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 representa...

• Type: Conference
• Year: 2007
• Where: CVPR
• Authors: Pengdong Xiao, Nick Barnes, Tibério S. Caetano, Paulette Lieby
• Keywords: Computer Vision, CVPR 2007, Gaussian Curvature, Markov Random Field, Random Field Graph, Sample Instance Graph, Shape Matching