perceptually optimized coding of color images for band‐limited information networks

7/27/2019 Perceptually Optimized Coding of Color Images for BandLimited Information Networks

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InternationalJournalofCommunications(IJC)Volume2Issue2,June2013 www.seipub.org/ijc

49

PerceptuallyOptimizedCodingofColor

ImagesforBandLimitedInformation

Networks

EvgenyGershikov

DepartmentofElectricalEngineering,OrtBraudeAcademicCollegeofEngineering,Karmiel,Israel

andDepartmentofElectricalEngineering,TechnionIIT,Haifa,Israel

[email protected]

Abstract

The Mean Square Error (MSE) or the Peak Signal to Noise

Ratio (PSNR) are common distortion measures used toassess imagequality. Nevertheless, theyare usually chosen

duetotheirsimplicityandnottheirperformanceastheyare

notalwayssuitablecomparedtothehumanobserver.Inthis

workwepresentaRateDistortionapproach tocolor image

compressionbasedonsubbandtransformsusingperceptual

optimization of the compression quality. This approach is

basedonminimizationof theWeightedMeanSquareError

(WMSE)oftheencoded image,whichbettercorrespondsto

thequalityassessmentofthehumaneye.TheWMSEcanbe

measuredintheYCbCrcolorspace,forwhichvisualweights

are relatively easily derived. Based on the new approach,

new

optimized

compression

algorithms

are

introduced

using the Discrete Cosine Transform and the Discrete

Wavelet Transform. We compare the new algorithms to

presentlyavailablealgorithmssuchasJPEGandJPEG2000.

Our conclusion is that the new WMSE optimization

approach outperforms presently available compression

systemswhenahumanobserver isconsidered.

Keywords

ColorImageCompression; WeightedMeanSquareError;Discrete

CosineTransform;DiscreteWaveletTransform;PerceptualRate

DistortionModel;OptimalColorComponentTransform;Optimal

Rate

Allocation

Introduction

Many color image coding algorithms are based on

subband transforms for thecompressionprocess.The

complexity of such algorithms varies from systems

based on elementaryblock transforms like the DCT

(DiscreteCosineTransform)[14]used,forexample,in

JPEG [21] to more complicated algorithmsbased on

the Lapped Biorthogonal Transform (LBT), the

Discrete Wavelet Transform (DWT), wavelet packets

and filterbanks, such as EZW (Embedded ZerotreeWavelet)[19], JPEG2000 [13][15], JPEG XR [2][16] or

uniform DFT filterbanks [18]. Still it is not always

clear that the added complexity also improves the

compression results. The recently introduced Rate

Distortion (RD)model forsubband transformcoders

[5] can be used in such applications to assess the

performance of the compression algorithm. This RD

model, however, approximates the MSE distortion of

the compression results, which is not always well

correlatedwithsubjectiveimagequalityasseenbythe

humaneye.Morecomplicateddistortionmeasurescan

be proposed, such as calculating the MSE distortion

between two imagesafteran intensity transformation

and filtering for grayscale images [11] or a similar

process using a nonlinear transformation of the

primarycolorcomponents,followedbyfiltering,fora

colorimage[1].Abasicmeasurethatissimilartothe

MSE,but can incorporate perceptual weights is the

Weighted MSE (WMSE). This measure assigns a

different weight to the MSE of each subband of the

image, thus simulating the varying sensitivity of the

Human Visual System (HVS) to different horizontal

and vertical spatial frequencies. As a more realistic

tool,itcanimprovetheassessmentofthemodel.

ThegoalofthisworkistodevelopaperceptualRate

Distortion (RD) model of subband transform coders

based on the WMSE as the distortion measure. We

demonstrate the efficiency of the new model for

subbandtransformcodingbypresentinganewtypeof

compression algorithms based on perceptual

optimization of the preprocessing stage and of the

subbandratesallocation.

ObjectiveRateDistortionTheoryofSubband

TransformCoders

Considerageneralsubbandtransformcoderforcolor

images. Typically, the image samples are first pre

processed,

then

subband

transformed

and

quantized

and finally postprocessed losslessly. A detailed

descriptionofthesestagesisgivenbelow.


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www.seipub.org/ijc International Journal of Communications (IJC) Volume 2 Issue 2, June 2013

50

1) PreprocessingHereaCCT(ColorComponentsTransform)isapplied

totheRGBcolorcomponentsoftheimage.Wedenote

the RGB components in vector form as

and thenewcolorcomponentsas .The

sizeCCTmatrixisdenotedasM.Thisstagecanbewrittenas:

(1)

ThegoalofusingtheCCTtransformisusuallytode

correlate the highly correlated RGB components

[7][10][15][23].TheCCTtransformisoftenfollowedby

level shifting as for example is the case inJPEG2000

[13] so that the sample range of values becomes

symmetricaroundzero.

