A graph theoretic approach to scene matching

The ability to match two scenes is a fundamental requirement in a variety of computer vision tasks. A graph theoretic approach to inexact scene matching is presented which is useful in dealing with problems due to imperfect image segmentation. A scene is described by a set of graphs, with nodes representing objects and arcs representing relationships between objects. Each node has a set of values representing the relations between pairs of objects, such as angle, adjacency, or distance. With this method of scene representation, the task in scene matching is to match two sets of graphs. Because of segmentation errors, variations in camera angle, illumination, and other conditions, an exact match between the sets of observed and stored graphs is usually not possible. In the developed approach, the problem is represented as an association graph, in which each node represents a possible mapping of an observed region to a stored object, and each arc represents the compatibility of two mappings. Nodes and arcs have weights indicating the merit or a region-object mapping and the degree of compatibility between two mappings. A match between the two graphs corresponds to a clique, or fully connected subgraph, in the association graph. The task is to find the clique that represents the best match. Fuzzy relaxation is used to update the node weights using the contextual information contained in the arcs and neighboring nodes. This simplifies the evaluation of cliques. A method of handling oversegmentation and undersegmentation problems is also presented. The approach is tested with a set of realistic images which exhibit many types of sementation errors

A general computational tool for structure synthesis

Synthesis of structures is a very difficult task even with only a small number of components that form a system; yet it is the catalyst of innovation. Molecular structures and nanostructures typically have a large number of similar components but different connections, which manifests a more challenging task for their synthesis. This thesis presents a novel method and its related algorithms and computer programs for the synthesis of structures. This novel method is based on several concepts: (1) the structure is represented by a graph and further by the adjacency matrix; and (2) instead of only exploiting the eigenvalue of the adjacency matrix, both the eigenvalue and the eigenvector are exploited; specifically the components of the eigenvector have been found very useful in algorithm development. This novel method is called the Eigensystem method. The complexity of the Eigensystem method is equal to that of the famous program called Nauty in the combinatorial world. However, the Eigensystem method can work for the weighted and both directed and undirected graph, while the Nauty program can only work for the non-weighted and both directed and undirected graph. The cause for this is the different philosophies underlying these two methods. The Nauty program is based on the recursive component decomposition strategy, which could involve some unmanageable complexities when dealing with the weighted graph, albeit no such an attempt has been reported in the literature. It is noted that in practical applications of structure synthesis, weighted graphs are more useful than non-weighted graphs for representing physical systems. Pivoted at the Eigensystem method, this thesis presents the algorithms and computer programs for the three fundamental problems in structure synthesis, namely the isomorphism/automorphism, the unique labeling, and the enumeration of the structures or graphs