基于凸松弛方法的医学 B 超图像快速分割

利用活动轮廓线方法进行图像分割的一个重要缺陷是目标函数是非凸的, 这不仅使得分割结果容易陷于局部极小, 而且还使得一些快速算法无法开展.本文首先从贝叶斯风险估计的方法出发,针对B超幅度图像, 给出一种基于Rayleigh分布的活动轮廓线模型. 然后结合凸松弛的方法,得到一个新的放松的凸模型.原有模型和放松后模型的关系可由定理1给出. 最后结合分裂Bregman算法, 给出基于B超分割模型的快速算法.与传统梯度下降法相比较,本文提出的算法不仅能得到全局最优解,而且在算法收敛速度上也 大大优于梯度下降法.

Fast B-ultrasound Image Segmentation Based on a Convex Relaxation Method

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.