一种非线性扩散滤波器的设计方法及其应用

非线性滤波器在保留图像重要特征方面表现出良好的性能，这些非线性图像滤波大多源于求解初始值为输入图像的非线性扩散方程，设计合适的扩散系数可以控制扩散方程的扩散行为，使得在平滑图像的同时能够保留图像的重要特征信息，该文给出了一种非线性异性扩散滤波器的设计方法，通过引入图像特征来选取合适的局部坐标系，将整体坐标系中的扩散系数矩阵的设计问题转化为局部坐标系中沿各坐标方向的扩散系数的设计，这种设计方法简单，便于更好地理解扩散滤波器的扩散行为，具有更加明确的物理意义，实验结果说明了此方法的可行性，在图像的保边光滑处理方面具有明显的效果。

A Design Method for Nonlinear Diffusion Filter and Its Application

Nonlinear filters show good performance in preserving important features. These filters may boil down to solving nonlinear diffusion equations with initial values being input images. Designing appropriate diffusion coefficients can control the action of diffusion equations, so the important features of images can be preserved while the images are smoothing. In this paper, a design method for nonlinear diffusion filter is proposed. Choosing an appropriate coordinate by introducing image feature, we turn the design problem of diffusion matrix into the design of diffusion coefficients along local coordinates by a coordinate transform. This design method for the diffusion filter is simple, and helps us to understand the diffusion action of the diffusion filter and has obvious physical meaning. Some experimental results are given to show that this design method is feasible, and reaches an obvious effect in terms of edge-preserving image processing.