrelate the spatial

coherence of each mesh frame and also to adaptively transmit mesh frames with various

spatial resolutions. To reduce the temporal redundancy, the first proposed method applies

multi-order differential coding (MDC) to the temporal sequences obtained from SWA.

MDC determines the optimal order of the differential coder by analyzing the variance of

prediction errors. Comparing with the first-order differential coding (FDC) scheme, the

method can improve the compression performance. The second proposed method applies

temporal wavelet analysis (TWA) to the temporal sequences. In particular, this method

offers spatiotemporal multi-resolution coding. Through simulations, we prove that our

approaches not only have better coding efficiency than some methods but also enable

efficient lossy-to-lossless compression for 3-D mesh sequences.


With the remarkable progress of multimedia and information technologies, 3-D data has

been more and more widely used in various applications such as virtual reality, video

44 Compression for 3-D Mesh Sequences

games, animation movies and medical images.

Polygonal meshes provide an efficient representation of 3-D objects, since they can be

rapidly rendered by existing graphics hardware. Like as the categorization of 2-D still

images and motion pictures, they can be classified into static meshes and mesh sequences.

Static meshes contain two kinds of principal information, the locations of vertices and

their topological connections – geometry and connectivity, respectively. Similar to mo-

tion pictures, a 3-D mesh sequence consists of consecutive static meshes. The motion of

meshes is usually represented by vertex displacements. These kinds of mesh sequences

have constant connectivity information over all mesh frames. On the other hand, some

mesh sequences might have variable connectivity over all or partial mesh frames. In this

chapter, we address only mesh sequences with constant connectivity.

Generally, mesh sequences obtained by 3-D scanners or mesh design tools such as 3-D

Studio MAX require huge capacity or enormous bandwidth to be stored or transmitted.

For that reason, it has become an important issue to develop efficient compression methods

for 3-D mesh sequences. Similar to 2-D motion picture compression, spatial and temporal

redundancies are mainly exploited to minimize data size. To reduce the spatial redundancy,

the geometry and connectivity information of a single mesh frame can be modeled for

entropy coding. The geometrical coherence in temporal direction between consecutive

mesh frames can be used to reduce the temporal redundancy. Clearly, other attributes such

as normal vectors or texture information could be also regarded as important components

to be compressed. Note that we focus on geometry coding in this chapter.

Since Lengyel [Lengyel, 1999] proposed a geometry compression method for 3-D mesh

sequences, there have been several attempts to reduce the spatial and geometry redundan-

cies [Yang et al., 2002,Lengyel, 1999,Zhang and Owen, 2005,Alexa and Muller, 2000,Karni

and Gotsman, 2004,Ibarria and Rossignac, 2003,Ahn et al., 2002,Guskov and Khodakovsky,

2004,Cho et al., 2006b,Payan and Antonini, 2005]. In [Lengyel, 1999], the original meshes

are segmented into small rigid body meshes. The motion of each rigid body mesh is rep-

resented by affine transform coefficients, then the coefficients and residuals are quantized

and encoded by an entropy coder. This algorithm uses temporal coherence of rigid body

meshes to reduce temporal redundancy. However, this method has difficulties to obtain


precise segmentation and cannot have good coding performance for the mesh sequences

with high geometrical complexity. A quantization based method was also presented by

Zhang and Owen [Zhang and Owen, 2005]. They proposed a hybrid compression method

combining delta and octree coding schemes. For each mesh frame, the geometry informa-

tion is encoded by using selectively one of two coding schemes which has smaller prediction

errors. This technique requires high processing time, because it iterates the encoding pro-

cesses until the predetermined visual quality of the decoded mesh sequences. Some PCA

(Principal Component Analysis) based methods have been presented [Alexa and Muller,

2000,Karni and Gotsman, 2004]. Alexa and Muller [Alexa and Muller, 2000] represented

3-D mesh sequences using several principal bases obtained by PCA. Karni and Gots-

man [Karni and Gotsman, 2004] expanded it to a hybrid method combining PCA and

LPC (Linear Prediction Coding). However, these methods essentially require high com-

putational complexity to calculate the eigenvectors. Ibarria and Rossignac [Ibarria and

Rossignac, 2003] introduced an efficient compression method which can simultaneously

reduce the temporal and spatial redundancies by using a space-time replica predictor.

Some methods [Yang et al., 2002,Ahn et al., 2002,Guskov and Khodakovsky, 2004,Cho

et al., 2006b] applied the motion picture coding techniques, which have been widely used

in MPEG (Motion Pictures Experts Group) and H.26x, to 3-D mesh sequence compres-

sion. Yang et al. [Yang et al., 2002] used two-stage vertex-wise motion vector prediction.

In the first stage, they first define the topological neighborhood of a vertex and predict

the motion vector. To improve the compression performance, in the second stage, the pre-

diction errors are once more decorrelated by four optional modes – no prediction mode,

temporal prediction mode, spatial prediction mode, and spatiotemporal prediction mode

– applying R-D (Rate-Distortion) optimization. Ahn et al. [Ahn et al., 2002] proposed

a motion compensated coding scheme. The method extracts triangle strips using the

connectivity of the first mesh frame, and then divides each triangle strip into several seg-

ments. The segments can be regarded as macro blocks in motion picture coding. Each

segment is independently motion estimated, and its motion vector is encoded. These two

algorithms [Yang et al., 2002,Ahn et al., 2002] enable both a simple and an efficient com-

pression via conventional 2-D video coding schemes. Recently, scalability has become an


important issues in video coding, as it facilitates to adaptively manage bit-rates according

to different conditions of bandwidth or capacity [Sun et al., 2005]. From the viewpoint of

scalable coding, wavelet transform – SWA (Spatial Wavelet Analysis) and/or TWA (Tem-

poral Wavelet Analysis) – is suitable for 3-D mesh sequences. Some wavelet-based meth-

ods have been introduced [Payan and Antonini, 2005,Guskov and Khodakovsky, 2004,Cho

et al., 2006b]. Payan and Antonini [Payan and Antonini, 2005] used a TWA to reduce

temporal redundancy. Although they achieved good compression performance by using

their optimal bit allocation scheme, they did not consider the spatial redundancy. Guskov

and Khodakovsky [Guskov and Khodakovsky, 2004] introduced a SWA-based compression

algorithm. They encoded the differential errors between the wavelet coefficients of previ-

ous and current frames. Here, the wavelet coefficients are obtained from the Burt-Adelson

style pyramid scheme. The method can provide the spatial resolution scalability.

In this chapter, we propose two compression techniques of the mesh geometry for 3-

D mesh sequences with constant connectivity. To reduce the spatial redundancy, both

proposed methods use the SWA technique which employs an exact integer analysis and

synthesis filter bank [Valette and Prost, 2004a]. The filters can be directly applied to irreg-

ular meshes. Besides, they can easily achieve lossy-to-lossless compression 1. In order to

reduce the temporal redundancy, we consider two different techniques, MDC (Multi-order

Differential Coding) and TWA. The first method uses SWA and MDC schemes. In our pre-

vious work [Cho et al., 2006b], we used a FDC (First order Differential Coding) technique

employing IPPP frame pattern coding which combines Intra-mesh and Predicted-mesh

coding. To improve the coding efficiency, we introduce a more sophisticated approach

in which the variances of prediction errors are analyzed to find the optimal order. The

second method employs both SWA and TWA schemes. Although TWA scheme was ap-

plied in a previous algorithm [Payan and Antonini, 2005], there has been no attempt

to apply SWA and TWA, simultaneously. Both proposed methods can provide lossy-to-

lossless compression if input mesh sequences have integer coordinates. The first method

1In general, lossy compression gain is determined by quantization via R-D optimization. Note that, in

this chapter, we regard ‘multi-resolution transmission (or representation)’ as ‘lossy compression’ because

it could also reduce data size.

3.2 Wavelet-based Multi-resolution Analysis 47

can reconstruct mesh sequences with various spatial resolutions, and the second enables

temporal multi-resolution coding as well as spatial one.

The rest of this chapter is organized as follows. In Section 3.2, SWA and TWA tech-

niques, which are used in our compression schemes, are introduced. Two compression

methods using wavelet-based multi-resolution analysis are proposed in Section 3.3. Sec-

tion 3.4 shows the simulation results of the proposed methods in terms of lossless and

lossy compression performances. Finally, Section 3.5 summarizes this chapter.

3.2 Wavelet-based Multi-resolution Analysis

Early compression methods for multimedia data have been mainly concentrated on the

development of single-rate coding system [Peng et al., 2005]. Although single-rate cod-

ing has enough performance in a network environment with fixed bandwidth, it might

be difficult to be promptly applied to variable bandwidth conditions. For that reasons,

scalable coding techniques such as the annexed functionalities of MPEG (Motion Picture

Experts Group)-2 and -4 have been intensively researched. In general scalable decoding

frameworks, the coarsest version is first reconstructed from the base layer, and higher

resolution versions are adaptively produced from the enhancement layers depending on

channel conditions. It has been well-known that wavelet-based multi-resolution analysis

techniques are useful for scalable coding. Besides, they provide good coding performance,

as the PDF (Probability Density Function) of the wavelet coefficients can be approximated

to Laplacian distribution with a sharp peak [Cho et al., 2006b]. These are the reasons

why we use SWA and TWA in order to design efficient 3-D mesh sequence compression

systems. In the following sub-sections, SWA and TWA schemes are summarized.

3.2.1 SWA (Spatial Wavelet Analysis) and Its Synthesis

The wavelet-based multi-resolution scheme for 3-D static meshes was firstly introduced

by Lounsbery [Lounsbery, 1994]. Fig. 3.1 shows an example of SWA and its synthesis

processes. From the original mesh CJ , the SWA is performed by two analysis filters, Aj


(a)

(b)

Figure 3.1: (a) SWA (Spatial Wavelet Analysis) and (b) its synthesis processes


(low-pass filter) and Bj (high-pass filter) as follows,

Cj−1 = AjCj (3.1)

Dj−1 = BjCj for 0 ≤ j ≤ J (3.2)

where j is the spatial resolution level, and Cj is a vj × 3 matrix representing the vertex

coordinates (x-, y-, and z-coordinates) of the input mesh having vj vertices. A fine mesh

Cj is decomposed into a coarse mesh Cj−1 and wavelet coefficients Dj−1. The wavelet

coefficients represent the lost details. We obtain a hierarchy of meshes from the original

CJ to the simplest one, C0, so-called base mesh.

The reconstruction is done by two synthesis filters, P j and Qj . It is formulated as

Cj = P jCj−1 +QjDj−1 (3.3)

A fine mesh is reconstructed from the coarse one and the corresponding wavelet coefficients.

If the filter-banks satisfy the following constraint, we can achieve perfect reconstruction.[Aj

Bj

]=

[P j |Qj

]−1 (3.4)

Lounsbery’s scheme handles meshes with one-to-four (1:4) subdivision connectivity. The

mesh hierarchy can be considered as successive quadrisections of a base mesh (C0) faces

followed by deformation of edge midpoints to fit the surface to be approximated. The

vertices of coarse mesh have arbitrary valences while the subdivided mesh interiors and

boundary vertices have valence six and four, respectively. Conversely, four-to-one (4:1) face

coarsening in Eq. (3.1) is the inverse operation of quadrisection. The wavelets functions,

in this scheme, are hat functions associated with odd vertices of the mesh at resolution

j and linearly vanishing on the opposite edges. This wavelet is often called the ‘Lazy

wavelet’. The scaling functions are also hat function but with a twice wider support and

are associated with the even vertices. However, wavelets are not orthogonal to scaling

functions. Then a primal 2-ring lifting is used to construct new wavelets which are more

orthogonal to the scaling functions. These wavelets produce the coarse meshes with good

quality in terms of approximation.

Recently the wavelet multi-resolution analysis has been extended to irregular mesh

(vertices can have any valence) by Valette and Prost [Valette and Prost, 2004a]. In [Valette


and Prost, 2004b], they also introduced an exact integer analysis and synthesis with the

lifting scheme based on Lazy filter-banks and the Rounding transform [Jung and Prost,

1998,Calderbank et al., 1998]. Now, the analysis is sequentially performed by the lifted

Lazy filter-banks.

