用非线性扩散滤波预处理图像，让分割更准且边缘清晰。
Pre-process for segmentation task with nonlinear diffusion filters
- 提出新型扩散系数，基于反向扩散机制增强边缘保持。
- 实现分段常数图像，计算量低且边缘无模糊。
- 适合需要高精度边缘的医学或工业图像分割任务。
本文研究使用非线性扩散滤波作为图像分割前的预处理步骤，以生成分段常数图像。首先，给出非线性扩散方程的内在形式化表达，确立滤波器设计条件。基于此理论框架，提出一类新的扩散系数，源自非线性扩散技术并关联于反向扩散，旨在生成闭合轮廓、内部灰度均匀且边缘无模糊的图像。证明所提滤波器满足半离散与全离散尺度空间的适定性要求。通过半隐式格式求解正向非线性扩散方程，实现边缘保持过程。在扩散系数设定条件及扩散时间停止准则下，可高效获得分段常数图像。最后，在真实图像上测试，验证了所提扩散函数的有效性。代码已开源：https://github.com/cplatero/NonlinearDiffusion。
原文摘要 · Abstract (English)
This paper deals with the case of using nonlinear diffusion filters to obtain piecewise constant images as a previous process for segmentation techniques. We first show an intrinsic formulation for the nonlinear diffusion equation to provide some design conditions on the diffusion filters. According to this theoretical framework, we propose a new family of diffusivities; they are obtained from nonlinear diffusion techniques and are related with backward diffusion. Their goal is to split the image in closed contours with a homogenized grey intensity inside and with no blurred edges. We also prove that our filters satisfy the well-posedness semi-discrete and full discrete scale-space requirements. This shows that by using semi-implicit schemes, a forward nonlinear diffusion equation is solved, instead of a backward nonlinear diffusion equation, connecting with an edge-preserving process. Under the conditions established for the diffusivity and using a stopping criterion for the diffusion time, we get piecewise constant images with a low computational effort. Finally, we test our filter with real images and we illustrate the effects of our diffusivity function as a method to get piecewise constant images. The code is available at https://github.com/cplatero/NonlinearDiffusion.
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