A Multi-scale Generative Model for Animate Shapes and Parts

This paper presents a multi-scale generative model for representing animate shapes and extracting meaningful parts of objects. The model assumes that animate shapes (2D simple closed curves) are formed by a linear superposition of a number of shape bases. These shape bases resemble the multi-scale Gabor bases in image pyramid representation, are well localized in both spatial and frequency domains, and form an over-complete dictionary. This model is simpler than the popular Bspline representation since it does not engage a domain partition. Thus it eliminates the interference between adjacent B-spline bases, and becomes a true linear additive model. We pursue the bases by reconstructing the shape in a coarse-to-fine procedure through curve evolution. These shape bases are further organized in a tree-structure where the bases in each subtree sum up to an intuitive part of the object. To build probabilistic model for a class of objects, we propose a Markov random field model at each level of the tree representation to account for the spatial relationship between bases. Thus the final model integrates a Markov tree (generative) model over scales and a Markov random field over space. We adopt EM-type algorithm for learning the meaningful parts for a shape class, and show some results on shape synthesis.