Anti-Faces for Detection Daniel Keren Rita Osadchy Haifa 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

Our Contribution 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.

Previous Work Eigenfaces and Eigenface Based Approaches. Neural Networks. Support Vector Machines. Fisher Linear Discriminant.

Eigenfaces for Recognition M. Turk and A. Pentland W B

Eigenface Based Approaches Probabilistic Visual Learning for Object Representation. B. Moghaddam and A. Pentland DIFS DFFS 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.

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

“Separating functioal” Training Support Vector Machines margin Support Vectors “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 Implicit set representation is more appropriate than an explicit one, for determining whether an element belongs to a set. The value of is a very simple indicator as to whether is close to the circle or not.

In general: characterize a set P by If is the class to be detected, the following should hold: P . should be simple to compute. should be small. If , there should be a low probability that, for every , .

However… this fails miserably: 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:

Orthogonal detectors for pocket calculator Many false alarms (and failure to detect true instance) when using these detectors

Our model for random smooth. 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 To Summarize: The functionals used for detection are linear: where d is a detector for a class  , I an input image, and n the image size. The functional F(I) must be large for random natural (smooth) images, and small for the images of . Otherwise, there are many false alarms.

Class Detection Using Smooth Detectors Boltzman distribution for smooth images: It follows that where are the DCT coefficients of d. since for to be large, d is smooth. should be concentrated in small

Class Detection Using Smooth Detectors 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.

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

Class Detection Using Smooth Detectors Trade-off between Smoothness of the detector. Orthogonality to the training set. Detection:

Schematic Description of the Detection “Direction of smoothness” Templates Natural images Eigenface method positive set Anti-face method positive set

False Alarms in Detection P - f.a. probability. P << 1. m independent detectors give The detectors are independent if are independent random variables. This holds iff

Finding the Detectors Choose an appropriate value M for 2 Minimize 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.

Finding the Detectors Using a binary search on , set it so that Incorporate the condition for independent detectors into the optimization scheme to find the other detectors.

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

Number of Eigenvalues for 90% Energy Detection Results Number of Eigenvalues for 90% Energy

Detection Results The results refer to “rotate + scale” case.

Fisher Linear Discriminant Results: “Esti” class Three 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: Model object and shadows. Detect objects and shadows in the logarithm of the image. Remove “shadow only” instances, using “shadow only” detectors.

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

Event Detection psychology psychological crocodile anthology “Anti-psychology”

Future Research Develop a general face detector. Develop a detector with non-convex positive set. Speech recognition.