Anti-Faces for Detection

Daniel Keren Rita OsadchyHaifa University

Craig Gotsman Technion

*

* Journal Version:

http://www.cs.technion.ac.il/~gotsman/AmendedPubl/Anti-Faces/anti-faces-pami.pdf

Problem Definition

Given a set T of training images from an object class , locate all instances of any member of in test image P.

Images from training set Test image

• Simple detection process (inner product). Can be implemented by convolution.

• Very fast: For an image of N pixels, usually requires operations, where

• Implicit representation.

• Uses natural image statistics.

• Simple independent detectors.

Our Contribution

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Previous Work

• Eigenfaces and Eigenface Based Approaches.

• Neural Networks.

• Support Vector Machines.

• Fisher Linear Discriminant.

Eigenfaces for RecognitionM. Turk and A. Pentland

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• Probabilistic Visual Learning for Object Representation. B. Moghaddam and A. Pentland

Eigenface Based Approaches

DIFS

DFFS

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F x

• Visual Learning Recognition of 3-D from Appearance. H. Murase and S. Nayar

Neural Networks for Face Detection

• Neural Network Based Face Detection.

H. Rowly, S. Baluja, and T. Kanade

• Rotation Invariant Neural Network Based Face Detection.

H. Rowly, S. Baluja, and T. Kanade

Training Support Vector Machines

• Training Support Vector Machines: an Application to Face Detection. E. Osuna, R. Freund, and F. Girosi

• Training Support Vector Machines for 3-D Object Recognition.

M. Pontil and A. Verri

• A General Framework for Object Detection.C.P. Papageorgiou, M. Oren, and T. Poggio

Training Support Vector Machines

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Support Vectors

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ii ),(sgn)(

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)||||exp(),(2

ixx

ixxK

“Separating functioal”

Fisher Linear Discriminant

• Eigenfaces vs. Fisherfaces: Recognition Using Class Specific Linear Projection. P. N.

Belhumeur, P. Hespanha, and D. J. Kriegman

Drawbacks of the Described Methods• Eigenface based methods:

– Very high dimension of face-space is needed.– Distance to face-space is a weak discriminator

between class images and non-class natural images.

• Neural networks, SVM:– Long learning time. – Strong training data dependency.– Many operations on input image are required.

• Fisher Linear Discriminant :– Too simple.

• Implicit set representation is more appropriate than an explicit one, for determining whether an element belongs to a set.

Implicit Set Representation

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00 , yx

The value of is a very simple indicator as to

whether is close to the circle or not.

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),(00

yx

In general: characterize a set P by

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xfxfxP

if should be simple to compute.

n should be small.

If , there should be a low probability that,

iii

yf |)(|for every ,

.

If is the class to be detected, the following should hold:

.

P

y

Implicit Set Representation

The natural extension of this idea to detection is:

Find functionals which attain a small value on the object class , and use them for detection. The first guess: inner product with vectors orthogonal to ‘s elements. So, iff ,… .

However… this fails miserably:

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dI |),(|

Orthogonal detectors for pocket calculator

Many false alarms (and failure to detect true instance) when using these detectors

Implicit Set Representation

Conclusion: It’s not enough for the detectors to attain small values on the object class, they also have to attain larger values on “random” images.

Our model for random smooth.

Implicit Approach for Detection

where d is a detector for a class , I an input image, and n the image size.

nRdIdIIF , ,

• The functionals used for detection are linear:

• The functional F(I) must be large for random natural (smooth) images, and small for the images of . Otherwise, there are many false alarms.

To Summarize:

Class Detection Using Smooth Detectors

• Boltzman distribution for smooth images:

eIP )( dxdyx y

II )( 22

)0,0(),( 22

22

2

3

)(

),(~]),[(

ji ji

jidIdE

where ),(~ jid are the DCT coefficients of d.

It follows that

,1),(~2 jidsince ]),[( 2IdEfor to be large,

),(~ jid should be concentrated in small ji, d is smooth.

• The average response of a smooth detector on a smooth image is large.

• This relation was checked on 6,500 different detectors, each one on 14,440 natural images.

Class Detection Using Smooth Detectors

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.080

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Relationship between theoretical and empirical expectation of squared inner product with detector d

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)0,0(),( 2

3

)(

),(~

22

2

ji ji

jid

Class Detection Using Smooth Detectors

• Trade-off between – Smoothness of the detector.– Orthogonality to the training set.

• Detection:

otherwize

, if

I

IdI

Schematic Description of the Detection

Templates

Natural images

Eigenface method positive set

Anti-face method positive set

“Direction of smoothness”

Schematic Description of the Detection

False Alarms in Detection

• P - f.a. probability. P << 1.

m independent detectors give m

PPP ...21

• The detectors are independent if

02

3

)(

),(~),(~

22

21 ji

jidjid

)0,0(),( ji

21

, , , dIIdII 2

,1

dd

are independent random variables. This holds iff

Finding the Detectors

1 Choose an appropriate value M for It should be substantially smaller than the absolute

value of the inner product of two “random images”.

2 Minimize

The optimization is performed in DCT domain, and the inverse DCT transform of the optimum is the desired detector.

tdTt

,max 1

11

,max dStdTt

),(~)()( where2

1

22

1 jidjidS)0,0(),( ji

Finding the Detectors

3 Using a binary search on , set it so that

4 Incorporate the condition for independent detectors into the optimization scheme to find the other detectors.

MtdTt

,max1

Three of the “Esti” images

The first four “anti-Esti” detectors

Detection result: all ten

“Esti” instances were located, without false

alarms

Eigenface method with the subspace of dimension 100

Detection Results

Number of Eigenvalues for 90% Energy

rotation rotation+ scale

linear

Anti-faces(number ofdetectors)

3 4 4

Eigenfaces(face-spacedimension)

12 74 145

rotation rotation+scale linear

13 38 68

Detection ResultsNumber ofdetectors

Numberof F. A.

Probabilityof F.A.

1 4892 0.034

2 211 0.0015

3 3 0.00002

4 0 0.0

The results refer to “rotate + scale” case.

Fisher Linear Discriminant Results:

“Esti” classThree random image sets

(A) (B)

(C)

(A) and (B) Anti-Faces with 8 detectors.

(C) Eigenface method with the subspace of dimension 8. Eigenface method requires the subspace of dimension 30 for correct detection.

Detection of 3D objects from the COIL database

Detection of COIL objects on arbitrary background

Detection Under Varying Illumination:

Detect objects and shadows in the logarithm of the image.

Model object and shadows.

Remove “shadow only” instances, using “shadow only” detectors.

Osadchy, Keren: “Detection Under Varying Illumination and Pose”, ICCV 2001.

psychology psychological crocodile

anthology “Anti-psychology”

Event Detection

Future Research

• Develop a general face detector.

• Develop a detector with non-convex positive set.

• Speech recognition.