隐式曲面上图像扩散的高阶模型

用零水平集函数表达3维曲面，应用曲面上图像梯度的切投影表达其内蕴梯度，把基于梯度的图像扩散变分模型从平面图像拓展到了隐式曲面上的图像处理。基于内蕴梯度的变分模型对曲面上的图像进行扩散的同时可有效地保持其边缘，但像平面图像扩散的变分模型一样会在本该光滑的区域产生明显的阶梯效应。为消除阶梯效应，引入内蕴散度建立了基于内蕴梯度和内蕴散度的隐式曲面上图像扩散的变分模型，并以TV (total variation) 模型、PM(peronamalik)模型为例对所提出的模型的有效性进行了数值验证，实验结果表明该类模型在保持图像边缘的同时可以有效地抑制阶梯效应。

High-order image diffusion model on implicit surfaces

The classic variational image diffusion models for planar image processing are extended to image diffusion on implicit surfaces using intrinsic image gradients defined based on implicit surfaces and expressed by zero level set functions, which can preserve edges effectively during image diffusion. But the models using only intrinsic gradients of image intensity show staircase effects beyond edges. In order to reduce the staircase effects, a general hybrid variational diffusion model is presented including regularizers based on intrinsic gradients and intrinsic divergence. The TV model and PM model are implemented as examples to validate the formulation in reducing staircase effects.