An MRF and Gaussian Curvature Based Shape Representation for Shape Matching

Matching and registration of shapes is a key issue in Computer Vision, Pattern Recognition, and Medical Image Analysis. This paper presents a shape representation framework based on Gaussian curvature and Markov random fields (MRFs) for the purpose of shape matching. The method is based on a surface mesh model in R³, which is projected into a two-dimensional space and there modeled as an extended boundary closed Markov random field. The surface is homeomorphic to S². The MRF encodes in the nodes entropy features of the corresponding similarities based on Gaussian curvature, and in the edges the spatial consistency of the meshes. Correspondence between two surface meshes is then established by performing probabilistic inference on the MRF via Gibbs sampling. The technique combines both geometric, topological, and probabilistic information, which can be used to represent shapes in three dimensional space, and can be generalized to higher dimensional spaces. As a result, the representation can be used for shape matching, registration, and statistical shape analysis.