An importance sampling approach to learning structural representations of shape

This paper addresses the problem of learning archetypal structural models from examples. This is done by providing a generative model for graphs where the distribution of observed nodes and edges is governed by a set of independent Bernoulli trials with parameters to be estimated, however, the correspondences between sample node and model nodes is not known and must be estimated from local structure. The parameters are estimated maximizing the likelihood of the observed graphs, marginalizing it over all possible node correspondences. This is done adopting an importance sampling approach to limit the exponential explosion of the set of correspondences. The approach is used to summarize the variation in two different structural abstraction of shape: Delaunay graph over a set of image features and shock graphs. The experiments show that the approach can be used to recognize structures belonging to a same class.