2) SubbandTransformingandQuantizingAsubbandtransform,suchastheDCTortheDWTis

applied to each color component. The subband

coefficients of each color component are then

quantized. An independent uniform scalar quantizer

foreachsubbandisused.

3) PostprocessingThequantizedcoefficientsareencodedlosslessly.The

goal is to reduce the number ofbits required for the

coefficients without loss of information. Techniques

such

as

runlength

encoding,

zero

trees,

delta

modulation and entropy coding are used here. This

stagehastobeadaptedtothesubbandtransformused.

Toderive theRDbehaviorof thealgorithm, first the

RD of a scalar uniform quantizer needs to be

considered. Assuming that a random signal with

variance isquantizedbysuchaquantizer,itsRate

Distortionbehaviorhasbeenapproximatedby[6][20]:

(2)

where R is the rate and is a constant dependent

upon thedistributionof .Thenbasedon (2) theRD

model of a general monochromatic subband coder

with subbandscanbeexpressedas:

(3)

Here istheMSEofsubband ,

is its variance, is its energy gain [20] and is the

rate allocated to it. Also is its sample rate, i.e., the

relativepartofthenumberofcoefficientsinitfromthe

total number of samples in the signal. is a constant

equalto .

Consider now a color image. The coding algorithm

described in the beginning of this section may be

regardedasapplyingaCCTtotheimage,followedby

monochromaticly subband coding each of the new

color components. The RateDistortion model of this

algorithmis

[2]:

(4)

where and have the same meaning asbefore,

but for subband of color component ( ).

Optimalratesallocationforthesubbandscanbefound

by minimizing the expression of Equation (4) under

therateconstraint:

(5)

for some total image rate . Here downsampling

factors havebeen used. denotes how much the

number of samples of color component has been

reducedbydownsampling.Forexample,ifthedown

samplingisbyafactorof2horizontallyandvertically

then:

The optimal rates under the rate constraint of (5) as

wellasnonnegativityconstraintsare:

3 1

3

1

2 2 1

1 23

1

( )

1,

( )k k

j jj

bi

j jj

T

i b biii

i

T Act

k kkk

kk

RR

G

lna

GM

MM

MM

(6)


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51

Wherei

b Act with iAct denoting the

setofnonzero(oractive)ratesinthecolorcomponent

,i.e.,

(7)

Also

(8)

The structure of this work is as follows. In the next

section the perceptual RateDistortion model is

introduced. Section Perceptually Optimized

Compression presents new color compression

algorithms optimized according to this modelbased

on the DCT subband transform and on the DWT.

Simulationsofthenewalgorithmsandcomparisonto

presently available algorithms are provided in this

section.

Our

conclusions

and

summary

are

given

in

thefinalsection.

The Perceptual R-D Model

We assume here that we are given the visual

perception weightscorresponding to thesubbandsof

a certain subband transform (SBT) in a color space.

Sucha space canbe, for example,YCbCr aswe have

chosen in this work. We now wish to derive an

expression for the WMSEdistortion of a coderbased

on thesubband transform.Thesame coderdescribed

in Subsection Objective RateDistortion theory ofsubbandtransformcodersisassumed,sothataCCT

isapplied to the RGBcolorcomponentsof the image

priortocodingandtheactualimagedatacompression

isperformed inanothercolorspacedenotedC1C2C3.

We denote as the vector of theSBT

coefficientsat some index in subband in the YCbCr

color space. Similarly, the vector of subband

coefficients in the C1C2C3 color space is denoted

.DuetothelinearityoftheSBT,the

followingrelationshipholds:

(9)

where stands for the CCT matrix from the YCbCr

color space to the C1C2C3 space. If is the CCT

matrixfromRGBtoC1C2C3and istheRGBto

YCbCrmatrix,then:

(10)

SincetheSBTcoefficientsarelossyencoded,errorsare

introducedbetweenthereconstructedcoefficients

in the YCbCr color space and the original ones. The

error

covariance

matrix

for

the

subband

in

the

YCbCrdomainis:

(11)

where denotes statistic mean. Similarly in the

C1C2C3domain:

(12)

andusing(9)wecanexpress by as:

(13)

The MSE distortions of the YCbCr color

componentsinsubband arethediagonalelementsof

andthus:

(14)

where is the row of in column form. In a

similar fashion, the diagonal elements of canbe

recognized as the MSE distortions of the , ,

colorcomponents,givenby (2)andslightlyrewritten

tobecome:

(15)

where andbi

R and , denote the

rateandvarianceofsubband ofcolorcomponent ,

respectively. Note that we continue here with the

consistent notation of a tilde for the variables related

to the C1C2C3 color space. Assuming that the

quantization errors of the three color components in

eachsubbandintheC1C2C3domainareuncorrelated,

becomesadiagonalmatrixand(14)becomes

(16)

once(15)issubstitutedfor .Nowif,forthesakeof

convenience,wedenote theYCbCrcolorcomponents

at each pixel as a vector , then the

WMSEofthe colorcomponent is:

(17)

Ascanbeseen,thisexpressionincorporatestheenergy

gainsofthesubbands aswellastheirsamplerates

.

