Surface-to-Surface Registration Using Level Sets Mads Fogtmann Hansen 1 , Søren Erbou 1 , Martin Vester-Christensen 1 , Rasmus Larsen 1 , Bjarne Ersbøll 1 , and Lars Bager Christensen 2 1 Technical University of Denmark 2 Danish Meat Research Institute Abstract. This paper presents a general approach for surface-to-surface registration (S2SR) with the Euclidean metric using signed distance maps. In addition, the method is symmetric such that the registration of a shape A to a shape B is identical to the registration of the shape B to the shape A. The S2SR problem can be approximated by the image registration (IR) problem of the signed distance maps (SDMs) of the surfaces con- fined to some narrow band. By shrinking the narrow bands around the zero level sets the solution to the IR problem converges towards the S2SR problem. It is our hypothesis that this approach is more robust and less prone to fall into local minima than ordinary surface-to-surface registration. The IR problem is solved using the inverse compositional algorithm. In this paper, a set of 40 pelvic bones of Duroc pigs are registered to each other w.r.t. the Euclidean transformation with both the S2SR approach and iterative closest point approach, and the results are com- pared. 1 Introduction This paper addresses the problem of shape registration or alignment which plays an essential role in shape analysis. Many registration procedures such as gener- alized Procrustes analysis [9,7] rely on a prior manual annotation of landmarks. The main drawback with these approaches is the reliance on manual annota- tion which becomes cumbersome and infeasible for larger 2Ddatasets and for 3D data. Methods for explicitly deriving landmarks form training curves/surfaces based on information theoretic theory has been published [6]. Unfortunately these often suffer form exceeding use of computation time. The iterative closest point (ICP) algorithm by Besl et al. [2] solves the problem of landmark dependence by iteratively updating the point correspondence after the closest point criterium. Since the introduction in 1992 many extensions and improvements of original ICP have been proposed in literature [8,11,10]. Most of these methods still require a good initial estimate in order not to converge to a local minimum. Furthermore, common for these methods are that they do not utilize the knowledge of the connectedness of the point cloud, which is available in many cases. B.K. Ersbøll and K.S. Pedersen (Eds.): SCIA 2007, LNCS 4522, pp. 780–788, 2007. c  Springer-Verlag Berlin Heidelberg 2007