Entropy-Based Particle Systems for Shape Correspondence

This paper presents a new method for constructing statistical representations of ensembles of similar shapes. The proposed method relies on an optimal distribution of a large set of surface point correspondences, rather than the manipulation of a specific surface parameterization. The optimal configuration is defined as one in which the entropy or information content of each shape is balanced against the entropy of the ensemble of shapes. The correspondences are modeled as sets of dynamic particles that are manipulated using a gradient descent on the entropies of the shapes and the ensemble, but constrained to lie on a set of implicit surfaces. The proposed, particle-based method for finding correspondences requires very little preprocessing of data or parameter tuning, and therefore makes the problem of shape analysis more practical for a wider range of problems. This paper presents the formulation and several synthetic and real shape examples in two and three dimensions.