Also

the

visual

weights

are

part

of

the

expression,providingvaryingsignificancetodifferent

subbands of the same color component as well as

between color components. Defining the total WMSE

astheaverageWMSEoftheYCbCrcolorcomponents,

weget:

3

1

3 1

1 0

1( )

3

1

3

i

i

B

b b bi b i

i b

WMSE WMSE x

G w d

YCbCr

(18)

and after substituting (16) for the expression

becomes:


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52

21 23 1 3

2

1 0 1

2121 3 3 _

2

0 1 1

_

1

3

1.

3

bk

bk

BaR

bkb b bi k i b k ik

BaR

bkb b k bib k i

ik

WMSE G w e

G e w

M

M

(19)

Tosimplify(19)wedenote:

(20)

sothattheWMSEexpressionbecomes:

(21)

Clearly,ifthevisualweights areallequalto1,the

WMSE expression of (21) should become the

expression for the MSE in the YCbCr domain. This

expression is given exactlyby (4) with the differencethat there is tobe replacedby in our case. From

thecomparisonofequations(21)and(4)weconclude

that in that case, which means

accordingto(20)that

(22)

Astraightforwardcheckprovesthatthisisindeedthe

case.

Decorrelation

of

the

Quantization

Errors

In the derivation of the WMSE expression of (21) we

haveassumedthatthequantizationerrorsofthe , ,

colorcomponentsareuncorrelatedineachsubband.

It is of interest to note that the assumption in the

derivationoftheMSEexpressionof(4)wasthelackof

correlation of the quantization errors in the image

domain [2], i.e. that and have zero

correlation for , . Note that

denotes here the reconstructed component. The

questionthat

rises

is

whether

the

assumption

of

zero

correlation in each subband means also zero

correlationintheimagedomain.

Using the vector space interpretation of subband

transforms[20],wecanwriteforthecolorcomponent

:

(23)

here is the color component in vector form after

lexicographic ordering. are the SBT synthesis

vectors. Also the sum on is on all the coefficient

indices in the subband, denotes the subband

coefficient of at index and is the same

coefficientafterquantizationandreconstruction.Now

consider the expression for

, where is the number of the image pixels.

UsingEquation(23),itcanbewrittenas:

(24)

where . Assuming zero

correlation of the quantization errors of the different

color components in each subband and between

subbands means that , hence

immediately follows

according to (24). But this means exactly zerocorrelationofthequantizationerrorsinimagedomain.

ThusthederivationoftheWMSEexpressionof(21)is

once again consistent with the derivation of the MSE

expressionof(4).

BasicOptimizationUsingtheWMSEModel

AfterderivingtheWMSEexpression,thenaturalnext

step is touse it to find theoptimalratesandoptimal

CCT in the WMSE sense. First we wish to minimize

the WMSE of (21), subject to the rate constraint

, resulting in the followingLagrangian( istheLagrangemultiplier):

(25)

whichisminimizedbytheoptimalratesgivenby:

(26)

Here

(27)

Notethatnoconstraintsfornonnegativityoftherates

are used here, which means that high rates are

assumed.As for theoptimal CCTmatrix : it canbe

foundbyminimizingthetargetfunction ,that is

actuallythedenominatorofthe in(26)aftersome

straightforwardmanipulations:

(28)


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Weshouldremindhere that is a functionof as

given in (20). Also the variances depend on , or

more specifically on . These variances are the

diagonalelementsofthesubband covariancematrix

intheC1C2C3imagedomain:

(29)

andcanalsobeexpressedusingthe matrixandthe

subband b covariance matrix in the RGB image

domain:

,T

Y YE Y Y

b b

RGB RGB RGB RGB

b b b

Y E Y bRGB RGB

b

(30)

accordingto:

(31)

Here is defined similarly to the

definitions in thebeginning of the section of . Also

denotesthe rowofthe matrixinvectorform.