Dj−1 =⌊Bj

lazyCj⌋

(3.5)

Cj−1 = AjlazyC

j +⌊αjDj−1

⌋(3.6)

where Ajlazy and Bj

lazy are Lazy analysis filters, and αj is a vj−1 ×(vj − vj−1

)matrix

chosen to ensure that Cj−1 is the best approximation of Cj . The synthesis is done by

Cj =⌈P j

lazy

(Cj−1 −

⌊αjDj−1

⌋)+Qj

lazyDj−1

⌉(3.7)

where P jlazy and Qj

lazy are Lazy synthesis filters, and b·c and d·e are the floor and ceiling

operators, respectively. These modified filter-banks make it possible to implement a loss-

less compression for the given meshes with integer coordinates. In addition, they can be

applied to irregular meshes by using an irregular subdivision scheme [Valette and Prost,

2004b]. Note that the Lounsbery’s method based on regular subdivision scheme [Louns-

bery, 1994] cannot work on irregular ones. These are the reasons why our methods use

this exact integer analysis/synthesis scheme and an irregular coarsening approach. The

notation ‘SWA’ indicates the exact integer spatial wavelet analysis in the rest of this dis-

sertation. For more details about the SWA, refer to [Valette and Prost, 2004a], [Valette

and Prost, 2004b] and [Valette, 2002].

3.2.2 TWA (Temporal Wavelet Analysis) and Its Synthesis

Fig. 3.2 shows an example of the TWA and its synthesis processes. In the wavelet

analysis process, the original signal x (n) (for 1 ≤ n ≤ N , and N is the number of

samples) is decomposed into low and high frequency band signals, y0 (n) and y1 (n), by an

analysis filter-bank, h0 (n) and h1 (n). Low and high frequency band signals correspond

to the coarse version of the original signal and its details, respectively. To obtain more

resolution levels, the analysis process can be repeatedly applied to the low frequency band

signal. In the wavelet synthesis process, the two sub-band signals are transformed into


(a)

(b)

Figure 3.2: 2-channel (a) TWA (Temporal Wavelet Analysis) and (b) its synthesis pro-

cesses


a reconstructed signal x (n) by a synthesis filter-bank, g0 (n) and g1 (n). Note that the

implementation allows lossless compression using a lifting scheme [Sweldens, 1996, Jung

and Prost, 1998,Adams and Kossentini, 2000].

In our second compression method (See Section 3.3.2), TWA is applied to whole tem-

poral sequences. Here, temporal movement of each coordinate is regarded as a 1-D signal

as in [Payan and Antonini, 2005].

3.3 Proposed Compression Methods

The proposed methods mainly use the exact integer SWA scheme [Valette and Prost,

2004b] introduced in Section 3.2.1. The SWA can efficiently reduce the spatial redundancy

and also offer a progressive transmission from the base mesh to the original one for static

irregular meshes. Clearly, this scheme can be applied to each frame of 3-D mesh sequences,

and therefore provide an adaptive transmission for mesh sequences when the bandwidth

is not fixed because it can produce mesh sequences with various spatial resolutions.

To reduce the temporal redundancy existing in the base mesh and spatial wavelet

coefficients of mesh sequences, two different techniques are used in our proposed methods.

The first proposed method employs the MDC which determines the optimal order of

the differential encoder by evaluating the variance of the prediction error. The MDC

provides simple and adaptive differential coding technique. The second employs the TWA

scheme. This approach allows spatiotemporal multi-resolution coding in a single frame

work. Although TWA was already used for geometry compression in temporal domain

[Payan and Antonini, 2005], there has been no attempt to use simultaneously both SWA

and TWA. In the following sub-sections, we describe our proposed methods in details.

3.3.1 The Proposed Compression Method Using SWA and MDC

Fig. 3.3 shows the encoding process of the proposed method using SWA and MDC tech-

niques. We assume the original mesh sequences are represented by integer coordinates.

First, each mesh frame is transformed by the exact integer SWA [Valette and Prost, 2004b].

Two kinds of major information are obtained from this transform for each frame, namely

3.3 Proposed Compression Methods 53

the connectivity and the geometry. The geometry information contains the coordinates of

the base mesh and of wavelet coefficients corresponding to each spatial resolution level.

The connectivity is the topological connections of the vertices.

The second step is connectivity coding. The connectivity information obtained from

the first step is entropy coded by an arithmetic coder [Schindler, 1998]. Note that this

process is performed only for the first frame, because the mesh sequence has constant

connectivity. The reader can refer to [Valette and Prost, 2004b] for more details of the

connectivity coding.

The third step is geometry coding to reduce the temporal redundancy. Each coordinate

of the base mesh vertices and of the spatial wavelet coefficients is processed independently

as 1-D signal with N samples along temporal direction. Here, N is the number of frames.

For a given r-th base mesh vertex c0r = (xr, yr, zr) (c0r ∈ C0 for 1 ≤ r ≤ R, and R is the

number of base mesh vertices), each coordinate is independently treated as ‘base mesh

vertex sequence’: xr (n), yr (n), and zr (n) (for 1 ≤ n ≤ N). Similarly, for a given s-

th wavelet coefficient of the j-th spatial resolution level djs =

(xj

s, yjs, z

js

)(dj

s ∈ Dj for

1 ≤ s ≤ S, and S is the number of wavelet coefficients in each spatial resolution level),

each coordinate is independently treated as ‘spatial wavelet coefficient sequence’: xjs (n),

yjs (n), and zj

s (n). Consequently, the ‘temporal sequences’ consist of the base mesh vertex

sequences and the spatial wavelet coefficient sequences. Note that MDC is applied to each

temporal sequence.

Before discussing MDC technique, the first order differential operation for the temporal

sequences is formulated by

∆(1)u (n) = u (n)− u (n− 1) , u ∈xr, yr, zr, x

js, y

js, z

js

(3.8)

The prediction errors obtained from Eq. (3.8) might still have some redundancy. Then, the

remaining redundancy could be reduced by repeatedly applying the differential operation

to the prediction errors. This is named MDC and given by

∆(m)u (n) = ∆(m−1)u (n)−∆(m−1)u (n− 1) (3.9)

where m (m ≥ 2) is the order of differential coding. Then this order can be easily deter-

mined by finding the optimal order with smaller entropy via analyzing the variance of the


Figure

3.3:T

heencoding

processof

theproposed

method

usingSW

Aand

MD

Ctechniques


prediction errors. In order to prove the correctness of our idea, we consider that the input

sequence is modeled as WSSMP (Wide Sense Stationary Markov Process). As proved

in Appendix, the first order predictor can be applied for a first order Markov process

(a first order autoregressive process, AR(1)) with a correlation coefficient existing in the

range of 0.5 < ρ < 1. The more the input samples are correlated (p-th order AR process,

AR(p)), the higher the efficiency of entropy coding is expected with higher order (p-th

order) differential coding.

To apply the MDC technique to practical 1-D temporal sequences, we use an iterative

approach as follows.

1) calculate the variance of input signal σ2u and let it be a reference variance such as

σ2ref = σ2

u;

2) initialize the parameter m as 1;

3) perform the m-th order differential operation via

∆(m)u(n) =

u(n)− u(n− 1) if m = 1;

∆(m−1)u(n)−∆(m−1)u(n− 1) if m ≥ 2;

4) calculate the variance of prediction errors through

σ2∆(m)u

= 1/N∑N

n=1

(∆(m)u(n)− µ∆(m)u

)2, where µ is mean value;

5) if σ2∆(m)u

< σ2ref , increase m (m = m+ 1), replace σ2

ref with σ2∆(m)u

and go back to

3);

6) or else stop and encode the (m− 1)-th order differential errors using the arithmetic

coder.

We can automatically find the optimal order by using this iterative approach. Note that

the entropy coding efficiency can be estimated using the variance of the prediction errors,

as mentioned in Appendix B. Fig. 3.4 shows the variances of prediction errors according

to different orders of MDC. Here, the x-coordinate of the first base mesh vertex sequence,

x1 (n) (1 ≤ n ≤ 1 024), of Face model is shown for a practical example. In this case,

the second order is selected for MDC, as its corresponding variance is the smallest. Fig.


Figure 3.4: Variances (σ2) of prediction errors of Face model according to different orders

(m) of MDC. The x-coordinate of the first base mesh vertex sequence of this model is

designated for a practical example.

3.5 depicts the distributions of prediction error for the first order and the second order

differential coding. From this figure, we can easily estimate that MDC is more efficient

than FDC.

In the third step, the optimal order of each sequence should be also transmitted as

side-information whose bitrate is given by

dlog2omaxe × 3N

(bits/vertex/frame) (3.10)

where omax is the maximum optimal order. Note that the side-information is very negli-

gible.

The entropy coded connectivity and geometry including the side-information are finally

merged into the compressed bit-stream. Note that the transmitted bit-stream, in the

decoder side, can be sequentially reconstructed from the coarsest signals to finer ones with

various spatial resolutions. We call this approach SWA+MDC method.


(a)

(b)

Figure 3.5: Prediction error distributions of Face model in terms of (a) FDC and (b) MDC


3.3.2 The Proposed Compression Method Using SWA and TWA

Fig. 3.6 shows the encoding process of the proposed compression method using SWA and

TWA techniques. As the first two steps of this encoding process are identical to those

mentioned in Section 3.3.1, the peculiar steps of this scheme are described in detail. Note

that the same notations with the previous section are used for the sake of simplicity.

Up to the second step, each frame of the original mesh sequence is transformed by the

exact integer SWA [Valette and Prost, 2004b], and the connectivity information for only

the first frame is entropy coded by the arithmetic coder.

The third step performs the geometry coding to reduce the temporal redundancy.

For geometry coding, the proposed method applies TWA to the temporal sequences of

the base mesh vertices (xr (n), yr (n), and zr (n)) and of the spatial wavelet coefficients

(xjs (n), yj

s (n), and zjs (n)). Note that the efficiency of entropy coding depends on the

performance of frequency decomposition according to temporal wavelet filter-banks. Many

analysis and synthesis filter-banks have been developed [Adams and Kossentini, 2000].

We consider three well-known filter-banks such as Haar (2/2 tap), Le Gall (5/3 tap) and

Daubechies (9/7 tap) filters. These filter-banks can be applied for lossless compression of

3-D mesh sequences by implementing in integer lifting form, because the input sequences

have integer coordinates. Fig. 3.7 shows the distributions of temporal wavelet coefficients.

Here, the x-coordinate of the first base mesh vertex sequence, x1 (n) (1 ≤ n ≤ 1024), of

Face model is chosen for a practical example. From this figure, we can expect Le Gall and

Daubechies filters to be more efficient than Haar filter. We experimentally evaluate the

coding efficiency according to these filters in Section 3.4.2.

In the third step, the low and high frequency band signals obtained from both SWA

and TWA are entropy coded by the arithmetic coder.

The entropy coded connectivity and geometry information are finally merged into the

compressed bit-stream. Note that the transmitted bit-stream, in the decoder side, can be

sequentially reconstructed from the coarsest signals to finer ones with various spatial and

temporal resolutions, simultaneously. We call the approach, SWA+TWA method.


Fig

ure

3.6:

The

enco

ding

proc

ess

ofth

epr

opos

edm

etho

dus

ing

SWA

and

TW

Ate

chni

ques


(a)

(b)

Figure 3.7: Distributions of wavelet coefficients of the x-axis of the first base mesh sequence

of Face model using (a) Haar (2/2 tap) filters, (b) Le Gall (5/3 tap) filters (continued on

next page)


(c)

Figure 3.7: (c) Daubechies (9/7 tap) filters (continued from previous page)


Simulations are carried out on two 3-D irregular triangle mesh sequences, Cow (with 204

frames and 2 904 vertices/frame) and Face (with 10 002 frames and 539 vertices/frame).

The number of vertices and their connectivity information are fixed over all frames. To

apply TWA to mesh sequences, the number of frames should be an integer power of two.

Therefore, we use only the first 128 and 1 024 frames of Cow and Face, respectively.

Each coordinate is uniformly quantized, coded to 12 bits, and used for the original like

as in [Karni and Gotsman, 2004]. Fig. 3.8 shows several frames of the original mesh

sequences as examples.

To measure the quality distortion between the original mesh sequence and decom-

pressed one, we use the average of HD (Hausdorff Distance) (See Eq. (2.14)) over all

frames, called AHD (Average HD), E (Vn,V′n):

E(Vn,V′

n

)=

1N

N−1∑n=0

En

(Vn,V′

n

)(3.11)

where, Vn and V′n represent the original and decompressed surfaces of meshes at the


Table 3.1: The lossless compression results of SWA+MDC method compared with SWA

and SWA+FDC methods

Method ModelBitrate

(bits/vertex/frame)

SWACow 22.40

Face 30.04

SWA+FDCCow 14.22

Face 11.49

SWA+MDCCow 13.57

Face 10.52

n-th frame, respectively.

3.4.1 SWA+MDC Method

To evaluate the coding efficiency of the proposed SWA+MDC method, we perform also

two other methods, SWA method and SWA+FDC method. Here, the SWA method does

not consider the temporal redundancy. Table 3.1 shows the lossless compression results.

