Abstract.
Estimating a meaningful average or mean shape from a set of shapes represented by unlabeled point-sets is a challenging problem since, usually this involves solving for point correspondence under a non-rigid motion setting. In this paper, we propose a novel and robust algorithm that is capable of simultaneously computing the mean shape from multi- ple unlabeled point-sets (represented by finite mixtures) and registering them nonrigidly to this emerging mean shape. This algorithm avoids the correspondence problem by minimizing the Jensen-Shannon (JS) diver- gence between the point sets represented as finite mixtures. We derive the analytic gradient of the cost function namely, the JS-divergence, in order to effciently achieve the optimal solution. The cost function is fully sym- metric with no bias toward any of the given shapes to be registered and whose mean is being sought. Our algorithm can be especially useful for creating atlases of various shapes present in images as well as for simul- taneously (rigidly or non-rigidly) registering 3D range data sets without having to establish any correspondence. We present experimental results on non-rigidly registering 2D as well as 3D real data (point sets).