Thusthetargetfunction canberewrittenas:

3 1_

1 0

213 _

1

( ) ( ) ,

.

bB

T

b bk

k b

bk bi

i ik

f m m G

w

k b kM

M

(32)

OptimalRateswithDownSampling

When considering potential downsampling of some

ofthecolorcomponents,therateconstraintbecomes(5)

and the Lagrangian that incorporates this constraint,

as well as constraints for the nonnegativity of the

subbandrates,is:

21 3

2

0 1

3 1 3 1

1 0 1 0

1{ }, , ,{ }

3

,

bk

BaR

bkbi bi b b k bk

b k

B B

i b bi bi bii b i b

L R G e

R R R

M

(33)

where are the Lagrange multipliers for the new

constraints.Theratesthatminimize(33)are:

3

1

3

1

2 2

2

3

1

1,

k k

j jj

bi

j jj

i b bi bk

i

Act Act

k k k

kk

RR

G

lna

GM

(34)

wherei

b Act with iAct defined in (7)while

andi

areasin(8).Asfor ,itisgivenby:

(35)

Perceptually Optimized Compression

Inthissectionwepresentageneralapproachtocolor

image compression using a subband transform with

perceptual optimization of the CCT and of the

subbandratesallocation.Thisapproachconsistsofthe

stagesdescribedinthebeginningofSectionObjective

RateDistortion theoryofsubband transform coders.

Thedifferenceshereisthatinthepreprocessingstage,

theperceptuallyoptimalCCT transform isapplied to

thecolorcomponentsandinthequantizationstagethe

perceptually optimal rates allocation is used. Wedemonstrate this approachboth for the DCT and the

DWT in the following subsections. Note that a

probabilitydistributionmodelcanbeusedfortheSBT

coefficients to improve the performance of the

algorithms withrespect toruntime and compression

quality [4]. For example, the Laplacian probability

modelcanbeassumedforDCTcoefficients[9].

DCTBasedCompressionAlgorithm

Since the DCT is a subband transform, the Rate

Distortion theory of Section The Perceptual RDModel canbe applied to it. To find the DCT visual

weights we use the HVS CSF (Contrast Sensitivity

Function)curvesfortheYCbCrcolorspacethatcanbe

found, forexample, in [20].Toconvert thecpd (cycle

perdegree)unitsof thesegraphs tospatialfrequency

unitsfortheDCT, theequationsproposed in [22]can

be used. We consider, for example,

512 512 images displayed as

onadisplaywithdotpitchof0.25mm.

Theviewingdistance isassumed tobe four times the

imageheight[12],i.e.,inthisexample50cm.Similarlywe can consider images displayed as

onabigscreenataviewingdistance

of100cm.

Thestagesoftheproposedalgorithmareasfollows:

1. FindtheoptimalCCT byminimizing(32).2. Apply the CCT to the RGB colorcomponentsoftheimagetoreceivethenewcolor

components , , .

3. Apply theDCTblock transform toeachcolorcomponent , .


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54

4. Calculate the optimal rates according to (34)substituting there the used CCT matrix and the

variancesoftheDCTsubbands.Tofindtheactive

subbands, the algorithm presented in [5] canbe

used.

5. QuantizetheDCTcoefficientsusingauniformscalar quantizer in each subband. The (optimal)

quantization steps are found using an iterative

algorithm[5].

6. Use postquantization coding similar to theone used inJPEG. Adaptive Huffman coding is

employed and the codes are sent with the image

data.Thisstage is losslessanddoesnotaffectthe

imagedistortion.

It is of interest to compare the performance of this

algorithm to the other DCTbased compressionalgorithms, such as the MSE optimized algorithm

proposed in [5] andJPEG. A comparison for several

imagesisgiveninTable1.Weconsiderheretheabove

algorithm with WMSE RD optimization of the rates

allocation and CCT, as well as another version that

usesoptimalrates,but in theYCbCrcolorspace.The

PSPNRmeasureusedhereis:

(36)

where for each color component is calculated

in the DWT domain in the YCbCr color space

accordingtothevisualweightssuggestedin[20].Then

theaveragePSPNRonthe3colorcomponentsistaken.

Based on our experience and results, this is a good

measureofsubjectiveimagequality.

Note that each image in the table wascompressedat

the same compression rate (given in the last column

fromtheleft)foreachofthealgorithms,buttherateis

not the same for different images. The reason is that

thethe

rate

was

chosen

to

achieve

the

same

objective

performance (PSNR) for the first algorithm (from the

left) to allow meaningful comparison of average

algorithmperformances.SeealsoTable2below.

TABLE1Perceptuallybasedresults(PSPNR)for(fromlefttoright):TheDCTbasedWMSEoptimizedalgorithmintheYCbCrdomain;Thesame

algorithmwithoptimalCCT;TheMSEoptimizedalgorithm;JPEG.Thecompressionrateforeachimageisshownintherightcolumn.

