模糊分段光滑图像分割模型及其快速算法

Fuzzy piecewise smooth image segmentation model and a fast algorithm

灰度分布不均图像是图像分割中一个难点,为此提出一种模糊分段光滑(FPS)图像分割模型。借鉴分段光滑Mumford-Shah(MS)模型与模糊聚类思想,新模型通过两个定义在图像域的光滑函数描述区域特征,并利用模糊隶属度函数代替MS模型中的特征函数。同时,边界检测算子的引入能够有效保护图像中的边界信息。数值求解采用分裂Bregman方法与Gauss-Seidel迭代相结合的快速算法。对合成图像以及真实图像分割实验表明,本文算法能够有效分割灰度分布不均图像,同时具有较高的计算效率。

A fuzzy piecewise smooth（FPS） model is proposed aiming at the intensity-inhomogeneous image segmentation.Motivated by piecewise smooth Munford-Shah（MS） model and fuzzy clustering,two smooth functions were used to represent the region characteristics respectively and a fuzzy membership function was adopted to replace the hard membership function of MS model.An edge detection operator was also incorporated into the minimization ernergy function.The new energy is convex for the membership function,and the final segmentation does not depend on the initial contour.For numerical computation,a fast algorithm based on split Bregman method and Gauss-Seidel iteration was employed.Experimental results for synthetic and real images show desirable performance of the proposed method.