The great challenge in image registration and 3D object matching is to devise computationally efficient algorithms for aligning images so that their details overlap accurately and retrieving similar shapes from large databases of 3D models. The first problem addressed is this thesis is medical image registration, which we formulate as an optimization problem in the information-theoretic framework. We introduce a viable and practical image registration method by maximizing an entropic divergence measure using a modified simultaneous perturbation stochastic approximation algorithm. The feasibility of the proposed image registration approach is demonstrated through extensive experiments.
The rest of the thesis is devoted to a joint exploitation of geometry and topology of 3D objects for as parsimonious as possible representation of models and its subsequent application in 3D object representation, matching, and retrieval problems. More precisely, we introduce a skeletal graph for topological 3D shape representation using Morse theory. The proposed skeletonization algorithm encodes a 3D shape into a topological Reeb graph using a normalized mixture distance function. We also propose a novel graph
matching algorithm by comparing the relative shortest paths between the skeleton endpoints. Moreover, we describe a skeletal graph for 3D object matching and retrieval. This skeleton is constructed from the second eigenfunction of the Laplace-Beltrami operator defined on the surface of the 3D object. Using the generalized eigenvalue decomposition, a matrix computational framework based on the finite element method is presented to compute the spectrum of the Laplace-Beltrami operator. Illustrating experiments on two standard
3D shape benchmarks are provided to demonstrate the feasibility and the much improved performance of the proposed skeletal graphs as shape descriptors for 3D object matching and retrieval
