Mathematical Models for Object Matching and Their Application to Computer Vision and Biomedical Imaging.

摘要

Object matching is an important problem and has extensive uses in computer vision and medical image analysis. Object matching aims at recovering an object's pose in a 2D input scene image. In this thesis, we propose several mathematical models to solve the object matching problem. Although the matching problem is usually modeled as NP-hard problems, our models are able to obtain approximately global minimum via different optimization techniques. We propose different mathematical models to handle objects with different representations, i.e., objects represented by shapes or by feature points.;On one hand, objects can be represented by their shapes (or contours). Object matching can therefore be solved as shape matching problems. We improve the classical Iterative Closest Point (ICP) method with a robust shape dissimilarity metric and an asymmetric shape representation which allows the objective function to be efficiently evaluated. Such efficiency enables using an approximately global optimizer. Compared with other ICP-based methods, our proposed method is able to generate matching results with smaller average L2 distances between corresponding points. On the other hand, objects can be represented by groups of feature points. We propose a novel locally affine invariant geometric constraint which results in a linear programming model for matching feature points that can be solved efficiently. We also propose a new matching framework supporting all geometric transformation models that can be expressed by convex functions with convex constraints. The final objective function can be efficiently optimized by convex optimization techniques.;Our methods can be applied to locate deformable objects in input scene images for computer vision applications. We also apply matching methods to segment and track polymerizing actin filaments in a time-lapse image sequence. We treat this problem as a tip matching problem and solve it by dynamic programming.