As shown in this table, both SWA+FDC and SWA+MDC methods achieve quite high

compression performance comparing to SWA method, because they exploit the temporal

coherence. SWA+MDC method is more efficient than SWA+FDC method. It shows that

the first order of differential coder is not good enough to reduce the temporal redundancy.

Fig. 3.9 shows the distribution of practical optimal orders. Actually, 56% and 55%

of the temporal sequences obtained from SWA need second or third order differential

coding in Cow and Face models, respectively. Although the proposed method requires

side information to transmit the optimal order of each sequence, the amount is so small as

to be negligible. In this simulation, two bits per temporal sequence are assigned to transmit

the order. Cow and Face models need 4.69 × 10−2 and 5.86 × 10−3 (bits/vertex/frame)

for the side information, respectively.

The lossy-to-lossless compression performances according to various spatial resolutions

are evaluated in terms of AHD and bitrates. Fig. 3.10 depicts the R-D (Rate-Distortion)


(a)

1-s

tfr

am

e(b

)64-t

hfr

am

e(c

)128-t

hfr

am

e

Fig

ure

3.8:

Ori

gina

lm

esh

sequ

ence

s,(a

)-(c

)C

owm

odel

s(c

onti

nued

onne

xtpa

ge)


(d)

1-st

fram

e(e)

512-th

fram

e(f)

1024-th

fram

e

Figure

3.8:(d)-(f)

Facem

odels(continued

fromprevious

page)


(a)

(b)

Figure 3.9: Distributions of practical optimal orders of the differential coder in

SWA+MDC for (a) Cow and (b) Face models


(a)

(b)

Figure 3.10: R-D curves of SWA, SWA+FDC and SWA+MDC methods for (a) Cow and

(b) Face models


curves of SWA, SWA+FDC and SWA+MDC methods. Cow and Face models are decom-

posed into 19 and 11 spatial levels. Here, we present the results of five highest resolution

levels. As shown in Fig. 3.10, the proposed method enables to reconstruct the mesh se-

quences at various spatial resolutions. Similar to lossless compression results, SWA+MDC

method has better coding efficiency than the others.

3.4.2 SWA+TWA Method

For the evaluation of SWA+TWA method, three different temporal wavelet filter-banks

– Haar, Le Gall and Daubechies filters – are applied to the temporal sequences obtained

from SWA. Each temporal sequence is decomposed into several sub-bands in the dyadic

form using lifting scheme [Daubechies and Sweldens, 1998]. The lossless coding efficiency is

evaluated according to different temporal wavelet decomposition levels as shown in Table

3.2. For comparison, we also present the compression results of the method which applies

only TWA to original mesh sequences. We denote it TWA method. As shown in this table,

TWA method has poor performance. It means that the spatial redundancy should also be

exploited. In particular, Cow model have relatively high spatial redundancy. SWA+TWA

method has lower bitrates than TWA method. The coding efficiency depends on the kind

of temporal wavelet filter-banks. Le Gall and Daubechies filter-banks are more efficient

than Haar filter-banks. The bitrate decreases as a function of the decomposition level.

However the performance of SWA+TWA is slightly lower than that of SWA+MDC.

Lossy-to-lossless compression performances are evaluated by R-D curves. Fig. 3.11

shows the R-D curves according to different spatial resolutions and three temporal wavelet

filter-banks. Here, temporal sequences are reconstructed in full temporal resolution. As

shown in Fig. 3.11, Le Gall and Daubechies filters have similar coding efficiency and are

more efficient than Haar filter at all spatial resolutions. Although SWA+TWA method has

slightly lower performance than SWA+MDC, it provides both spatial and temporal scal-

ability. Fig. 3.12 shows the R-D curves according to different spatiotemporal resolutions.

Here, temporal sequences are decomposed into five levels using Daubechies filter-banks.

This figure demonstrates that we can properly select the bitrates at various spatiotempo-

ral resolutions. However, the bitrates should be carefully selected for the mesh sequences


Table 3.2: The lossless compression results of SWA+TWA method compared with TWA

scheme according to temporal wavelet decomposition levels and three temporal wavelet

filter-banks: Haar (2/2 tap), Le Gall (5/3 tap) and Daubechies (9/7 tap) filters

# of TWA

LevelsTWA Filter Model

Bitrate (bits/vertex/frame)

Method

TWA SWA+TWA

1

HaarCow 32.78 18.21

Face 24.84 20.77

Le GallCow 30.19 16.39

Face 22.05 19.01

DaubechesCow 29.93 16.53

Face 22.13 19.44

3

HaarCow 30.60 16.30

Face 17.52 14.99


Face 13.86 12.58

DaubechiesCow 26.49 13.93

Face 13.47 12.95

5

HaarCow 30.43 16.11

Face 16.06 13.83


Face 12.52 11.54

DaubechiesCow 26.34 13.73

Face 12.12 11.83

3.5 Summaries 69

having large movement such as Cow model.

3.5 Summaries

In this chapter, we proposed two geometry compression methods for irregular 3-D mesh

sequences with constant connectivity. To reduce the spatial redundancy, both methods

employ an exact integer spatial wavelet analysis (SWA). Temporal redundancy is reduced

by multi-order differential coding (MDC) and temporal wavelet analysis (TWA), respec-

tively, in two proposed methods. The method SWA+MDC offers spatial scalability and

the method SWA+TWA provides spatiotemporal multi-resolution coding. In addition,

both methods enable lossy-to-lossless compression. The method SWA+MDC has slightly

better performances than SWA+TWA method in both lossless and lossy compressions.


(a)

(b)

Figure 3.11: R-D curves of SWA+TWA method at different spatial resolutions where three

temporal wavelet filter-banks are used for (a) Cow and (b) Face models

3.5 Summaries 71

(a)

(b)

Figure 3.12: R-D curves of SWA+TWA method at different spatiotemporal resolutions,

where the temporal sequences are decomposed into five levels using Daubechies filter banks

for (a) Cow and (b) Face models

Chapter 4

Joint Watermarking and

Compression for 3-D Mesh

Sequences

This chapter presents a joint watermarking and compression method for 3-D mesh se-

quences. Our approach is mainly based on the SWA (Spatial Wavelet Analysis) + TWA

(Temporal Wavelet Analysis) compression scheme proposed in Section 3.3.2. This com-

pression scheme allows us not only to efficiently compress mesh sequences but also to

promptly transmit them as various versions with spatiotemporal multi-resolutions. For

the copyright protection of mesh sequences, a watermarking technique expanded from our

3-D static mesh watermarking scheme proposed in Section 2.2.2 is applied to the interme-

diate step of the compression process. The variance of spatiotemporal wavelet coefficients

belonging to specific spatial and temporal sub-bands, to embed watermark, is modified by

the same histogram mapping function used in Section 2.2.2. The hidden watermark can

be quite robust against several intra-frame and inter-frame attacks because a statistical

feature is employed as the watermark carrier in the proposed method. Through simula-

tions, we prove that our approach enables to efficiently compress 3-D mesh sequences and

to strictly protect their ownership in a single framework.

74 Joint Watermarking and Compression


Watermarking and data compression have been mainly treated on independent frame-

works. Their combination has not been briskly studied due to an opposition of two tech-

nologies; watermarking within compressed domain could seriously affect the auditory or

visual quality of reconstructed data, and conversely lossy compression might be an attack

which interferes with the ownership assertion of watermarked data. Nevertheless, digital-

ized data is usually distributed through a network channel with limited bandwidth, and

at the same time the owner of this data never wants that it is illegally used by pirates.

Consequently, these two research topics should be simultaneously considered.

Joint watermarking and compression system can be designed by two major strategies.

One is to sequentially perform compression after watermarking (and vice versa) [Denis

et al., 2005], and the other is to embed watermark in the intermediate process of compres-

sion [Wang et al., 2004,Xu et al., 2001,Siebenhaar et al., 2001,Wong and Au, 2002,Suhail

and Obaidat, 2001,Seo et al., 2001,Li and Zhang, 2003,Su et al., 2001,Hartung and Girod,

1998,Kang et al., 2004,Wang et al., 2005,Wang and Pearmain, 2006]. The former allows

an easy and simple implementation because any existing compression (or watermarking)

algorithm can be combined with any existing watermarking (or compression) algorithm.

However, it could be inefficient from the viewpoint of system complexity since the time

and computational costs for entire processes are nearly same as the sum of each cost which

is produced by watermarking and compression. Clearly, the latter is more efficient than

the former because the watermark embedding can be completed before the compressed

bit-stream is entirely generated.

Several joint watermarking and compression techniques for audio clips [Wang et al.,

2004,Xu et al., 2001,Siebenhaar et al., 2001], two-dimensional (2-D) still images [Wong

and Au, 2002, Suhail and Obaidat, 2001, Seo et al., 2001, Li and Zhang, 2003, Su et al.,

2001], and 2-D video sequences [Hartung and Girod, 1998,Kang et al., 2004,Wang et al.,

2005,Wang and Pearmain, 2006] have been introduced, being encouraged by some inter-

national coding standards such as JPEG (Joint Photographic Experts Group)/JPEG-2000

and MPEG (Moving Picture Experts Group). Wang and Chao [Wang et al., 2004] pre-


sented an audio watermarking method which embeds watermark into the low frequency

coefficients of MDCT (Modified Discrete Cosine Transform) obtained from the analysis

filter-bank of MP3 (MPEG-1 Layer-3) coder. In [Xu et al., 2001], another audio water-

marking scheme was proposed. It first extracts several frames from compressed bit-stream,

then selects specific frames according to the features of audio content and the masking

threshold of HAS (Human Auditory System). The watermark is embedded into the se-

lected frames via bit hopping and hiding techniques. Siebenhaar et al. [Siebenhaar et al.,

2001] also designed an audio watermarking system for MPEG-2/4 AAC coding. It embeds

watermark into the transform coefficients before quantization step by using the spread

spectrum technique [Cox et al., 1997]. Although these schemes [Wang et al., 2004, Xu

et al., 2001, Siebenhaar et al., 2001] are robust against MP3 or AAC compression with

various bit-rates, the robustness against other common attacks, for example, adding noise,

down sampling, band-pass filtering, echo addition, equalization and so on, was not vali-

dated. Wong and Au [Wong and Au, 2002] proposed a blind watermarking method for

JPEG compressed image. Their algorithm embeds watermark into a vector set obtained

from the coefficients of 8×8 block DCT by using spread spectrum technique. It also used

an iterative watermark embedding technique for the purpose of robustness. In [Suhail

and Obaidat, 2001,Seo et al., 2001,Su et al., 2001], some JPEG-2000 based watermarking

schemes were introduced. Suhail and Obaidat [Suhail and Obaidat, 2001] used the spread

spectrum technique for watermark embedding. They implanted the watermark into low

frequency coefficients of DWT (Discrete Wavelet Transform) by using a β function which

represents the characteristics of HVS (Human Visual System). On the other hand, Seo

et al. [Seo et al., 2001] proposed a method to embed watermark on the intermediate step

of lifting. Their method can achieve a quite secure system as it allows us to choose a

certain sub-band as well as lifting step. In [Su et al., 2001], Su et al. presented another

JPEG-2000-based approach which embeds watermark into some significant wavelet coef-

ficients. This algorithm can extract watermark from a progressive decoding step or from

a ROI (Region of Interest) by properly grafting their watermark embedding scheme into

the EBCOT (Embedded Block Coding with Optimized Truncation) technique. Hartung

and Girod [Hartung and Girod, 1998] proposed a watermarking method for uncompressed


video and compressed MPEG-2 video. Concentrating on compressed video, the watermark

is embedded into 8×8 DCT-block by using the spread spectrum technique. Their method

causes distortion propagation due to the watermark embedded in every I(Intra)-frames.

Although it applies a drift compensation technique to cope with this problem, the addi-

tional processing increases the system complexity. Kang et al. [Kang et al., 2004] proposed

a robust watermarking scheme for MPEG video. This algorithm embeds watermark into

I-frame and P(Predicted)-/B(Bi-directional)-frames by applying different methods, re-

spectively. For I-frame watermarking, it used the RCOB (Relative Complexity of a Block)

from quantized DCT coefficients and the QP (Quantization Parameter) from rate control

as watermark carrier. For P-/B-frames watermarking, the method directly altered VLC

(Variable Length Coding) stream. The authors experimentally demonstrated that their

algorithm is robust against additive Gaussian noise, low-pass filtering, median filtering,

and histogram equalization as well as MPEG re-encoding. Another MPEG-based video

watermarking method [Wang et al., 2005] embeds watermark by modifying the direction

of motion vector obtained from half-pixel accuracy on the basis of one-pixel accuracy. This

method could not be robust against frame dropping attack because it utilizes the motion

vectors as the watermark carrier. Most of MPEG video watermarking are performed by

altering the 8×8 block DCT coefficients [Hartung and Girod, 1998, Kang et al., 2004].

