Simultaneous nonrigid registration of multiple point sets and atlas construction

Authors:
Fei Wang;Baba C. Vemuri;Anand Rangarajan;Ilona M. Schmalfuss;Stephan J. Eisenschenk
Affiliations:
Department of Computer & Information Sciences & Engr., University of Florida, Gainesville;Department of Computer & Information Sciences & Engr., University of Florida, Gainesville;Department of Computer & Information Sciences & Engr., University of Florida, Gainesville;Departments of Radiology, University of Florida, Gainesville;Department of Neurology, University of Florida, Gainesville
Venue:
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part III
Year:
2006

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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 multiple 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) divergence between the point sets represented as finite mixtures. We derive the analytic gradient of the cost function namely, the JS-divergence, in order to efficiently achieve the optimal solution. The cost function is fully symmetric 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 simultaneously (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).