Inexact Graph Matching Using Symbolic Constraints

Relational graphs are a fundamental type of scene representation for medium and high level computer vision tasks. They provide a generic way of encoding entities and relationships. The comparison and matching of such graphs is an important and challenging problem under the conditions of uncertainty and corruption which exist in most vision problems. In this thesis a method for matching relational graphs is developed which is based on symbolic constraints. The topology of the graph relations is used to calculate the consistency of a particular match using a Bayesian probability model of the processes at work in the matching process. The result is a global consistency criterion which measures the quality of match. A discrete relaxation technique is used to locate the optimal mapping between graphs using a MAP update rule. The technique is evaluated using both real-world image data and simulated graphs. Three methods of eliminating spurious elements from the graphs are also studied. The first method involves a constraint-filtering method which is applied after matching has taken place. The second method is an optimisation technique in which noise elements are identified and labelled during the matching process. The final method involves the dynamic reconfiguration of the graphs to remove noise elements during the matching phase. Detailed evaluations of these methods are performed on simulated data. A theoretical analysis of the criterion is carried out which allows prediction of the expectation value of the criterion at a given level of graph corruption. The performance of the symbolic criterion is compared to that of other alternatives reported in the literature. Finally the symbolic methods developed earlier are extended both to the use of probabilistic relaxation to match relational graphs, and to the matching of hierarchical graphs.