A Game Theoretic Approach to Learning Shape Categories and Contextual Similarities

The search of a model for representing and evaluating the similarities between shapes in a perceptually coherent way is still an open issue. One reason for this is that our perception of similarities is strongly influenced by the underlying category structure. In this paper we aim at jointly learning the categories from examples and the similarity measures related to them. There is a chicken and egg dilemma here: class knowledge is required to determine perceived similarities, while the similarities are needed to extract class knowledge in an unsupervised way. The problem is addressed through a game theoretic approach which allows us to compute 2D shape categories based on a skeletal representation. The approach provides us with both the cluster information needed to extract the categories, and the relevance information needed to compute the category model and, thus, the similarities. Experiments on a database of 1000 shapes showed that the approach outperform other clustering approaches that do not make use of the underlying contextual information and provides similarities comparable with a state-of-the-art label-propagation approach which, however, cannot extract categories.