基于PM模型的曲面去噪变分水平集方法

PM（perona-malik）模型是一种经典的非线性图像扩散模型，该模型能根据设定的阈值对图像光滑区域进行扩散，并能自适应地保持图像边缘。本文将曲面法矢量与一般灰度图像的强度进行类比，将经典的图像扩散的PM模型转化为曲面几何噪声处理的自适应扩散变分模型，在使曲面光滑的同时，能够保持曲面边缘。曲面采用隐函数的零水平集表达，能量泛函中的数据项用初始水平集函数的Heaviside函数与演化后水平集函数的Heaviside函数差的平方表达，能量泛函中的光滑项基于几何曲率定义。此外，在能量泛函中增加了水平集函数为符号距离函数的惩罚项，避免了水平集函数需要不断重新初始化的问题。数值实验验证了所提出模型的曲面噪声去除及曲面边缘保持效果。

A Variational Level Set Method for Surface Denoising Based on PM Model

PM(perona-malik)is a classical nonlinear image diffusion model with adaptive properties of image smoothing and edge preserving.It is transformed to geometric surface smoothing,edge preserving variational model using variational level set method based on the analogue of normal vector of surface and general image intensity in this paper.The energy functional includes three parts.The first part is a data term using the square of the difference between the Heaviside function of initial level set function and th...