Edge reinforcement using parametrized relaxation labeling

The problem of reinforcing local evidence of edges while suppressing unwanted information in noisy images is considered using a form of relaxation labeling. The methodology is based on parameterizing a continuous set of edge orientation labels using a single vector. A sigmoidal thresholding function similar to that used in artificial neural networks to bias neighborhood-influence and insure convergence to meaningful stable states is also utilized. A global optimization function is defined, and a decentralized parallel algorithm is derived that uses a steepest-gradient-descent approach to arrive at the optimal point on the functional surface, corresponding to desirable edge-reinforced and noise-suppressed labelings. In addition, a modification to the functional is presented which incorporates a thinning operation to insure that each edge is marked by only a single-pixel-wide response. Results from several image data sets indicate that the algorithm performs as well as or better than other relaxation labeling methods, and with improved computational efficiency