凸松弛Chan-Vese模型的快速分割方法

Fast Segmentation Methods for Convex Relaxation Chan-Vese Model

Chan-Vese模型是图像分割模型中效率较高的一种。传统的分割方法解决Chan-Vese模型出现了计算效率低、占用内存大、对于解决结构复杂的模型运行时间长等问题。针对上述问题,提出了FADMM和ACPDM两种新的快速分割方法。基于离散的二值标记函数,将两相分割模型转化为凸优化模型,结合FISTA算法和Chambolle-Pock算法对ADMM和对偶方法进行改进,采用变分的思想,通过引入辅助变量和拉格朗日乘子,交替迭代直至收敛到泛函的极值。实验结果表明,两种方法在保持图像区域边界的条件下,收敛速度可提高两倍以上。

The Chan-Vese model is one of the most efficient image segmentation models. Traditional segmentation methods solve the problems of the Chan-Vese model, such as low computational efficiency, large memory footprint, and long running time for solving complex models. To solve these problems, FADMM and ACPDM methods were proposed in this paper. Based on the discrete binary tag function, the two-phase segmentation model was transformed into a convex optimization model. Combing the FISTA algorithm and the Chambolle-Pock algorithm, the ADMM and the dual method were improved. By adopting the idea of variational, introducing the auxiliary variables and Lagrange multiplier, the iteration was alternated until it converged to the functional extremum. The experimental results show that the convergence rate of the two methods can be increased by more than two times under the condition of maintaining the boundary of the image region.