Diffeomorphic point matching with applications in medical image analysis
Hongyu Guo, Anand Rangarajan · 2005
Diffeomorphic matching of unlabeled point sets is very important to non-rigid registration and many other applications but it has never been done before. It is a very challenging problem because we have to solve for the unknown correspondence between the two point sets. In this work we propose a joint clustering method to solve for a simultaneous estimation of the correspondence and the diffeomorphism in space. The cluster centers in each point set are always in correspondence by virtue of having the same index. During clustering, the cluster center counterparts in each point set are linked by a diffeomorphism and hence are forced to move in lock-step with one another. We devise an objective function and design an algorithm to find the minimizer of the objective function. We apply the algorithm to 2D and 3D shapes in medical imaging. We further propose to use a graph representation for the shape topology information. Results are given for prescribed topologies like chain topology, ring topology---which are very common in dealing with 2D contour shapes---and genus zero closed surface topology in 3D. We also investigate the topology problem in general and the learning of topology with a nearest neighbor graph.