In this thesis, we make several significant achievements towards defining a medial axis based shape descriptor which is compact, yet discriminative. First, we propose a novel medial axis spectral shape descriptor called the medial axis spectrum for a 2D shape, which applies spectral analysis directly to the medial axis of a 2D shape. We extend the Laplace-Beltrami operator onto the medial axis of a 2D shape, and take the solution to an extended Laplacian eigenvalue problem defined on this axis as the medial axis spectrum. The medial axis spectrum of a 2D shape is certainly more efficient to compute than spectral analysis of a 2D region, since the efficiency of solving the Laplace eigenvalue problem strongly depends on the domain dimension. We show that the medial axis spectrum is invariant under uniform scaling and isometry of the medial axis. It could also overcome the medial axis noise problem automatically, due to the incorporation of the hyperbolic distance metric. We also demonstrate that the medial axis spectrum inherits several advantages in terms of discriminating power over existing methods. Second, we further generalize the medial axis spectrum to the description of medial axes of 3D shapes, which we call the medial axis spectrum for a 3D shape. We develop a newly defined Minkowski-Euclidean area ratio inspired by the Minkowski inner product to characterize the geometry of the medial axis surface of a 3D mesh. We then generalize the Laplace-Beltrami operator to the medial axis surface, and take the solution to an extended Laplacian eigenvalue problem defined on the surface as the medial axis spectrum. As the 2D case, the medial axis spectrum of a 3D shape is invariant under rigid transformation and isometry of the medial axis, and is robust to shape boundary noise as shown by our experiments. The medial axis spectrum is finally used for 3D shape retrieval, and its superiority over previous work is shown by extensive comparisons. / published_or_final_version / Computer Science / Doctoral / Doctor of Philosophy

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A Distributed Constraint Satisfaction Problem (DisCSP) is a CSP which is divided into several inter-related complex local problems, each assigned to a different agent. Thus, each agent has knowledge of the variables and corresponding domains of its local problem together with the constraints relating its own variables (intra-agent constraints) and the constraints linking its local problem to other local problems (inter-agent constraints). DisCSPs have a variety of practical applications including, for example, meeting scheduling and sensor networks. Existing approaches to Distributed Constraint Satisfaction can be mainly classified into two families of algorithms: systematic search and local search. Systematic search algorithms are complete but may take exponential time. Local search algorithms often converge quicker to a solution for large problems but are incomplete. Problem solving could be improved through using hybrid algorithms combining the completeness of systematic search with the speed of local search. This thesis explores hybrid (systematic + local search) algorithms which cooperate to solve DisCSPs. Three new hybrid approaches which combine both systematic and local search for Distributed Constraint Satisfaction are presented: (i) DisHyb; (ii) Multi-Hyb and; (iii) Multi-HDCS. These approaches use distributed local search to gather information about difficult variables and best values in the problem. Distributed systematic search is run with a variable and value ordering determined by the knowledge learnt through local search. Two implementations of each of the three approaches are presented: (i) using penalties as the distributed local search strategy and; (ii) using breakout as the distributed local search strategy. The three approaches are evaluated on several problem classes. The empirical evaluation shows these distributed hybrid approaches to significantly outperform both systematic and local search DisCSP algorithms. DisHyb, Multi-Hyb and Multi-HDCS are shown to substantially speed-up distributed problem solving with distributed systematic search taking less time to run by using the information learnt by distributed local search. As a consequence, larger problems can now be solved in a more practical timeframe.

This thesis describes a new test generating algorithm, depth-first algorithm. This algorithm detects the reconvergent fanout. The controllability and observability measures are included in this algorithm to guide the forward and consistency drives. The major objective of this research is to develop a test vector generatiang algorithm, which is modified from D-algorithm, and to link this algorithm with SCIRTSS programs. This depth-first algorithm is more accurate and more efficient than D-algorithm. Serveral circuits are tested under DF3 and SCR3 and the results are listed in this paper.

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