Image WMSEAlg.inthe

YCbCrdomain

WMSEAlg.inthe

optimaldomain

MSEAlg. JPEG Rate[bpp]

Lena 39.4 40.6 38.9 37.6 0.76

Peppers 39.6 39.6 38.1 36.6 0.81

Baboon 42.0 42.5 39.2 36.1 1.76

Cat 41.3 43.1 41.3 39.9 1.30

Landscape 42.5 42.5 40.5 38.0 1.85

House 39.8 40.3 39.2 38.1 0.54

JellyBeans 38.5 38.6 38.3 37.5 0.47

Fruits 41.0 42.3 40.4 38.9 0.71

Sails 41.0 42.9 39.7 37.6 1.84


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Monarch 39.8 40.2 38.7 37.5 1.03

Goldhill 42.9 43.4 41.9 40.6 2.17

Mean 40.7 41.5 39.7 38.0

TABLE2SameasTable1,butforPSNRinsteadofPSNR.NotethatoptimizationofPSPNR,asinducedbythehumanobserver,doesnot

necessarilymeanoptimizationofthearbitrarilyusedPSNR(seetext).

PSNR Image WMSEAlg.inthe

YCbCrdomain

WMSEAlg.inthe

optimaldomain

MSEAlg. JPEG Rate[bpp]

Lena 30.0 30.5 30.7 29.7 0.76

Peppers 30.0 30.1 30.5 29.3 0.81

Baboon 30.0 29.0 30.5 26.5 1.76

Cat 30.0 29.6 31.3 29.5 1.30

Landscape 30.0 30.1 30.3 25.9 1.85

House 30.0 30.2 30.3 29.5 0.54

JellyBeans 30.0 30.3 30.6 29.7 0.47

Fruits 30.0 29.8 30.6 30.6 0.71

Sails 30.0 29.7 30.6 28.9 1.84

Monarch 30.0 29.6 30.6 29.4 1.03

Goldhill 30.0 30.2 31.7 29.2 2.17

Mean 30.0 29.9 30.7 28.9

It can be concluded from the table that the WMSE

optimized algorithm with the optimal CCT achieves

thehighestPSPNR,which is1.8dBhigheronaverage

thanthePSPNRoftheMSEoptimizedalgorithmand

3.5dB above JPEG. The use of the optimal CCT in

WMSEsenseincreasestheperformancebyalmost1dB

(0.8dB) on average when perceptually optimal rates

areemployed.Anothercomparisonofinterestisofthe

standardorobjectivedistortionsofthealgorithm,i.e.,

the PSNR as presented in Table 2. As expected, the

MSEoptimizedalgorithmissuperiorhere,butwhatis

perhaps less intuitive is the fact that the use of the

optimal CCT slightly decreases the PSNR, indicating

thatPSNRandPSPNRaredifferentmeasures.Ascan

beseenintheexamplesofFigs.1 2below,thehuman

observerjudgement is closely related to the PSPNR,

not the PSNR. Despite this both WMSE algorithms

have MSE performance superior toJPEG with a gain


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56

of1.1dB in thePSNRwithoutusing theoptimalCCT

and slightly less (1dB) with the optimal CCT. We

conclude this section by presenting a visual

comparisonof thealgorithmsascanbeseen inFig.1

fortheLenaimageandinFig.2fortheBaboonimage.

Itcanbeseen that theWMSEalgorithmprovides the

bestresultsforbothimagesvisually,whiletheresults

of theMSEalgorithmareslightly lesspleasing to the

eye.YetbothalgorithmsaresuperiortoJPEG.

FIG.1COMPRESSIONRESULTSFORLENAAT0.72BPP.ORIGINALIMAGE(TOPLEFT);IMAGECOMPRESSEDBYTHEWMSE

OPTIMIZEDALGORITHM(TOPRIGHT,PSPNR=40.4DB);IMAGECOMPRESSEDBYJPEG(BOTTOMLEFT,PSPNR=37.7DB);IMAGE

COMPRESSEDBYTHEMSEOPTIMIZEDALGORITHM(BOTTOMRIGHT,PSPNR=39.3DB).ASEXPECTED,THEWMSEALGORITHM

OUTPERFORMSTHEOTHERMETHODS,ESPECIALLYINTHEMARKEDAREAS.

FIG.2COMPRESSIONRESULTSFORTHEBABOON(ZOOMEDIN)AT0.88BPP.ORIGINALIMAGE(TOPLEFT);IMAGECOMPRESSEDBY

THEWMSE

OPTIMIZED

ALGORITHM

(TOP

RIGHT,

PSPNR=36.9DB);

IMAGE

COMPRESSED

BY

JPEG

(BOTTOM

LEFT,

PSPNR=33.6DB);

IMAGECOMPRESSEDBYTHEMSEOPTIMIZEDALGORITHM(BOTTOMRIGHT,PSPNR=35.6DB).HEREAGAIN,THEWMSE

ALGORITHMOUTPERFORMSTHEOTHERMETHODS.