Clearly, these algorithms are very fragile to synchronization attack such as cropping. To

cope with this problem, Wang and Pearmain [Wang and Pearmain, 2006] introduced a

MPEG-2 video watermarking methods which embeds repeatedly the same watermark bit

into the same row (or the same column) of coefficients belonging to 8×8 DCT-block.

In [Wang and Pearmain, 2006], the authors also proposed two other techniques which are

robust against down-sampling and frame dropping, respectively. The second scheme em-

beds watermark by altering only the low frequency coefficients obtained from full DCT.

This method allows the hidden watermark to be robust against down-sampling attack

because the spatial down-scaling of a frame has roughly equivalent effect to the trunca-

tion of high frequency band in its full DCT domain. For the robustness against frame

dropping attack, the third scheme first segments the picture frames into several groups

and embeds the same watermark into the same group. Their techniques provide good


solutions to cope with major attacks which should be considered for robust video wa-

termarking. Unlike the cases of universal multimedia data such as audio clips, 2-D still

images and 2-D video sequences, the investigations of joint watermarking and compression

schemes for 3-D graphics data have hardly proceeded. Denis et al. [Denis et al., 2005]

presented a watermarking method for compressed 3-D static meshes. Their algorithm first

compresses original meshes by using a sub-division-based coding technique [Lavoue et al.,

2005] and embeds watermark by modifying the transform coefficients obtained from the

spectral analysis [Karni and Gotsman, 2000]. This method could not be efficient since

watermarking and compression are individually performed in different domains.

In this chapter, we address a joint watermarking and compression technique for 3-D

mesh sequences. To our knowledge, there have been no attempts for this kind of 3-D

graphics data. From the view point of joint watermarking and compression, the following

requirements should be considered: low complexity, compression gain, invisibility and

robustness.

• Low complexity : As previously mentioned, a watermark embedding process should

be included to the intermediate step of a compression procedure for the purpose of

low system complexity.

• Compression gain : Clearly, the compression module should be effectively able to

reduce the spatial and temporal redundancies. The compression ratio is generally

dependent on the prediction model to be encoded by an entropy coder. Consequently,

the watermarking scheme should not disturb the well-produced prediction model.

• Invisibility (low distortion of visual quality): A joint system should embed

watermark information and control the compression ratio minimizing the distortion

of visual quality.

• Robustness: The watermark hidden into 3-D sequences could suffer from two kinds

of attacks: intra-frame and inter-frame attacks. The former includes whole attacks

which are considered in 3-D static mesh watermarking, i.e., distortion attacks such

as adding noise, uniform quantization, smoothing, simplification and sub-division,

and distortion-less attacks such as vertex re-ordering and similarity transforms (See


Section 2.1). The latter includes frame dropping. The watermarking scheme should

be designed to be robust against intra-frame and inter-frame attacks.

Considering the above requirements, we propose a joint watermarking and compres-

sion method for 3-D mesh sequences. The proposed scheme is mainly based on the SWA

(Spatial Wavelet Analysis) + TWA (Temporal Wavelet Analysis) compression scheme

presented in Section 3.3.2. This compression method allows us not only to efficiently

compress mesh sequences but also to promptly transmit them as various versions with

spatiotemporal multi-resolutions. The proposed method embeds watermark, before en-

tropy coding, into the spatiotemporal wavelet coefficients obtained from SWA and TWA.

For the robustness and invisibility of watermark, specific sub-bands are selected in spatial

and temporal wavelet domain, respectively, and their corresponding signals are modified.

To embed a watermark bit, the proposed method changes the variance of a selected 1-D

temporal sequence which consists of spatiotemporal wavelet coefficients belonging to the

same vertex index and the same axis over all mesh frames by using the same histogram

mapping function used in Section 3.3.2. The proposed method can reduce the system

complexity because this watermark embedding scheme is performed at the intermediate

step of compression. Besides, the watermark can be quite robust against intra-frame and

inter-frame attacks since a statistical feature is employed as the watermark carrier. The

watermark is extracted by an oblivious watermark detection technique.

The rest of this chapter is organized as follows. The proposed joint watermarking and

compression method is presented in Section 4.2. Section 4.3 shows the simulation results

in terms of compression performances and robustness against intra-frame and inter-frame

attacks. Finally, Section 4.4 summarizes this chapter.

4.2 Proposed Joint Watermarking and Compression Method

for 3-D Mesh Sequences

To provide an efficient combined watermarking and compression system for 3-D mesh

sequences, we apply a watermarking method expanded from our 3-D mesh watermarking

technique proposed in Section 2.2.2 to an intermediate step of SWA+TWA compression

4.2 Proposed Joint Watermarking and Compression Method 79

scheme presented in Section 3.3.2.

SWA+TWA scheme can efficiently reduce the spatial and temporal redundancies. It

uses wavelet coefficients as good prediction models for entropy coding; the spatial and

temporal wavelet coefficients can be approximated to Laplacian distribution with sharp

peak [Cho et al., 2006b]. In addition, SWA+TWA scheme enables a flexible transmission

at different conditions of bandwidth because it is able to reconstruct mesh sequences with

various spatiotemporal resolutions. From the viewpoint of watermarking, wavelet-based

multi-resolution analysis provides a suitable watermark carrier for robust and invisible

watermarking since we can embed the watermark with relatively high energy into a specific

sub-band [Cox et al., 2001]. This is the reason why we employ SWA+TWA technique as

the base framework of our proposed method.

To guarantee the robustness against intra-frame and inter-frame attacks, a watermark-

ing technique which uses statistical feature of signals is applied to the intermediate step of

the compression process. This watermarking method implants watermark by altering the

distribution of specific sub-band (high or middle frequency bands) signals after SWA and

TWA steps of the compression scheme. The main idea is as follows. We first translate the

distribution of low frequency coefficients in order that its mean value is mapped onto zero.

It means that the translated coefficients can be divided into two subsets which have nearly

same number of positives (+) and negatives (−), respectively. Next, the high (or middle)

frequency band signals are selectively classified into two subsets referring to the corre-

sponding low frequency coefficients. Since wavelet transform simultaneously provides the

time (or spatial) and frequency information, we can easily determine the high frequency

coefficient that corresponds to a low frequency coefficient. Note that the low frequency

coefficients are used just to determine two subsets of high frequency coefficients and the

selected high frequency coefficients are employed to embed watermark. This is caused

by the facts that the low frequency sub-band is hardly changed through common signal

processing, and that HVS is very sensitive to small alterations in the low frequency. The

high frequency coefficients in two subsets are modified by using the histogram mapping

function, such that one subset has bigger (or smaller) variance than the other according

to the watermark bit to be embedded. Fig. 4.1 illustrates how to modify the distributions


Figure 4.1: Proposed watermarking method by changing the variances of high frequency

sub-band signal: (a) distributions of two subsets, A and B, of high frequency sub-band

signal, the modified distributions of the two subsets for embedding watermark (b) +1 and

(c) −1, where, we assume that the initial two subsets have the same Laplacian distributions

for the simple illustration.

of the two subsets. As the proposed method modifies the high frequency band coefficients

that correspond to the low frequency coefficients, it can achieve good performances both

in terms of the robustness and invisibility of watermark. In the following sub-sections,

we describe on the entire procedure of our joint watermarking and compression system

according to the functional blocks.

4.2.1 Encoding Process Including Compression and Watermark Embed-

ding

Fig. 4.2 shows the encoding process including compression and watermark embedding.

The same notations with Section 2.2 and Section 3.3 are used for the sake of simplicity.

First, each mesh frame is transformed by the exact integer SWA. Two kinds of major

information – geometry and connectivity – are obtained from this transform for each frame.


Fig

ure

4.2:

The

enco

ding

proc

ess

ofth

epr

opos

edjo

int

wat

erm

arki

ngan

dco

mpr

essi

onsc

hem

e


The geometry information contains the coordinates of the base mesh and of wavelet coef-

ficients corresponding to each spatial resolution level. The connectivity is the topological

connections of the vertices.

The second step is connectivity coding. The connectivity information obtained from

the first step is entropy coded by an arithmetic coder [Schindler, 1998]. Note that this

process is performed only for the first frame because we assume that the mesh sequence

has a constant connectivity. The reader can refer to [Valette and Prost, 2004b] for more

details of the connectivity coding.

The third step performs TWA. Each coordinate of the base mesh and of the spatial

wavelet coefficients is processed independently as 1-D signal with N samples along tem-

poral direction [Payan and Antonini, 2005]. Here, N is the number of frames. For a given

r-th base mesh vertex c0r = (xr, yr, zr) (c0r ∈ C0 for 1 ≤ r ≤ R, and R is the number of base

mesh vertices), each coordinate is independently treated as ‘base mesh vertex sequence’:

xr (n), yr (n), and zr (n) (for 1 ≤ n ≤ N). Similarly, for a given s-th wavelet coefficient

of the j-th spatial resolution level djs =

(xj

s, yjs, z

js

)(dj

s ∈ Dj for 1 ≤ s ≤ S, and S is

the number of the wavelet coefficients in each spatial resolution level), each coordinate is

independently treated as a ‘spatial wavelet coefficient sequence’: xjs (n), yj

s (n), and zjs (n).

Note that TWA is applied to each temporal sequence u (n) (u ∈ xr, yr, zr, xjs, y

js, z

js). In

the third step, the temporal sequence u (n) is decomposed into low and high frequency

band signals, v0 (n) and v1 (n) (where v is a representative vector to denote the temporal

wavelet coefficients of u (that is, ‘spatiotemporal wavelet coefficient sequences’), by TWA

scheme, assuming that only two-channel sub-band decomposition is applied for the sim-

plicity. Clearly, more temporal resolutions can be produced by repeatedly applying TWA

to the low frequency band.

The fourth step performs the watermark embedding. In this step, specific spatiotempo-

ral wavelet coefficient sequences vp (vp0 , v

p1 ∈ vp ∈ v) are firstly selected to guarantee the

invisibility of watermark and only the selected sequences vp are used to embed watermark.

Fig. 4.3 shows the watermark embedding process in detail. This process is independently

applied to each selected temporal sequence. It means that we can embed a watermark bit

into a single temporal sequence. The high frequency band signals vp1 (n) are mapped into


Fig

ure

4.3:

The

wat

erm

ark

embe

ddin

gpr

oces

s


the normalized range of [−1, 1]. It is denoted by vp1 (n). As reported in 3, the PDF of

vp1 (n) is modeled by Laplaian distribution. Then, the high frequency coefficients vp

1 (n) is

selectively classified into two subsets A and B referring to vp0 (n), as follows.

A =vp1 (l) |l ∈ Ω+

for Ω+ =

l|vp

0 (l)− µvp0> α · σvp

0

B =

vp1 (l) |l ∈ Ω−

for Ω− =l|vp

0 (l)− µvp0< −α · σvp

0

(4.1)

where, the distribution of low frequency coefficients is translated by means of vp0 (l)− µvp

0

in order that two subsets Ω+ and Ω− (equivalently A and B) have nearly same number of

coefficients1, and α · σvp0

is a threshold value to select the high frequency band coefficients

of which the corresponding low frequency band coefficients have high energy. Assuming

that low frequency band has Gaussian distribution, about 31.7% of high frequency band

coefficients are selected for α = 1. That is, the trade-off between robustness and trans-

parency of watermark can be adjusted by determining α. Note that two subsets A and

B now have the same distribution very close to Laplacian over the interval [−1, 1]. The

coefficients in each subset are transformed by the histogram mapping function proposed

in Section 2. In Section 2, this function has been originally used to modify the variance

of uniform distribution. We prove that it can be also applied to Laplacian distribution

in Appendix A.3. The variance of the two subsets is modified according to watermark

bit. To embed watermark ω = 1 (or ω = −1), the variances of subsets A and B, σ2A and

σ2B, become respectively greater (or smaller) and smaller (or greater) than that of whole

normalized high frequency coefficients σ2vp1:

σ2A > (1 + β) · σ2

vp1

and σ2B < (1− β) · σ2

vp1

if ω = +1

σ2A < (1− β) · σ2

vp1

and σ2B > (1 + β) · σ2

vp1

if ω = −1 (4.2)

where β(0 < β < 1) is the watermark strength factor that can control the trade-off between

robustness and the transparency of watermark. To change the variance to the desired level,

the parameter k in Eq. (A.9) cannot be exactly calculated in practical environments. For

such reasons, we use an iterative approach to find proper k as follow.

