Learning class-specific affinities for image labelling

Spectral clustering and eigenvector-based methods have become increasingly popular in segmentation and recognition. Although the choice of the pairwise similarity metric (or affinities) greatly influences the quality of the results, this choice is typically specified outside the learning framework. In this paper, we present an algorithm to learn class-specific similarity functions. Mapping our problem in a Conditional Random Fields (CRF) framework enables us to pose the task of learning affinities as parameter learning in undirected graphical models. There are two significant advances over previous work. First, we learn the affinity between a pair of data-points as a function of a pairwise feature and (in contrast with previous approaches) the classes to which these two data-points were mapped, allowing us to work with a richer class of affinities. Second, our formulation provides a principled probabilistic interpretation for learning all of the parameters that define these affinities. Using ground truth segmentations and labellings for training, we learn the parameters with the greatest discriminative power (in an MLE sense) on the training data. We demonstrate the power of this learning algorithm in the setting of joint segmentation and recognition of object classes. Specifically, even with very simple appearance features, the proposed method achieves state-of-the-art performance on standard datasets.