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57

DWTBasedCompressionAlgorithm

When the DWT is considered, there are quite a few

options for the wavelet filterbank tobe used for the

decomposition. We have chosen the Daubechies 9/7

filter

bank,

but

obviously

other

choices

can

be

consideredaswell.Notiling[13]isused.Thechoiceof

the visual weights is according to [20]. The stages of

theproposedalgorithmare:

1. FindtheoptimalCCT byminimizing(32).2. Apply the CCT to the RGB colorcomponentsoftheimagetoreceivethenewcolor

components , , .

3. ApplytheDWTtreedecompositionuptotherequired depth of the tree (3, 4, 5 or higher

according to imagesize) toeachcolorcomponent, .

4. Calculate the optimal rates according to (34)substituting there the used CCT matrix and the

variances, sample rates and energy gains of the

DWT subbands. The determination of the active

subbands is the same as for the DCTbased

algorithmoftheprevioussubsection.

5. Quantize the DWT coefficientsby a uniformquantizer with a central deadzone in each

subbandsimilartotheoneusedinJPEG2000PartI

[8].Useoptimalquantizationsteps.

6. Use thepostquantizationcodingof the EZWalgorithm[19]onthequantizedsubbandcoefficients.Thisstage is losslessand includesbit

plane coding using zero trees. The bit plane

coding is split into two passes (dominant and

subordinate) and a separate arithmetic coder is

employedforeachpass.

Itis interestingtocomparetheproposedalgorithmto

JPEG2000. We have considered the JPEG2000

implementationusingtheJasPersoftwarepackage[24]

andanotherversionofthe implementationwithfixed

visual

weighting

at

subband

level

using

the

CSF

weightsof [20].Thevisualresults for theLena image

canbeseeninFig.3.ThePSNRresultshereare29.5dB

for theproposedWMSEoptimizedalgorithm,28.6dB

for JPEG2000 (original JasPer implementation) and

28.5dB forJPEG2000 with CSF weights. We conclude

that the use of CSF weights, that affects the tier2

codingstageoftheJPEG2000algorithm,decreasesthe

PSNR,butslightlyimprovesthevisualperformance.

FIG.3COMPRESSIONRESULTSFORLENAAT0.52BPP.ORIGINALIMAGE(TOPLEFT);IMAGECOMPRESSEDBYTHEDWTBASED

WMSEOPTIMIZED

ALGORITHM

(TOP

RIGHT,

PSPNR=19.7DB);

IMAGE

COMPRESSED

BY

JPEG2000

(BOTTOM

LEFT,

PSPNR=19.1DB);

IMAGECOMPRESSEDBYJPEG2000WITHCSFWEIGHTS(BOTTOMRIGHT,PSPNR=19.2DB).

ALSOHERE,THEWMSEALGORITHMISSUPERIORTOTHEREST.


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58

Also the proposed algorithm produces an image that

ismuchmorepleasingtotheeyethanJPEG2000.

Similar results canbe seen in the comparison of the

proposed algorithm andJPEG2000 for other example

images inFigs.4,5and6.InFig.4the lossofspatial

details at high frequencies in the Landscape andHouse images as well as the introduction of false

contoursintheJellyBeans imageshouldbenotedfor

JPEG2000. These effects can be seen in the marked

regions. In Fig. 5 once again the superiority of the

WMSEoptimizedalgorithmonJPEG2000canbeseen

in regions of high frequency details as demonstrated

bytheFruitsandCatimages.Forexample,thedetails

oftheappletextureintheFruitsimageandofthefur

andmustachetexturesintheCatimagearelost.Inthe

case of the Peppers image, the compression result of

JPEG2000 is less pleasing to the eye due to the color

artifacts introduced. Fig. 6 further demonstrates the

loss of spatial details in the case of JPEG2000

compression

of

the

Sails

image,

theblurring

of

the

contoursintheMonarchimageandbotheffectsinthe

Goldhill image (see the top marked area for the

blurred contour effect and, for example, thebottom

left marked area for the loss of spatial details).

Furthermore, color artifacts are introduced by

JPEG2000 in the Goldhill image as indicated, for

instance,inthemarkedareainthecenteroftheimage.

FIG.4LANDSCAPE,HOUSEANDJELLYBEANSIMAGES FROMLEFTTORIGHT:ORIGINAL,COMPRESSEDBYTHEWMSE

ALGORITHM(WMSEALG.)ANDCOMPRESSEDBYJPEG2000.

