两种保持符号距离函数的水平集分割方法

Two algorithms for level set method preserving signed distance functions

Chan-Vese模型在图像分割领域正被广泛应用。然而,传统的水平集方法存在两个重要的数值问题:水平集函数不能隐式地保持为符号距离函数;由于采用梯度降方法求解使水平集演化速度缓慢。针对该问题提出两种快速分割方法加快演化速度:对偶方法和分裂Bregman方法。为了让水平集保持符号距离函数特性,利用投影方法加以约束,并采用增广Lagrangian方法加快收敛速度。实验结果表明,提出的两种快速分割方法比传统的梯度降方法分割效果好、计算效率高。

The well-known Chan-Vese model has been widely used in image segmentation.However,the original model is limited by two important numerical issues.Firstly,the level set method does not implicitly preserve the level set function as a signed distance function.Secondly,the level set method is slow because of the gradient descent equation.In this paper,two fast algorithms,a dual method and a split Bregman method,were proposed to improve the computation efficiency.In order to force the level set function to be a signed distance function during evolution,a projection approach was proposed to solve the constraint,and then the augmented Lagrangian method was used to speed up the convergence rate.The experimental results demonstrate that the proposed methods not only have better performance,but also are more efficient than the gradient descent method.