3-D Shape Matching and Non-Rigid Correspondence for Hippocampi Based on Markov Random Fields

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.