PSPNRFORTHELANDSCAPEIMAGE:17.1DB(WMSEALG.)AND15.7DB(JPEG2000).

PSNR:28.7DB(WMSEALG.)AND25.3DB(JPEG2000)AT0.97BPP.

PSPNRFORTHEHOUSEIMAGE:19.4DB(WMSEALG.)AND19.0DB(JPEG2000).


PSPNRFORTHEJELLYBEANSIMAGE:18.8DB(WMSEALG.)AND18.2DB(JPEG2000).

PSNR:32.3DB

(WMSE

ALG.)

AND

32.1DB

(JPEG2000)

AT

0.48BPP.

INTHEONLYCASEWHERETHEPSNROFJPEG2000ISHIGHERTHANTHENEWALGORITHM(HOUSE),THEPSPNRRESULT

SUPPORTSTHEFACTTHATVISUALLYTHENEWALGORITHMPROVIDESSUPERIORRESULTS.


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FIG.5FRUITS,CATANDPEPPERSIMAGES FROMLEFTTORIGHT:ORIGINAL,COMPRESSEDBYTHEWMSEALGORITHM(WMSE

ALG.)ANDCOMPRESSEDBYJPEG2000.

PSPNRFORTHEFRUITSIMAGE:22.2DB(WMSEALG.)AND21.1DB(JPEG2000).


PSPNRFORTHECATIMAGE:17.0DB(WMSEALG.)AND16.2DB(JPEG2000).


PSPNRFORTHEPEPPERSIMAGE:20.3DB(WMSEALG.)AND19.3DB(JPEG2000).


ASCANBESEEN,PSNRANDPSPNRRESULTSARESUPERIORFORTHENEWALGORITHMCOMPAREDTOJPEG2000.ITISALSO

OBSERVEDVISUALLY EXAMPLESAREINDICATEDINTHEMARKEDAREAS.


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FIG.6SAILS(ZOOMEDIN),MONARCH(ZOOMEDIN)ANDGOLDHILLIMAGES FROMLEFTTORIGHT:ORIGINAL,COMPRESSEDBYTHEWMSEALGORITHM(WMSEALG.)ANDCOMPRESSEDBYJPEG2000.

PSPNRFORTHESAILSIMAGE:19.2DB(WMSEALG.)AND18.0DB(JPEG2000).


PSPNRFORTHEMONARCHIMAGE:19.9DB(WMSEALG.)AND19.6DB(JPEG2000).


PSPNRFORTHEGOLDHILLIMAGE:17.6DB(WMSEALG.)AND16.6DB(JPEG2000).


ONCEAGAIN,THEPSNRANDPSPNRRESULTSARESUPERIORFORTHENEWALGORITHMCOMPAREDTOJPEG2000(SEE

EXAMPLESINDICATEDINTHEMARKEDAREAS).

Summary

A perceptuallybased model for the RateDistortion

functionofcolorsubbandcodershasbeenintroduced.

ThenewmodelapproximatestheWMSEdistortionof

an image inagivencolorspace,suchasYCbCr.This

distortion is then minimized to achieve perceptual

optimizationofthecompression.Whentheweightsin

the WMSE calculation are taken based on the CSF

curves of the human visual system, better

correspondence to image quality assessment by the

humaneyeisachieved.

Based on the RateDistortion model, new algorithms

havebeen introduced consisting of a preprocessing

stageusingaCCT,followedbyasubbandtransform,

quantizationstage,andlosslessentropyencoding.Thealgorithms are optimized with regard to the color

component transform in the preprocessing stage of

the compression as well as the quantization tables

usedinthecodingstage,bothwithrespecttoWMSE.

TheproposedDCTbasedalgorithmoutperformsboth

JPEG and the corresponding MSE optimized

algorithm. The DWTbased algorithm, as expected,

achieveshighercompressionratiosforthesameimage

quality than DCTbased techniques. We demonstrate

in this work that even when a relatively basic

algorithm is used in the postprocessing stage(introducedforEZW),superiorresultsareobtainedby


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the proposed algorithm when compared to other

DWTbasedalgorithms,suchasJPEG2000.Thisholds

even if the same WMSE distortion is used in both

JPEG2000andtheproposedalgorithm.Ourconclusion

is thatbased on the new perceptual RateDistortion

model,

optimized

compression

algorithms

can

be

designed with compression results superior to

presentlyavailabletechniques.

ACKNOWLEDGMENT

This research was supported in partby the HASSIP

Research Program HPRNCT200200285 of the

EuropeanCommission,andbytheOllendorffMinerva

Center.MinervaisfundedthroughtheBMBF.