1After the classification of two subsets A and B, the low frequency coefficients returns to the original

values using vp0 (l) + µv

p0.


For embedding ω = +1 into a temporal sequence:

1) Calculate the variance of vp1 through σ2

vp1

= 1L

∑Ll=1 v

p1 (l)2, where L is the

number of coefficients in vp1 ;

2) Initialize the parameter k as 1;

3) Transform the high frequency band signals belonging to two subsets A and B

by vp′

1 = sign (vp1) |v

p1 |

k;

4) Calculate the variance of A′ and B′ through

σ2A′ = 1

LA

∑LAl=1

vp′

1 (l)2

, where vp′

1 (l) ∈ A′ and LA is the number of coeffi-

cients in A′

σ2B′ = 1

LB

∑LBl=1

vp′

1 (l)2

, where vp′

1 (l) ∈ B′ and LB is the number of coeffi-

cients in B′;

5) If σ2A′ < (1 + β) · σ2

vp1, decrease k (k = k −∆k) and go back to 3);

6) If σ2B′ > (1− β) · σ2

vp1, increase k (k = k + ∆k) and go back to 3);

7) Replace the high frequency band signals with transformed ones using vp1 = vp′

1 ;

8) End.

For embedding ω = −1 into a temporal sequence:

5) If σ2A′ > (1− β) · σ2

vp1, increase k (k = k + ∆k) and go back to 3);

6) If σ2B′ < (1 + β) · σ2

vp1, decrease k (k = k −∆k) and go back to 3);

All high frequency band coefficients including modified coefficients vp′

1 are mapped onto

the original range. Note that the low frequency band coefficients vp0 are kept intact in the

watermark embedding process.

In the sixth step, the watermarked spatiotemporal wavelet coefficient sequences are

entropy coded by the arithmetic encoder.

The entropy coded connectivity and geometry information are finally merged into the

compressed bit-stream.


4.2.2 Decoding Process Including Decompression and Watermark Ex-

traction

Fig. 4.4 shows the decoding process including decompression and watermark extraction.

This process is performed by the inverse procedure of the encoding. The compressed bit-

stream is entropy decoded and the spatiotemporal wavelet coefficient sequences on which

the watermark is embedded are obtained in the first and second steps. From the first step,

connectivity information is also decompressed.

The third step extracts the hidden watermark from the spatiotemporal wavelet co-

efficient sequences. Fig. 4.5 shows the watermark extraction process. Similar to the

watermark embedding process, two subsets of high frequency band coefficients, A′′ and

B′′, are obtained from each watermarked temporal sequence. And then, the variances

of the two subsets, σ2A′′ and σ2

B′′ , are respectively calculated and compared. The hidden

watermark ω′′ is extracted by means of

ω′′ =

+1, if σ2A′′ > σ2

B′′

−1, if σ2A′′ < σ2

B′′

(4.3)

Note that the watermark detection process does not require the original signal.

In the fourth step, all spatiotemporal wavelet coefficient sequences are inversely trans-

formed by the TWS (Temporal Wavelet Synthesis) process. From this step, the temporal

sequences of the base mesh vertex and of the spatial wavelet coefficients are obtained.

Finally, the reconstructed mesh sequence is obtained by applying the SWS (Spatial

Wavelet Synthesis) process.


Simulations were carried out on two 3-D irregular triangle mesh sequences, Cow (with 128

frames and 2 904 vertices/frame) and Face (with 1 024 frames and 539 vertices/frame)

which were used in Section 3.4. The number of vertices and their connectivity information

are fixed over all frames.

To measure the quality distortion between the original mesh sequence and decom-

pressed one, we use AHD (Average Hausdorff Distance), E (Vn,V′n) (See Eq. (3.11)).


Fig

ure

4.4:

The

deco

ding

proc

ess

ofth

epr

opos

edjo

int

wat

erm

arki

ngan

dco

mpr

essi

onsc

hem

e


Figure

4.5:T

hew

atermark

extractionprocess


The robustness of the watermark is measured in terms of correlation between the original

watermark and the extracted one (See Eq. (2.15)).

Table 4.1 shows parameters used in our simulations. As mentioned in Section 4.2,

the proposed method can embed watermark into specific sub-bands in both spatial and

temporal wavelet domain. Cow and Face are decomposed into 19 and 11 levels using the

exact integer SWA scheme [Valette and Prost, 2004b] and Le Gall (5/3 tap) filter bank with

6 decomposition levels is applied for TWA and its synthesis. Assuming that we transmit

the original mesh sequences with full spatiotemporal resolutions, middle frequency bands

can be a good watermark embedding region in terms of robustness and imperceptibility

[Cox et al., 2001]. For that reason, to embed watermark information, we selected three sub-

bands in spatial wavelet domain and one sub-band in temporal wavelet domain as listed in

Table 4.1. In our method, the number of watermark bits is dependent on the number of 1-D

temporal sequences: base mesh vertex sequences and spatial wavelet coefficient sequences.

It means that the amount of watermark can be increased by embedding watermark into

multiple sub-bands in the spatial wavelet domain. This is the reason why we selected

three middle frequency bands to embed watermark. However, the candidate sub-band to

embed watermark should be selected towards lower frequency bands in order to guarantee

robustness of hidden watermark when the original mesh sequence is transmitted in worse

condition of bandwidth. The threshold α to produce subsets A and B was differently

determined according to the frame lengths of two test mesh sequences. Note that bigger α

can be used for watermark transparency when the low frequency band in temporal wavelet

domain has more coefficients. Cow and Face respectively have 4 and 32 coefficients in

each low frequency band. In Table 4.1, we also listed the average numbers of coefficients

belonging to two subsets Ω+ and Ω−. In these simulations, the numbers of coefficients in

A and B are exactly equal to eight times of those in Ω+ and Ω−, respectively. Considering

visual quality, the strength factors of watermark β were properly determined according

to the spatial resolution levels, that is, we embedded more robust watermark into higher

frequency band because most energy of signals concentrates around the low frequency

band. Fig. 4.6 depicts several frames of the watermarked mesh sequences as examples.

The evaluation results of compression performance and watermark robustness when


Table

4.1:Param

etersused

inthe

simulations

Model

SWA

levelsto

embed

waterm

ark

(#of

waterm

ark)

TW

Alevel

to

embed

waterm

ark

Threshold

α

(Avg.

#of

Ω+,

Avg.

#of

Ω−)

Strength

factorβ

(SWA

level)

Cow

8th,9th,

10th(105bits)

5th0.00

(2.04,1.96)

0.25(8th),

0.30(9th),

0.35(10th)

Face5th,

6th,7th

(75bits)5th

1.00(5.12,

5.17)0.35

(5th),0.40

(6th),0.45

(7th)


(a)

1-s

tfr

am

e(b

)64-t

hfr

am

e(c

)128-t

hfr

am

e

Fig

ure

4.6:

Wat

erm

arke

dm

esh

sequ

ence

s,(a

)-(c

)C

owm

odel

s(c

onti

nued

onne

xtpa

ge)


(d)

1-st

fram

e(e)

512-th

fram

e(f)

1024-th

fram

e

Figure

4.6:(d)-(f)

Facem

odels(continued

fromprevious

page)


Table 4.2: Evaluation of compression performance and watermark robustness when no

attack

Model AHD

Compression performance Watermark

robustness(bits/vertex/frame)

SWA+TWA Joint method Corr

Cow 9.89 13.79 13.82 1.00

Face 1.22 11.54 11.53 1.00

no attacks are listed in Table 4.2 2. As shown in this table, the quality distortions caused

by embedding watermark are very small. Besides, the hidden watermark can be extracted

perfectly from all watermarked models. From the viewpoint of compression performance,

our watermarking method might affect the coding efficiency since it changes the variance

of the prediction models. It means that the bitrate could increase (or decrease) when the

variance of prediction models decreases (or increases). However, as the binary watermark

information is generated such that it has nearly uniform distribution, we can prevent

the hidden watermark from degrading the compression performance. Comparing with

SWA+TWA scheme in which only compression is performed, the compression performance

is nearly same although the prediction models (spatiotemporal wavelet coefficients) for

entropy coding are modified by watermark embedding process.

4.3.1 Attack Simulations

To evaluate the robustness of watermark against intra-frame attacks, some distortion and

distortion-less attacks (See Section 2.1) were applied to each frame of the watermarked

mesh sequences. Table 4.3 shows the performances of watermark extraction after intra-

frame attacks. For evaluating the resistance to distortion attacks, multiplicative binary

random noise, uniform quantization and smoothing were carried out. Binary random noise

was added to each vertex norm in each watermarked mesh frame with three different error

2Detailed lossy-to-lossless compression results are reported in Section 3.4. SWA+TWA method origi-

nally enables lossless compression. However, this joint watermarking and compression method can provide

near-lossless compression due to the watermark embedding.


rates: 1%, 5% and 10% [Yu et al., 2003b]. Here, the error rate represents the noise ampli-

tude as a fraction of the maximum vertex norm of each mesh frame. We performed each

noise attack five times using different random seeds and reported the median. To evalu-

ate the robustness against uniform quantization attacks, three different quantization rates

were applied to each watermarked mesh frame; each coordinate of vertices was represented

with 8bits, 6bits and 4bits. For evaluating the robustness against smoothing attacks [Field,

1988], three different pairs of iteration and relaxation were applied. We denote these fairs

as (# of iteration,relaxation) in Table 4.3. The effects of these distortion attacks are shown

in Fig. 4.7. The proposed method is fairly resistant to the noise, quantization and smooth-

ing attacks. This is due to the fact that low frequency band signals to be used to classify

middle frequency band signals into two subsets are not easily changed by these attacks

and also that the proposed method uses statistical feature as watermark carrier. However,

the robustness for Face is not as good as that of Cow. Note that it can be improved by

adjusting the threshold α and the strength factor β. In Section 4.3.2, we discuss this topic

in more detail. To evaluate the robustness of our methods against distortion-less attacks,

vertex re-ordering and similarity transforms were carried out. Vertex re-ordering attack

was performed iteratively 100 times, also changing the seed of random number generator

in each iteration. Here, the constant connectivity over all frames was kept intact by ap-

plying the same seed to whole frames in each iteration. Similarity transforms were carried

out with many combinations of rotation, uniform scaling and translation factors. Similar

to vertex re-ordering, the same factors were applied to whole frames in each trial. It is not

necessary to tabulate watermark detection performances because the hidden watermark

information was perfectly extracted after these distortion-less attacks.

To evaluate the robustness against inter-frame attack, we applied frame dropping with

three different ratios, 1/10, 1/5 and 1/2, to watermarked mesh sequences. Here, a ratio

1/10, 1/5 and 1/2 means that one frame is dropped per 10, 5 and 2 frames, respectively. For

watermark extraction, dropped frame was interpolated by bilinear interpolation technique.

It is also not necessary to tabulate watermark detection performances because the hidden

watermark information was perfectly extracted after this inter-frame attack. These results

are caused by the fact that the proposed method employ statistical feature to embed


(a)

1-s

tfr

am

e(b

)64-t

hfr

am

e(c

)128-t

hfr

am

e

Fig

ure

4.7:

Cow

mod

elat

tack

edby

(a)-

(c)

mul

tipl

icat

ive

bina

ryno

ise

wit

her

ror

rati

oof

1%(c

onti

nued

onne

xtpa

ge)


(d)

1-st

fram

e(e)

64-th

fram

e(f)

128-th

fram

e

Figure

4.7:(d)-(f)

6bits/coordinatequantization

(continuedfrom

previouspage

andcontinued

onnext

page)


(g)

1-s

tfr

am

e(h

)64-t

hfr

am

e(i

)128-t

hfr

am

e

Fig

ure

4.7:

(g)-

(i)

smoo

thin

gw

ith

iter

atio

nof

120

and

rela

xati

onof

0.03

(con

tinu

edfr

ompr

evio

uspa

ge)


Table 4.3: Evaluation of robustness against intra-frame attacks

Intra-frame

attackAttack intensity

Model

Cow Face

AHD Corr AHD Corr

Multiplicative

binary noise

1% 17.29 1.00 13.60 1.00

5% 57.56 0.94 63.11 0.49

10% 107.48 0.81 115.16 0.17

Uniform

quantization

8bits 739.16 1.00 1924.09 1.00

6bits 803.13 1.00 1108.52 0.89

4bits 826.51 0.96 1143.99 0.49

Smoothing

(120,0.03) 1452.24 0.96 2136.67 0.81

(360,0.03) 1479.37 0.79 2181.46 0.60

(600,0.03) 1500.57 0.68 2204.75 0.49

Average 775.92 0.90 1210.15 0.66

watermark.

