A new probabilistic relaxation scheme and its application to edge detection

This paper presents a new scheme for probabilistic relaxation labeling that consists of an update function and a dictionary construction method. The nonlinear update function is derived from Markov random field theory and Bayes' formula. The method combines evidence from neighboring label assignments and eliminates label ambiguity efficiently. This result is important for a variety of image processing tasks, such as image restoration, edge enhancement, edge detection, pixel classification, and image segmentation. The authors successfully applied this method to edge detection. The relaxation step of the proposed edge-detection algorithm greatly reduces noise effects, gets better edge localization such as line ends and corners, and plays a crucial role in refining edge outputs. The experiments show that our algorithm converges quickly and is robust in noisy environments.