Non-Rigid Point Matching: Algorithms, Extensions and Applications

Non-Rigid Point Matching: Algorithms, Extensions and Applications Haili Chui Yale University 2001 A new algorithm has been developed in this thesis for the non-rigid point matching problem. Designed as an integrated framework, the algorithm jointly estimates a one-to-one correspondence and a non-rigid transformation between two sets of points. The resulting algorithm is called “robust point matching (RPM) algorithm” because of its capability to tolerate noise and to reject possible outliers existed within the data points. The algorithm is built upon the heuristic of “fuzzy correspondence”, which allows for multiple partial correspondences between points. With the help of the deterministic annealing technique, this new heuristic enables the algorithm to overcome many local minima that can be encountered in the matching process. Devised as a general point matching framework, the algorithm can be easily extended to accommodate different speci£c requirements in many registration applications. Firstly, the modular design of the transformation module enables convenient incorporation of different non-rigid splines. Secondly, the point matching algorithm can be easily extended into a symmetric joint clustering-matching framework. It will be shown that by introducing a super point-set, the joint cluster-matching extension can be applied to estimate an average shape point-set from multiple point shape sets. The algorithm is applied to the registration of 3D brain anatomical structures. We proposed in this work a joint feature registration framework, which is mainly based on the joint clustering-matching extension of the robust point matching. The proposed framework provides an effective and uni£ed way to utilize spatial relationship existed between different brain structural features to improve the brain anatomical registration/normalization. For the £rst time, a carefully designed synthetic study is carried out to investigate and compare different anatomical features’ abilities to achieve such an registration/normalization. Other applications of the robust non-rigid point matching algorithm, such as key-frame animation and human face matching, will also be demonstrated in this work. Non-Rigid Point Matching: Algorithms, Extensions and Applications A Dissertation Presented to the Faculty of the Graduate School of Yale University in Candidacy for the Degree of Doctor of Philosophy by Haili Chui Dissertation Director: Anand Rangarajan January 2001 c © 2001 by Haili Chui ALL RIGHTS RESERVED.