The purpose of this paper is to recover dense correspondence between non-rigid shapes for anatomical objects, which is a key element of disease diagnosis and analysis. We proposed a shape matching framework based on Markov random fields to obtain non-rigid correspondence. We constructed an energy function by summing up two terms where one was a unary term and the other was a binary term. By using this formulation, shape matching was represented as an energy function minimisation problem. Loopy belief propagation (LBP) was then used to minimize the energy function. We adopted a new sparse update technique for LBP update to increase computational efficiency. At the same time, we also proposed to use a novel clamping technique, an expectation-maximization (EM) like approach, to enhance matching accuracy. Experiments with the hippocampal data from OASIS and PATH showed that the sparse update was 160 times faster than standard BP. By iteratively running the EM-like clamping procedure, we were able to obtain high quality non-rigid correspondence results to achieve 97% matching rate between two hippocampi. Our shape matching based approach overcomes the flip problem of first-order ellipsoid and does not assume pre-alignment unlike iterative closest point.

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.