Using Image Priors in Maximum Margin Classifiers Tali Brayer Margarita Osadchy Daniel Keren

Object Detection Problem: Locate instances of object category in a given image. Asymmetric classification problem! BackgroundObject (Category) Very largeRelatively small Complex (thousands of categories) Simple (single category) Large prior to appear in an image Small prior Easy to collect (not easy to learn from examples) Hard to collect

All images Intuition  Denote H to be the acceptance region of a classifier. We propose to minimize Pr(All images) ( Pr(bkg)) in H except for the object samples. Background Object class All images Background We have a prior on the distribution of all natural images

Other work: Combine small labeled training set with large unlabeled set – semi-supervised learning: EM with generative mixture models, Fisher kernel,self-training, co-training, transductive SVM, and graph-based methods… All good for the symmetric case, but We have more information: marginal background

Image smoothness measure Lower probability Distribution of Natural Images – “Boltzmann-like” In frequency domain:

Linear SVM Maximal margin Enough training data Class 1 Class 2 Not Enough training data

Linear SVM Class 1 Class 2

MM classifier with Prior Class 1 Class 2

Minimize the probability of natural images over H After some manipulations it reduces to Q

Random w with unit norm and random b from [-0.5, 0.5] % of images that wx+b>0 Relation between the number of natural random images in the positive half-space and the integral

Training Algorithm Probability constraint: ( δ→0 )

Convex Constraint convex

Results Tested categories: cars (side view), faces. Training: 5/10/20/60/(all available data) object’s images. All available background images. Test: Face set: 472 faces, 23,573 bkg. Images Cars test: 299 cars, 10,111 bkg. images Ran 50 trials for each set with different random choices of training data. Weighted SVM was used to deal with the asymmetry in class sizes. UIUC CBCL

Average recognition rate(%): Faces 51060all Weighted Linear SVM Weighted Kernel SVM MM_prior Linear MM_prior Kernel

Average recognition rate(%): Cars 51060all Weighted Linear SVM Weighted Kernel SVM MM_prior Linear MM_prior Kernel

Future Work Video. Explore additional and more robust features. Refining the priors (using background examples). Kernelization.