REFERENCES

[1] Faugeras,O.D.DigitalColorImageProcessingWithintheFrameworkofaHumanVisualModel.IEEETrans.

on Acoustics Speech and Signal Processing ASSP27

(1979):380393.

[2] Fiorucci,F.,Baruffa,G.andFrescura,F. Objectiveandsubjective quality assessment between JPEG XR with

overlap and JPEG 2000.", Journal of Visual

Communication and Image Representation 23 (Aug.

2012):835844.

[3] Gershikov, E. and Porat, M. A RateDistortionApproachtoOptimalColorImageCompression.Proc.

ofEUSIPCO,Florence,Italy,2006.

[4] Gershikov, E. and Porat, M. Data Compression ofColor Images using a Probabilistic Linear Transform

Approach, inLNCS#4310, T. Boyanov,S.Dimova, K.

Georgiev, G. Nikolov (Eds.), 582589, SpringerVerlag

BerlinHeidelberg,2007.

[5] Gershikov, E. and Porat, M. On color transforms andbitallocationforoptimalsubbandimagecompression.

SignalProcessing:ImageCommunication22(2007):118.

[6] Gersho, A. and Gray, R. M. Vector Quantization andSignalCompression,Boston,MA:Kluwer,1992,ch.2.

[7] GoffmanVinopal, L. and Porat, M. Color imagecompression using intercolor correlation. Proc. of

IEEEICIP(2002): II353 II356.

[8] JPEG 2000 Part I: Final Draft International Standard(ISO/IECFDIS154441),NCITS ISO/IECJTC1/SC29/WG1

N1855(Aug.2000).

[9] Lam, E. Y. and Goodman, J. W. A mathematicalanalysis of the DCT coefficient distributions for

images. IEEE Trans. on Image Processing 9 (2000):

16611666.

[10]LimbJ.O.andRubinsteinC.B.StatisticalDependenceBetween Components of A Differentially Quantized

ColorSignal.IEEETrans.onCommunicationsCom20

(Oct.1971):890899.

[11]Mannos, J. and Sakrison, D. The effects of a visualfidelitycriterionoftheencodingofimages. IEEETrans.

onInformationTheory20(Jul.1974):525536.

[12]Ngan, K. N., Leong, K. S. and Singh, H. Adaptivecosine transform coding of images in perceptual

domain. IEEETrans.onAcoustics,Speech,andSignal

Processing37(Nov.1989):17431750.

[13]Rabbani, M. andJoshi, R. An overview of theJPEG2000 still image compression standard. Signal

Processing:ImageCommunication17(2002):348.

[14]Rao, K. R. and Yip, P. Discrete cosine transform:algorithms, advantages, applications. AcademicPress,

1990.

[15]Richter, T. and Simon, S. On theJPEG 2000 ultrafastmode.Proc.ofICIP(Oct.2012):25012504.

[16]Richter,T. SpatialConstantQuantizationinJPEGXRisNearly Optimal. Proc. Of the Data Compression

Conference(March2010):7988.

[17]Roterman,Y.andPorat,M.Color imagecodingusingregional

correlation

of

primary

colors.

Image

and

VisionComputing25(2007):637651.

[18]Satt, A. and Malah, D. Design of Uniform DFT FilterBanksOptimizedforSubbandCodingofSpeech,IEEE

Trans. on Acoustics, Speech and signal Processing 37

(Nov.1989):16721679.

[19]Shapiro, J. M. Embedded Image Coding UsingZerotrees of Wavelet Coefficients, IEEE Trans. on

SignalProcessing41(1993):33453462.


14/14


62

[20]Taubman,D.S.andMarcellin,M.W.JPEG2000:imagecompression, fundamentals, standards and practice,

KluwerAcademicPublishers,2002.

[21]Wallace, G. K. The JPEG still picture compressionstandard.IEEETrans.ConsumerElectronics 38 (1992):

xviiixxxiv.

[22]Wang, C. Y., Lee, S. M. and Chang, L. W. DesigningJPEG quantization tables based on human visual

system. Signal Processing: Image Communication 16

(2001):501506.

[23]Yamaguchi,H. EfficientEncoding ofColored PicturesinR,G,BComponents.Trans.onCommunications32

(Nov.1984):12011209.

[24]http://www.ece.uvic.ca/mdadams/jasperEvgeny

Gershikov received his

Ph.D. in Electrical Engineering from

Technion Israel Institute of

Technology in Haifa, Israel in 2011.

His areas of interest are Signal and

Image Processing, Color Processing

and Vision, Computer Vision,

Pattern Recognition and Speech

Recognition.

perceptually optimized coding of color images for band‐limited information networks

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