Non-rigid motion behaviour learning : a spectral and graphical approach

In this thesis graph spectral methods and kernel methods are combined together for the tasks of rigid and non-rigid feature correspondence matching and consistent labelling. The thesis is divided into five chapters. In Chapter 1 we give a brief introduction and an outline of the thesis. In Chapter 2 we review the main techniques in the literature which are related to the developments in this thesis. Topics covered include data representation, the data classification methods, spectral graph matching, and the kernel methods. Chapter 3 aims at developing a new feature correspondence matching algorithm for rigid and articulated motion. We focus on the point features extracted from consecutive image frames. Specifically, a graph structure is used to represent the data-sets, and spectral graph theory is used for the correspondence localization. The novelty is that a kernel viewpoint is adopted in constructing the proximity matrix, and a consistent labelling process is incorporated into the matching process when the objects under investigation undergoes articulated motion. The algorithm is successfully applied to synthetic data-sets and a group of feature point-sets extracted from real world image sequences. Chapter 4 develops a new probabilistic relaxation labelling method, aimed at a broader range of applications for feature correspondence matching as well as data clustering. Here again the kernel methods are incorporated into the process, and the evidence combination and propagation steps are governed by a diffusion process defined on a support graph. The support graph is defined on the set of object-label assignments. The problem of consistent labelling thus becomes that of finding a state vector which gives the desired label probabilities. The newly developed algorithm is first applied to a toy labelling example which is taken from two classical relaxation labelling papers. Then the algorithm is applied to the problems of data classification and feature correspondence matching. In the feature correspondence matching application, the current label probabilities are regarded as noisy vector from the original correct one. Thus the process is viewed as running the diffusion process backwards in time. Experimental results on synthetic and real world data show encouraging results in both of the two cases. Finally, Chapter 5 concludes the thesis with a summary of the strengths and weaknesses of the thesis, and finally gives suggestions for future work.