| Hopfield networks have been commonly used as an associative memory or to solve optimization problems. In the later, the optimization problem has to be formulated as an energy function. Through minimizing this function, an optimal solution is ultimately reflected in the outputs of the neurons. A number of applications have been solved by Hopfield networks with such an approach, Travelling Salesman Problem (TSP), stereo matching, object recognition, for instance.; In this thesis, the feature matching problem by Hopfield neural network method is studied and two new approaches are presented. It is assumed that the object in the image can be represented by the attributed graphs in terms of extracted features and the geometric relations between them. The first approach is proposed for matching articulated objects and handling homomorphic mappings between graphs, which is called Accumulative Hopfield Matching system (AHM). The basic idea is, the system first divides an input graph into many subgraphs, and a modified Hopfield network is then constructed to obtain the isomorphism between each subgraph and model graph, the final result is deduced by accumulating all the subgraph isomorphic mappings. The second approach addresses the problem of using Hopfield network to handle the correspondence problem under more general geometric transformations, such as affine and projective transformations. Based on the invariant properties of affine and projective transformations, the higher-order form of Hopfield networks can be constructed. By taking advantage of the neighborhood information in the data, the order of the network can be reduced such that a standard second-order Hopfield network can be employed to solve the feature matching problem under affine and projective transformations. This approach can find reliable feature correspondences of images with large displacements taken by an uncalibrated camera; thus it has great potentials in various applications, such as robot navigation, image registration, and object recognition. Moreover, the proposed AHM system can also be applied to handle the articulated object recognition problem under affine or projective transformation, with the proposed Hopfield models for affine or projective invariant matching. The experimental results and evaluation of the methods will be shown in great details. |
