Bayesian Level Set Method Based on Statistical Hypothesis Test and Estimation of Prior Probabilities for Image Segmentation

A level set method based on the Bayesian risk and estimation of prior probabilities is proposed for image segmentation. First, the Bayesian risk is formed by false-positive and false-negative fraction in a hypothesis test. Second, through minimizing the average risk of decision in favor of the hypotheses, the level set evolution functional is deduced for finding the boundaries of targets. Third, the concave property of Kullback-Leibler information number is used to estimate the prior probabilities of each phase. Fourth, to prevent the propagating curves from generating excessively irregular shapes and lots of small regions, curvature and gradient of edges in the image are integrated into the functional. Finally, the Euler-Lagrange formula is used to find the iterative level set equation from the derived functional. Compared with other level-set methods, the proposed approach relies on the optimum decision; thus the approach has more reliability in theory and practice. Experiments show that the proposed approach can accurately extract the complicated textured and medical images; moreover, the algorithm is extendable for multiphase segmentation.