Group-wise point-set registration based on Rényi's Second Order Entropy

In this paper, we describe a set of robust algorithms for group-wise registration using both rigid and non-rigid transformations of multiple unlabelled point-sets with no bias toward a given set. These methods mitigate the need to establish a correspondence among the point-sets by representing them as probability density functions where the registration is treated as a multiple distribution alignment. Holder's and Jensen's inequalities provide a notion of similarity/distance among point-sets and Rényi's second order entropy yields a closed-form solution to the cost function and update equations. We also show that the methods can be improved by normalizing the entropy with a scale factor. These provide simple, fast and accurate algorithms to compute the spatial transformation function needed to register multiple point-sets. The algorithms are compared against two well-known methods for group-wise point-set registration. The results show an improvement in both accuracy and computational complexity.