隐式曲面上两相图像分割的变分水平集方法

在平面图像分割的Chan-Vese模型基础上，提出隐式曲面上两相图像分割模型。用静态水平集函数的零水平集表达图像所在的闭合曲面，用另一动态水平集函数的零水平集与静态水平集函数零水平集的交线表达静态曲面上图像分割的动态轮廓线。所研究模型的能量泛函的数据项即为曲面上两分割区域的图像强度与对应区域平均图像强度的差的平方，其轮廓线长度项为两水平集函数的零水平集交线的长度。为避免动态水平集函数的重新初始化，在能量泛函中引入水平集函数为符号距离函数的约束惩罚项。通过变分方法得到图像分割空间轮廓线演化的梯度降方程。通过显式差分格式对演化方程进行离散。实验结果表明，该模型能有效实现复杂封闭曲面上图像的两相分割。

A Variational Level Set Method for Image Segmentation on Implicit Surfaces

The classic Chan-Vese model for two-phases segmentation of planar images is extended to image segmentation on implicit surfaces. The zero level set of a static level set function is used to express the surface on which images to be segmented are defined. Its intersection with another zero level set of a dynamic level set function is used to express spatial active contours for image segmentation. The novel energy functional includes three parts, the first one is the sum of square of the difference between pixel intensity and mean values in two regions on the surface. The second one is the length of spatial contour, and the third one is a penalty term to enforce the dynamic level set function to be a signed distance function. The evolution equation of the dynamic level set function is obtained using variation technique and is discretized with a simple explicit finite difference method. Experimental results validate the capacity of the proposed model in two phase image segmentation on implicit surfaces.