Fast B-ultrasound Image Segmentation Based on a Convex Relaxation Method
基于凸松弛方法的医学B超图像快速分割

One main drawback of active contour method applied to image segmentation is that the objective function is not convex. The solution of a non-convex minimization problem is prone to get stuck in a local minima, and some fast algorithms to convex optimization problems can not be used in a non-convex active contour model. Using a Bayesian risk method, this paper presents a new level set model for B-ultrasound image segmentation based on a Rayleigh distribution. The directly obtained model is not convex. However, we can get a new relaxed convex model by using a convex relaxation method. The relation between the directly obtained model and the relaxed convex model is given by a theorem. Then, a split Bregman algorithm is incorporated to propose a fast algorithm to solve the relaxed convex model. Compared with the traditional gradient descent method, the proposed method can not only get a global minima, but also is quite faster than gradient descent method.