4.3.2 Parameters for Robustness

In this section, we analyze two parameters that can be adjusted to improve the watermark

robustness of the proposed method. One is the threshold α, and the other is the watermark

strength factor β. In order to enhance the performance reported in Section 4.3.1, Face was

watermarked with several fairs of α and β. Table 4.4 shows the fairs of two parameters.

Case I and II (or Case III and IV) adjust only the thresholds (or the strength factors)

keeping the strength factors (or the thresholds) used in 4.3.1 intact, and Case V does

both of them. These adjustments were carefully considered because they could produce

serious visual distortion. As listed in Table 4.5, new parameters were properly determined

considering the watermark transparency. In addition, they hardly affect the compression

performances.

To analyze the effect of new parameters for robustness of watermark, the watermarked

Face underwent the intra-frame attacks – multiplicative binary random noise, uniform


Table 4.4: Adjusted parameters to improve robustness (Face)

Threshold α Strength factor β (SWA level)

Case I 0.50 0.35 (5th), 0.40 (6th), 0.45 (7th)

Case II 0.00 0.35 (5th), 0.40 (6th), 0.45 (7th)

Case III 1.00 0.50 (5th), 0.55 (6th), 0.60 (7th)

Case IV 1.00 0.70 (5th), 0.75 (6th), 0.80 (7th)

Case V 0.00 0.70 (5th), 0.75 (6th), 0.80 (7th)

Table 4.5: Evaluation of compression performance and watermark robustness in terms of

different threshold α and different β (When no attack)

AHDCompression performance Watermark robustness

(bits/vertex/frame) Corr

Case I 1.83 11.55 1.00

Case II 2.26 11.56 1.00

Case III 1.62 11.54 1.00

Case IV 2.19 11.55 1.00

Case V 4.19 11.59 1.00


Table 4.6: Evaluation of robustness according to different threshold α and different β

(After intra-frame attacks applied to Face)

Intra-frame

attackAttack intensity

Corr

Case I Case II Case III Case IV Case V

Multiplicative

binary noise

1% 0.95 1.00 0.97 1.00 1.00

5% 0.69 0.79 0.73 0.63 0.77

10% 0.31 0.33 0.33 0.42 0.55

Uniform

quantization

8bits 1.00 1.00 1.00 1.00 1.00

6bits 0.92 0.92 0.92 0.97 0.97

4bits 0.47 0.47 0.55 0.55 0.60

Smoothing

(120,0.03) 0.76 0.84 0.81 0.79 0.87

(360,0.03) 0.66 0.74 0.63 0.65 0.76

(600,0.03) 0.58 0.60 0.55 0.66 0.66

Average 0.70 0.74 0.72 0.74 0.80

quantization and smoothing – having same intensities with Section 4.3.1. Table 4.6 shows

watermark extraction results in terms of several parameter pairs. Firstly, when the thresh-

old α is close to zero, the robustness can be improved as reported in the results of Case

I and II. This is mainly due to the fact that whole signals in the specific sub-band can

be referred (low frequency band signals) and modified (middle frequency band signals) to

embed watermark when α = 0. We can also improve the robustness via increasing the

strength factor, as higher strength factor enables to embed watermark with higher energy

(See the results of Case III and IV in this table). Taking advantage of adjusting both the

threshold and the strength factor, Case V has the best performance in these simulations.

4.4 Summaries

In this chapter, we proposed a joint watermarking and compression method for 3-D mesh

sequences. Based on SWA (Spatial Wavelet Analysis) + TWA (Temporal Wavelet Anal-

ysis) compression scheme, the proposed method embeds watermark into an intermediate

4.4 Summaries 101

step of compression. To embed watermark, the variances of spatiotemporal wavelet coef-

ficient sequences belonging to specific sub-bands are modified by the histogram mapping

function. Through the simulations, we proved that the proposed watermarking scheme can

be properly combined with the efficient compression method which provides spatiotem-

poral scalability. Moreover, it is quite robust against inter-frame attack including frame

dropping, as well as several intra-frame attacks including multiplicative binary noise, uni-

form quantization, smoothing, similarity transform and vertex re-ordering. However, there

are some drawbacks. Our proposal can not extract the hidden watermark after some syn-

chronization attacks such as simplification since spatial wavelet coefficients after these

kinds of attacks could have entirely different distribution from that of the watermarked

ones. Nevertheless, the proposed method presented a possibility to realize a well-designed

joint watermarking and compression system for 3-D mesh sequences.

Chapter 5

Conclusions and Perspectives

This dissertation dealt with three major research topics – watermarking, compression and

their combination – for three-dimensional (3-D) graphics data. Pursuing to develop an

efficient joint watermarking and compression system for 3-D mesh sequences as the final

goal of this dissertation, we have discussed two individual research topics and then derive

a combination system from both of them.

In Chapter 2, two oblivious watermarking methods for 3-D static meshes were pre-

sented. This chapter first re-classified general geometrical and topological attacks into

distortion and distortion-less attacks, and emphasized that distortion-less attacks is more

serious attacks on 3-D mesh watermarking because they could fatally destroy the hidden

watermark without any perceptual changes of watermarked mesh model. To effectively

cope with distortion-less as well as distortion attacks, two proposed methods use the sta-

tistical features of vertex norms to embed watermark. The first method shifts the mean

value of the distribution of vertex norms according to the watermark bit to be embedded

and the second method changes its variance. In our methods, histogram mapping func-

tions were newly introduced and used for the purpose of elaborate modification. Since

the statistical features are invariant to distortion-less attacks and less sensitive to various

kinds of distortion ones, robustness of watermark can be easily achieved. In addition, the

proposed methods employ a blind watermark detection scheme. Through the simulations,

we proved that both proposed methods are perfectly robust against distortion-less attacks

such as vertex re-ordering and similarity transforms. Moreover, they are fairly robust

104 Conclusions and Perspectives

against various kinds of distortion attacks, in particular, simplification and sub-division

operations. However, there are some drawbacks. Our proposals are not applicable to very

small size models and CAD models with flat regions, and are very vulnerable to clipping

attacks that cause severe alteration to the center of gravity of the model. Nevertheless,

the simulation results demonstrate a possible, oblivious watermarking method based on

statistical approach for 3-D polygonal mesh model.

In Chapter 3, two possible compression methods for 3-D mesh sequences were proposed:

SWA (Spatial Wavelet Analysis) + MDC (Multi-order Differential Coding) method and

SWA + TWA (Temporal Wavelet Analysis) method. Both proposed methods use the

SWA technique which employs an exact integer analysis and synthesis filters to reduce

the spatial redundancy. The filters have a powerful advantage that they can be directly

applied to irregular meshes. Besides, they provide spatial scalability. In order to reduce

the temporal redundancy, we employed two different techniques, MDC and TWA. Through

simulations, we verified that the SWA+MDC method has slightly better performances than

the SWA+TWA method in terms of both lossless and lossy compressions. On the other

hand, the SWA+TWA method offers spatiotemporal scalability while the SWA+MDC

does only spatial one.

As the final destination of this dissertation, a joint watermarking and compression

method was proposed in Chapter 4. This chapter first defined some requirements – low

complexity, compression gain, invisibility and robustness – and re-classified possible at-

tacks – intra-frame and inter-frame attacks – which should be guaranteed on 3-D mesh se-

quence watermarking. For the robustness and invisibility of watermark, specific sub-bands

are respectively selected in spatial and temporal wavelet domain and its corresponding sig-

nals are modified. To embed a watermark bit, the proposed method changes the variance

of a selected sequence of spatiotemporal wavelet coefficients by using a histogram mapping

function. The proposed method can reduce the system complexity because this watermark

embedding scheme is performed at the intermediate step of compression. Besides, the wa-

termark can be quite robust against intra-frame and inter-frame attacks since a statistical

feature is employed as the watermark carrier. The watermark is extracted by an oblivious

watermark detection technique. Through the simulations, we proved that the proposed

105

watermarking scheme can be well combined with the efficient compression method which

provides spatiotemporal scalability. Moreover, it is very robust against frame dropping

which is classified into inter-frame attacks, as well as several intra-frame attacks includ-

ing multiplicative binary noise, uniform quantization, smoothing, similarity transform and

vertex re-ordering. However, there are some drawbacks. Our proposal can not extract the

hidden watermark after some synchronization attacks such as simplification since spatial

wavelet coefficients after these kinds of attacks could have entirely different distribution

from that of the watermarked ones. Nevertheless, the proposed method presented a pos-

sibility to realize the well designed joint watermarking and compression system for 3-D

mesh sequences.

An interesting application on which the proposed methods can be used is medical image

protection and transmission systems. The medical images containing the affected parts

of patients should be strictly protected from unauthorized persons except few authorized

ones such as doctors and nurses. In addition, sometimes, these kinds of data should be

transmitted from a hospital to another. In this case, quality distortion might confuse for

doctor to accurately judge the condition of patient; it means that only lossless compression

should be used for the transmission systems of medical images assuming that the band-

width is enough guaranteed to avoid transmission problems such as packet loss and delay.

The proposed joint watermarking and compression method can be directly applied to these

kinds of systems if the medical images are represented as triangular mesh sequences. It

is caused by the fact that our method enables not only lossless compression to promptly

transmit medical images but also invisible and robust watermarking to effectively protect

its personal information. In addition to these systems, our watermarking, compression,

and their combination methods can be appropriately employed in many applications such

as 3-D movies, video games, cultural assets reconstructed as 3-D objects and so on.

106 Conclusions and Perspectives

Appendix A

Histogram Mapping Function

In this appendix, we show how to modify the mean value or variance of input signal into

desired one.

A.1 For Shifting Mean Value of Uniform Distribution

Let’s consider a continuous random variable X with uniform distribution over the interval

[0, 1]. Clearly, the expectation of the random variable E [X] is given by

E [X] =∫ 1

0xpX (x) dx =

12

(A.1)

where pX (x) is the PDF (Probability Density Function) of X. This expectation will be

used as a reference value when moving the mean of each bin to a certain level in the next

step. In our method, vertex norms in each bin are modified to shift the mean value. It

is very important to assure that the modified vertex norms also exist within the range of

each bin. Otherwise, vertex norms belonging to a certain bin could shift into neighbor

bins, which may have a serious impact on the watermark extraction. We now propose

a histogram mapping function, which can shift the mean to the desired level through

modifying the value of vertex norms while staying within the proper range. The use

of a mapping function is inspired from the histogram equalization techniques often used

in image enhancement processing [Gonzalez and Woods, 1992]. For a given continuous

random variable X, the mapping function is defined as

Y = Xk for 0 < k <∞ and k ∈ < (A.2)

108 Histogram Mapping Function

Figure A.1: Histogram mapping function, Y = Xk, for different parameters of k

where Y is the transformed variable, and the parameter k is a real value for 0 < k < ∞.

Fig. A.1 shows curves of the mapping function for different values of k. When the

parameter k is selected in the range 1 < k <∞, input variables are mapped into relatively

small values. Moreover, increases in k decrease the value of the transformed variable. It

means the reduction of mean value. On other hand, the mean value increases for decreasing

k when 0 < k < 1. Expectation of output random variable, E[Y ], is represented as

E [Y ] = E[Xk

]=

∫ 1

0xkpX (x) dx =

1k + 1

(A.3)

Fig. A.2 shows the expectation value of the output of the mapping function over

k. The expectation value decreases monotonically with the parameter k. Therefore, we

can easily adjust the mean value of the distribution by selecting a proper parameter. In

particular, the mapping function does not only guarantee to alter the variable within the

limited range, but also allows shifting of the mean value to the desired level.

A.2 For Changing Variance of Uniform Distribution 109

Figure A.2: Expectation of the output random variable via histogram mapping function

with different k, assuming that the input random variable is uniformly distributed over

unit range [0, 1].

A.2 For Changing Variance of Uniform Distribution

Now, let X be a continuous random variable with uniform distribution over [−1, 1]. As X

has a mean of zero, its variance is given by

E[X2

]=

∫ 1

−1x2pX (x) dx =

13

(A.4)

where E[X2] denotes the second moment of the random variable X. A variance of 13 will

be used as a reference when changing the variance of each bin according to the watermark

bit to be embedded. To change the variance, vertex norms in each bin should be modified

within the normalized range of [−1, 1]. For this purpose, we use a histogram mapping

function, which can change the variance to the desired level by modifying vertex norms

while staying within the specified range. For a given X, the mapping function is defined

by

Y = sign (X) |X|k for 0 < k <∞ and k ∈ < (A.5)


Figure A.3: Histogram mapping function, sign (X) |X|k, for different parameter of k

where Y is the transformed variable, and k is a real value for 0 < k < ∞. Fig. A.3

shows curves of the mapping function for different k. When the parameter is selected

for 1 < k < ∞, input variable is transformed into output variable with relatively small

absolute value while maintaining its sign. Moreover, the absolute value of transformed

variable becomes smaller as increasing k. It means a reduction of the variance. On the

other hand, variance increases for decreasing k on the range 0 < k < 1. The variance of

the output random variable E[Y 2

]is represented as

E[Y 2

]= E

[(sign (X) |X|k

)2]

=∫ 1

−1|x|2kpX (x) dx =

12k + 1

(A.6)

Fig. A.4 shows the variance of the output random variable over k of the mapping

function. Note that the variance decreases monotonically as k increases. Therefore, the

variance of the distribution can easily be adjusted by selecting a proper parameter.

