Simultaneous nonrigid registration of multiple point sets and atlas construction

Abstract

Group-wise registration of a set of shapes represented by unlabeled point-sets is a challenging problem since, usually this involves solving for point correspondence in a nonrigid motion setting. In this paper, we propose a novel and robust algorithm that is capable of simultaneously computing the mean shape represented by a probability density function from multiple unlabeled point-sets and registering them non-rigidly to this emerging mean shape. This algorithm avoids the correspondence problem by minimizing the Jensen-Shannon (JS) divergence between the point sets. We motivate the use of the JS divergence by pointing out its close relationship to hypothesis testing. We derive the analytic gradient of the cost function in order to efficiently achieve the optimal solution. JS-divergence is symmetric with no bias toward any of the given shapes to be registered and whose mean is being sought. A by product of the registration process is a probabilistic atlas defined as the convex combination of the probability densities of the input point sets being aligned. Our algorithm can be especially useful for creating atlases of various shapes present in images as well as for simultaneously (rigidly or non-rigidly) registering 3D range data sets without having to establish any correspondence. We present experimental results on real and synthetic data. © 2008 IEEE.