title: Simultaneous nonrigid registration of multiple point sets and atlas construction.
abstract: Groupwise registration of a set of shapes represented by unlabeled point sets is a challenging problem since, usually, this involves solving for point correspondence in a nonrigid motion setting. In this paper, we propose a novel and robust algorithm that is capable of simultaneously computing the mean shape, represented by a probability density function, from multiple unlabeled point sets(represented by finite-mixture models), 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 of Gaussian densities. We motivate the use of the JS divergence by pointing out its close relationship to hypothesis testing. Essentially,minimizing the JS divergence is asymptotically equivalent to maximizing the likelihood ratio formed from a probability density of the pooled point sets and the product of the probability densities of the individual point sets. 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. A by-product of the registration process is a probabilistic atlas, which is defined as the convex combination of the probability densities of the input point sets being aligned. Our algorithm can be especially useful for creating atlases of various shapes present in images and for simultaneously (rigidly or nonrigidly)registering 3D range data sets (in vision and graphics applications), without having to establish any correspondence. We present experimental results on nonrigidly registering 2D and 3D real and synthetic data (point sets).
authors.affiliation: IBM Almaden Research Center, G1-003, 650 Harry Road, San Jose, CA 95120, USA. wangfe@us.ibm.com
authors.forename: Fei
authors.initials: F
authors.lastname: Wang
authors.forename: Baba C
authors.initials: BC
authors.lastname: Vemuri
authors.forename: Anand
authors.initials: A
authors.lastname: Rangarajan
authors.forename: Stephan J
authors.initials: SJ
authors.lastname: Eisenschenk
mesh_terms: D001185:Artificial Intelligence; D003628:Database Management Systems; D016208:Databases, Factual; D007089:Image Enhancement / Q000379:methods; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D016247:Information Storage and Retrieval / Q000379:methods*; D010363:Pattern Recognition, Automated / Q000379:methods*
references.citation: IEEE Trans Pattern Anal Mach Intell. 2004 Mar;26(3):372-83
references.pmid: 15376883
references.citation: Proc IEEE Int Conf Comput Vis. 2005 Oct;2:1246-1251
references.pmid: 19169422
references.citation: IEEE Trans Pattern Anal Mach Intell. 2004 Feb;26(2):160-72
references.pmid: 15376892
references.citation: IEEE Trans Med Imaging. 1999 Jul;18(7):570-9
references.pmid: 10504091
references.citation: Neuroimage. 2007 Jan 1;34(1):44-60
references.pmid: 17035049
references.citation: IEEE Trans Image Process. 2002;11(8):868-72
references.pmid: 18244681