A.3 For Changing Variance of Laplacian Distribution

Consider a continuous random variable X with Laplacian distribution, of which the PDF

is defined by

px(x) =λ

2e−λ|x| (A.7)

A.3 For Changing Variance of Laplacian Distribution 111

Figure A.4: Variance of the output random variable via histogram mapping function with

different k, assuming that the input random variable is uniformly distributed over the

normalized range [−1, 1].

Clearly, the second moment (variance) of the random variable E[X2

]is given by

E[X2

]=

∫ ∞

−∞x2pX (x) dx =

2λ2

(A.8)

If the random variable X is transformed using the histogram mapping function that is

defined by

y =

sign(x) · |x|k, for − 1 ≤ x ≤ 1

x, otherwise(A.9)

where sign (x) is the sign of x and k is a real value for 0 < k <∞, the second moment of

the output random variable E [Y ] is obtained as follows:

E[Y 2

]=

∫ 1

−1x2kpX (x) dx+

∫ −1

−∞x2kpX (x) dx+

∫ ∞

1x2kpX (x) dx

=∞∑

n=0

(−1)n · λn+1

(n+ 2k + 1) · n!+ 2e−λ

(12

+2λ

+2λ2

)(A.10)

where n! indicates the factorial of positive integer n. The first term of Eq. (A.10) represents

the second moment of the transformed variable for the input variable existing over the


Figure A.5: Second moment (variance) of the output random variable via histogram map-

ping function with different k, assuming that the input variable has Laplacian distribution.

interval [−1, 1] and the second does that of the input variable being in intact outside

of the interval [−1, 1]. As results, the second moment of the output random variable is

represented by the summation of the two terms. The second term might be negligible,

if the variance of the input variable is smaller enough than one (λ >>√

2). Here, λ is

inversely proportional to the variance of the input variable. Fig. A.5 shows the second

moment of the output random variable over the parameter k of the mapping function, for

different λ. The output variance of output variable can be easily adjusted by selecting a

parameter k.

Appendix B

Estimation of Entropy Coding

Efficiency via Variance of Signal

In this appendix, we show that the entropy coding efficiency can be estimated using the

variance of prediction model.

To improve the entropy coding efficiency, there have been many trials to produce a good

prediction model whose distribution exhibits one sharp peak. The more the distribution

concentrates on a specific value, the better the coding efficiency can be expected. A good

statistical model for the prediction errors is a Laplacian distribution. The coding efficiency

can be estimated by using the variance of the distribution.

Consider a continuous random variable X with zero-mean Laplacian distribution for

which the PDF is defined by

pX (x) =λ

2e−λ|x|. (B.1)

Here, the sharpness of the distribution can be determined by the parameter λ. Clearly,

the entropy 1 of the random variable, H (X), is obtained as [A., 1965]

H (X) =∫ ∞

−∞pX (x) log2

1pX (x)

dx = log2

2λ

+1

ln2. (B.2)

1This type of entropy is named ‘continuous or differential entropy’. It could sometimes have negative

values and then be inefficient to measure the amount of information comparing with Shannon entropy. Note

that we just use continuous entropy to demonstrate the inter-relationship between entropy and variance

focusing on a statistical model, Laplacian distribution.

114 Estimation of Entropy

Figure B.1: Relationship between the entropy and the variance according to different σ

The variance, σ2, is given by the second moment E[X2

]:

σ2 = E[X2

]=

∫ ∞

−∞x2pX (x) dx =

2λ2. (B.3)

From Eq. (B.2) and (B.3), both the entropy and variance are functions of λ. Therefore

Eq. (B.2) can be rewritten as

H (X) = log2σ√

2 +1

ln2. (B.4)

Fig. B.1 shows a relationship between the entropy and the variance according to different

σ. As shown in this figure, the variance is highly correlated with the entropy. In our

approaches, the entropy coding efficiency is estimated using the variance of prediction

model.

Appendix C

Finding the Optimal Order of

MDC (Multi-order Differential

Coding)

In this appendix, we discuss the efficiency of the MDC (Multi-order Differential Coding)

according to the correlation coefficient of input signal.

Let an input data sequence u(n) (for 1 ≤ n ≤ N) be a WSSMP (Wide Sense Stationary

Markov Process) with zero mean.

The m-th order differential error sequence y(m) (n) can be expressed by

y(1) (n) = u (n)− u (n− 1)

y(2) (n) = y(1) (n)− y(1) (n− 1)

...

y(m) (n) = y(m−1) (n)− y(m−1) (n− 1) (C.1)

The impulse response of the differential coding system is defined as

h (n) = δ (n)− δ (n− 1) (C.2)

Using Eq. (C.1), the m-th order differential error sequence can be rewritten as

y(m) (n) = h (n) ∗ y(m−1) (n) (C.3)

116 Finding the Optimal Order

where, ∗ denotes the convolution operator.

The auto-correlation function of Eq. (C.3) can be calculated as

ϕy(m)(k) = ϕh(k) ∗ ϕy(m−1)(k) (C.4)

where,

ϕh(k) = h (k) ∗ h (−k) and ϕy(m−1)(k) = E[y(m−1)(k)y(m−1)(n+ k)

](C.5)

where, E [.] is expectation. According to Eq. (C.2), Eq. (C.5) is given by

ϕh(k) = −δ (k − 1) + 2δ (k)− δ (k + 1) (C.6)

Considering the first order differential coders, from Eq. (C.4)

ϕy(1)(k) = −ϕu(k − 1) + 2ϕu(k)− ϕu(k + 1) (C.7)

From Eq. (C.7):

ϕy(1)(0) = 2 (ϕu(0)− ϕu(1)) (C.8)

where ϕu (0) = σ2u and if we write the auto-correlation function of the input data sequence

as ϕu (k) = σ2uψ (k), (ψ (k) < 1, ∀k), ϕu (1) = σ2

uψ (1). Clearly, from Eq. (C.8), the

output variance of the first order differential coder is

σ2y(1) = ϕy(1)(0) = 2σ2

u (1− ψ (1)) (C.9)

If the input sequence u (n) is a first order stationary Markov process, ϕu(k) = E [u (n)u (n+ k)] =

σ2uψ (k) with ψ (k) = ρ|k|. Here, ρ (|ρ| ≤ 1) is the correlation coefficient. Therefore, Eq.

(C.9) can be rewritten as follow:

σ2y(1) = ϕy(1)(0) = 2σ2

u (1− ρ) (C.10)

From Eq. (C.10), σ2y(1) < σ2

u, if and only if 0.5 < ρ ≤ 1. Note that the WSSMP is a first

order autoregressive (AR(1)) process of the form:

u (n) = ρu (n− 1) +√

1− ρ2w (n) (C.11)

where w (n) is a white noise with zero mean and variance σ2u.

117

Clearly, for an AR(1) process, the optimal predictor is:

y1opt (n) = u (n)− ρu (n− 1) (C.12)

Then, its output variance is

σ2y1

opt= σ2

u (1− ρ)2 (C.13)

It follows that the output variance is more reduced for a predictor having larger corre-

lation coefficient. However, the (optimal) predictor requires both computational costs to

calculate the correlation factor and side information to be transmitted.

For an AR(1) process, it is easy to prove that the output variance of the MDC is

reduced if

0.7752 < ρ ≤ 1 for the second order

0.9199 < ρ ≤ 1 for the third order

0.9740 < ρ ≤ 1 for the fourth order

· · ·

Considering that the input sequence is modeled by a p-th order AR process (AR(p)), the

optimal differential coder has the order p:

y1opt (n) = u (n)−

p∑k=1

aku (n− 1) (C.14)

Clearly, the proposed m-th order MDC technique is a good alternative. In addition, the

method requires just to evaluate the optimal order of the differential coder in terms of

output variance and to transmit it.

118 Finding the Optimal Order

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List of Personal Bibliography

Journals

[Cho et al., 2007a] Cho, J., Prost, R., Jung, H., An oblivious watermarking for 3-D

polygonal meshes using distribution of vertex norms, IEEE Transaction on Signal

Processing, volume 55, no. 1, (2007), pp. 142-155.

Conferences

[Cho et al., 2007b] Cho, J., Kim, M., Valette, S., Jung, H., Prost, R., A 3-D mesh

sequence coding using the combination of spatial and temporal wavelet analysis,

Lecture Note in Computer Science, volume 4418, (2007), pp. 389-399.

[Kim et al., 2006a] Kim, M., Cho, J., Prost, R., Jung, H., Wavelet analysis based

blind watermarking for 3-D surface meshes, Lecture Note in Computer Science,

volume 4283, (2006), pp. 123-137.

[Cho et al., 2006b] Cho, J., Kim, M., Valette, S., Jung, H., Prost, R., 3-D dynamic

mesh compression using wavelet-based multiresolution analysis, in: Proceedings of

ICIP 2006, Atlanta, GA, USA, Oct. 2006, (pp. 529-532).

[Kim et al., 2006c] Kim, M., Cho, J., Prost, R., Jung, H., A robust blind water-

marking for 3D meshes using distribution of scale coefficients based on irregular

wavelet analysis, in: Proceedings of ICASSP 2006, Toulouse, France, May. 2006,

(pp. 477-480).

[Cho et al., 2005] Cho, J., Kim, M., Prost, R., Chung, H., Jung, H., Robust water-

marking on polygonal meshes using distribution of vertex norms, Lecture Note in

Computer Science, volume 3304, (2005), pp. 283-293.

Submitted Journals

[Cho et al., 2007c] Cho, J., Kim, M., Valette, S., Jung, H., Prost, R., 3-D mesh se-

quence compression using wavelet-based multi-resolution analysis, IEEE Transaction

on Circuits and Systems for Video Technology.

Curriculum Vitae

Personal Information

• Name: Cho, Jae-Won

• Date of birth: May 6, 1979

Educations

• Mar. 2005 - Dec. 2007 : Department of Electronics, INSA-Lyon (Institut National

des Sciences Appliquees de Lyon), France (Ph.D.)

• Sep. 2004 - Feb. 2008 : Department of Information and Communication Engineering,

Yeungnam University, Rep. of Korea (Ph.D.)

• Sep. 2002 - Aug. 2004 : Department of Information and Communication Engineer-

ing, Yeungnam University, Rep. of Korea (M.S.)

• Mar. 1998 - Aug. 2002 : Department of Information and Communication Engineer-

ing, Yeungnam University, Rep. of Korea (B.S.)

Research Areas

• Multimedia signal processing including audio clips, 2-D still images, 2-D video

streams, 3-D meshes, 3-D mesh sequences

• Data compression

• Digital watermarking

• Quality measurement

Professional Experiences

• Dec. 2006 - Jan. 2007 : Reviewer, Computer Graphics Forum (a Journal of Euro-

graphics)

• Sep. 2004 - Feb. 2008 : Professional researcher, Graduate School of Yeungnam

University

• Jan. 2004 - Feb. 2004 : Visiting researcher, CREATIS of INSA-Lyon

• Sep. 2002 - Aug. 2006 : Assistant teacher, School of EECS (Electrical Engineering

and Computer Science) of Yeungnam University

Research Projects

• Dec. 2006 - Nov. 2007 : Director, “A study of efficient coding method for 3-D mesh

sequences,” KRF (Korea Research Foundation), Rep. of Korea

• Aug. 2003 - Aug. 2007 : Assistant researcher, “A study on the QoS-guaranteed traf-

fic engineering and multimedia service platform in the next generation wired/wireless

integrated networking environment,” MIC (Ministry of Information and Communi-

cation), Rep. of Korea

• Sep. 2003 - Sep. 2005 : Assistant researcher, “Joint watermarking and compres-

sion in 3-D irregular meshes via multi-resolution wavelet analysis,” CNRS (Centre

National de la Recherche Scientifique), France and KOSEF (Korea Science and En-

gineeriing Foundation), Rep. of Korea

Award

The prize of excellent paper presentation, ASK (Acoustical Society Korea), Rep. of Korea

(Jul. 2003)

Patents

• Cho, J., Kim, M., Jung, H., “Encoding and decoding method for watermarking using

statistical analysis (10-2006-0080755),” Aug. 24, 2006, Rep. of Korea (Applied)

• Cho, J., Park, H., Jung, H., “Method for generating digital watermark and detecting

digital watermark (10-2006-0080756),” Aug. 24, 2006, Rep. of Korea (Applied)

• Cho, J., Chung, H., Jung, H., “System and method for transformation of digital

signal for measuring quality and for measuring a transmission quality of digital

signal (10-2006-0080757),” Aug. 24, 2006, Rep. of Korea (Applied)

Publications

International Journals

[Cho et al., 2007a] Cho, J., Kim, M., Valette, S., Jung, H., Prost, R., 3-D mesh se-

quence compression using wavelet-based multi-resolution analysis, IEEE Transaction

on Circuits and Systems for Video Technology, (Submitted).

