A Feature Registration Framework using Mixture Models.pdf

A Feature Registration Framework using Mixture Models Haili Chui and Anand Rangarajan  Departments of Electrical Engineering and Diagnostic Radiology Yale University, New Haven, CT 06520, USA Abstract We formulate feature registration problems as maximum likelihood or Bayesian maximum a posteriori estimation problems using mixture models. An EM-like algorithm is proposed to jointly solve for the feature correspondences as well as the geometric transformations. A novel aspect of our approach is the embedding of the EM algorithm within a de- terministic annealing scheme in order to directly control the fuzziness of the correspondences. The resulting algorithm— termed mixture point matching (MPM)—can solve for both rigid and high dimensional (thin-plate spline-based) non- rigid transformations between point sets in the presence of noise and outliers. We demonstrate the algorithm’s perfor- mance on 2D and 3D data. 1 Introduction Feature-based registration problems frequently arise in the domains of computer vision and medical imaging. With the salient structures in two images represented as compact geometrical entities (e.g. points, curves, surfaces), we need to find the spatial transformation/mapping as well as the correspondence between them. Point features, represented basically by the point locations, are the simplest form of features. However, the resulting point matching problem can be quite difficult because of various factors. One common factor is noise arising from the processes of image acquisition and feature extraction. The presence of noise makes it difficult to decide on the extent to which the features should be exactly matched. Another factor is the existence of outliers—many point features may exist in one point-set that have no corresponding points (homologies) in the other and hence need to be rejected during the matching process. Finally, the geometric transformations may need to incorporate high dimensional non-rigid mappings in or- der to account