[Cho et al., 2007b] Cho, J., Prost, R., Jung, H., An oblivious watermarking for 3-D

polygonal meshes using distribution of vertex norms, IEEE Transaction on Signal

Processing, volume 55, no. 1, (2007), pp. 142-155.

[Park et al., 2004a] Park, H., Cho, J., Oh, I., Prost, R., Chung, H., Jung, H., Multi-

ple echo hiding in sub-band signals, GESTS International Transaction on Acoustic

Science and Engineering, volume 2, no. 1, (2004), pp. 122-131.

Lecture Notes in Computer Science

[Cho et al., 2007c] Cho, J., Kim, M., Valette, S., Jung, H., Prost, R., A 3-D mesh

sequence coding using the combination of spatial and temporal wavelet analysis,

Lecture Note in Computer Science, volume 4418, (2007), pp. 389-399.

[Cho et al., 2006a] Cho, J., Chung, H., Jung, H., A robust blind audio watermarking

using distribution of sub-band signals, Lecture Note in Computer Science, volume

4105, (2006), pp. 106-113.

[Kim et al., 2006b] Kim, M., Cho, J., Prost, R., Jung, H., Wavelet analysis based

blind watermarking for 3-D surface meshes, Lecture Note in Computer Science,

volume 4283, (2006), pp. 123-137.

[Cho et al., 2005a] Cho, J., Kim, M., Prost, R., Chung, H., Jung, H., Robust wa-

termarking on polygonal meshes using distribution of vertex norms, Lecture Note in

Computer Science, volume 3304, (2005), pp. 283-293.

[Cho et al., 2004b] Cho, J., Park, H., Huh, Y., Chung, H., Jung, H., Echo watermark-

ing in sub-band domain, Lecture Note in Computer Science, volume 2939, (2004),

pp. 447-455.

International Conferences

[Cho et al., 2006c] Cho, J., Kim, M., Valette, S., Jung, H., Prost, R., 3-D dynamic

mesh compression using wavelet-based multiresolution analysis, in: Proceedings of

ICIP 2006, Atlanta, GA, USA, Oct. 2006, (pp. 529-532).

[Kim et al., 2006d] Kim, M., Cho, J., Prost, R., Jung, H., A robust blind water-

marking for 3D meshes using distribution of scale coefficients based on irregular

wavelet analysis, in: Proceedings of ICASSP 2006, Toulouse, France, May. 2006,

(pp. 477-480).

[Oh et al., 2005b] Oh, I., Cho, J., Chung, H., Jung, H., Multiple echo watermarking

using wavelet transform, in: Proceeding of the Kyushu-Youngnam Joint Conference

2005, Busan, Rep. of Korea, Jan. 2005, (pp. 13-16).

[Cho et al., 2004c] Cho, J., Kim, M., Chung, H., Jung, H., Robust 3-D watermarking

against distortionless attacks, in: Proceeding of 2004 Joint Workshop of Tohoku

Univ. and Yeungnam Univ., Gyeongsan, Rep. of Korea, Nov. 2004, (pp. 33-34).

[Oh et al., 2004d] Oh, I., Cho, J., Prost, R., Chung, H., Jung, H., Audio watermark-

ing in sub-band signals using multiple echo kernels, in: Proceeding of ICSLP 2004,

Jeju, Rep. of Korea, Oct. 2004, (pp. 2453-2456).

[Cho et al., 2003a] Cho, J., Park, H., Chung, H., Jung, H., An evaluation of blind wa-

termarking based on fast fourier transform, in: Proceeding of the Kyushu-Youngnam

Joint Conference 2003, Kyushu, Japan, Jan. 2003, (pp. 81-84).

Korean Domestic Journals

[Cho et al., 2007d] Cho, J., Yoo, K., Jung, H., Quality measurement methods for

transmitted multimedia data using statistical characteristics of signals, Journal of

Korea Multimedia Society, volume 11, no. 1, (2007), pp. 76-84.

[Kim et al., 2007e] Kim, M., Cho, J., Prost, R., Jung, H., A blind watermarking for

3-D mesh sequence using temporal wavelet transform of vertex norms, Journal of

Korea Multimedia Society, volume 32, no. 3, (2007), pp. 256-268.

[Cho et al., 2002a] Cho, J., Kim, M., H., Jung, H., A blind watermarking based on

fast fourier transform, Journal of the Institute of Information and Telecommunica-

tion, volume 9, no. 1, (2002), pp. 41-46.

Korean Domestic Conferences

[Cho et al., 2006e] Cho, J., Kim, M., Chung, H., Jung, H., Statistical character-

istics based audio watermarking using discrete wavelet transform, in: Conference

Proceeding of Acoustical Society of Korea, Daegu, Rep. of Korea, Nov. 2006, (pp.

441-446).

[Kim et al., 2006f] Kim, M., Cho, J., Chung, H., Jung, H., A blind watermarking for

3-D mesh sequences using temporal wavelet transform, in: Conference Proceeding of

Acoustical Society of Korea, Daegu, Rep. of Korea, Nov. 2006, (pp. 447-452).

[Cho et al., 2005c] Cho, J., Park, H., Kim, M., Chung, H., Jung, H., Quality measure-

ment for transmitted audio data using variance of sub-band signals, in: Conference

Proceeding of Acoustical Society of Korea, Gangwon, Rep. of Korea, Nov. 2005, (pp.

191-194).

[Kim et al., 2005d] Kim, M., Park, H., Cho, J., Chung, H., Jung, H., A watermark-

ing method for 3D irregular meshes based on multi-resolution wavelet analysis, in:

Conference Proceeding of Acoustical Society of Korea, Gangwon, Rep. of Korea,

Nov. 2005, (pp. 195-198).

[Park et al., 2005e] Park, H., Cho, J., Chung, H., Jung, H., Audio watermarking in

sub-band signals using multiple echo kernals, in: Conference Proceeding of Acoustical

Society of Korea, Gangwon, Rep. of Korea, Nov. 2005, (pp. 199-202).

[Cho et al., 2003b] Cho, J., Park, H., Chung, H., Jung, H., Echo watermarking based

on sub-band signals, in: Conference Proceeding of Korean Institute of Communica-

tion Sciences, Seoul, Rep. of Korea, Dec. 2003, (p. 491).

[Cho et al., 2003c] Cho, J., Park, H., Chung, H., Jung, H., Echo watermarking based

on wavelet transform, in: Conference Proceeding of Acoustical Society of Korea,

Jinhae, Rep. of Korea, Oct. 2003, (pp. 31-34).

[Cho et al., 2003d] Cho, J., Park, H., Chung, H., Jung, H., Echo watermarking based

on descrete wavelet transform, in: Conference Proceeding of Acoustical Society of

Korea, Changwon, Rep. of Korea, Jul. 2003, (pp. 397-400).

[Suk et al., 2003e] Suk, S., Kim, C., Cho, J., Jung, H., Chung, H., Speech and

character combined recognition system for PDA in wireless network environment, in:

Conference Proceeding of Acoustical Society of Korea, Gyeongjoo, Rep. of Korea,

Oct. 2003, (pp. 19-20).

[Cho et al., 2002b] Cho, J., Kim, M., Ryu, K., Chung, H., Jung, H., An evaluation

of digital watermarking based on fast fourier transform, in: Conference Proceeding

of Acoustical Society of Korea, Andong, Rep. of Korea, Oct. 2002, (pp. 55-58).

[Park et al., 2002c] Park, H., Cho, J., Chung, H., Jung, H., An efficient operation on

wavelet transform, in: Conference Proceeding of Acoustical Society of Korea, Busan,

Rep. of Korea, Nov. 2002, (pp. 295-298).

FOLIO ADMINISTRATIF

THESE SOUTENUE DEVANT L'INSTITUT NATIONAL DES SCIENCES APPLIQUEES DE LYON

NOM : CHO DATE de SOUTENANCE : le 7 Décembre (avec précision du nom de jeune fille, le cas échéant) Prénoms : Jae-Won TITRE : Watermarking, Compression, and Their Combination for 3-D Triangular Meshes NATURE : Doctorat Numéro d'ordre : 2007-ISAL-0099 Ecole doctorale : ÉLECTRONIQUE, ÉLECTROTECHNIQUE, AUTOMATIQUE Spécialité : IMAGES ET SYSTÈMES Cote B.I.U. - Lyon : T 50/210/19 / et bis CLASSE : RESUME : This dissertation deals with watermarking, compression, and their combination for three-dimensional (3-D) triangular meshes. We first propose algorithms individually in order to watermark static meshes and to compress mesh sequences. Finally we derive a combined system for joint compression and watermarking. Firstly, we propose two oblivious (or blind) watermarking techniques for 3-D static meshes. They mainly use statistical features of vertex norms to embed watermark; the first proposed method shifts the mean value of the distribution and the second proposed method changes its variance. Histogram mapping functions are introduced to modify the distribution. These mapping functions are devised in order to reduce the visibility of watermark as much as possible. Since the statistical features of vertex norms are less sensitive to signal alterations, the proposed methods can be robust against general attacks. In addition, our methods employ a blind watermark detection scheme, which can extract the watermark without referring to the original mesh model. Through simulations, we demonstrate that the proposed approaches are robust against several attacks such as adding binary noise, smoothing, uniform quantization, simplification, sub-division, vertex re-ordering, and similarity transform. Next, we present two compression methods for 3-D mesh sequences with constant connectivity. The proposed methods mainly use an exact integer spatial wavelet analysis (SWA) technique to efficiently decorrelate the spatial coherence of each mesh frame and also to promptly transmit mesh frames with various spatial resolutions under different bandwidth conditions (spatial scalability). To reduce the temporal redundancy, the first proposed method applies multi-order differential coding (MDC) to the temporal sequences after SWA of each mesh frame. MDC determines the optimal order of the differential coder by analyzing the variance of prediction errors. Compared to the first-order differential coding (FDC) scheme, the method can improve the compression performance. The second proposed method applies temporal wavelet analysis (TWA) to the 1-D temporal sequences. In particular, this method offers spatiotemporal multi-resolution coding. Through simulations, we prove that our approaches enable efficient lossy-to-lossless compression for 3-D mesh sequences. Finally, we present a joint compression and watermarking method for 3-D mesh sequences. Our approach is based on the proposed compression method using SWA and TWA. For robust and invisible watermark, a new watermarking technique derived from our second watermarking scheme is applied to the intermediate step of the compression process. Watermark embedding is carried out by the histogram mapping function which modifies the variance of spatiotemporal wavelet coefficients belonging to specific sub-bands. The hidden watermark is robust against several attacks such as additive binary noise, smoothing, frame dropping, because the employed watermark carrier is a statistical feature of spatiotemporal wavelet coefficients. Through simulations, we prove that our approach enables to efficiently compress 3-D mesh sequences and strictly protect its ownership in a single framework. MOTS-CLES : Watermarking, compression, joint compression and watermarking, 3-D static meshes, 3-D mesh sequences, and constant connectivity Laboratoire (s) de recherche : CREATIS-LRMN (Centre de Recherche Et d’Applications en Traitement des Images et du Signal), UMR CNRS 5220, U630 Inserm Directeur de thèse: Cotutelle INSA-Lyon /Yeungnam University Korea : M. Rémy PROST et M. Ho-Youl JUNG Président de jury : Mme. Isabelle MAGNIN Composition du jury : M. Marc ANTONINI (rapporteur), M. Ki-Ryong KWON (rapporteur), Mme. Françoise PRETEUX (examinatrice), M. Hyun-Soo KANG (examinateur), M. Kook-Yeol YOO (examinateur), Mme. Isabelle MAGNIN (présidente), M. Rémy PROST (co-directeur) et M. Ho-Youl JUNG (co-directeur)

watermarking, compression, and their combination for 3-d

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