Pre-process for segmentation task with nonlinear diffusion filters

TL;DR

This paper introduces a new family of nonlinear diffusion filters designed to produce piecewise constant images for segmentation, ensuring well-posedness and edge preservation with low computational effort.

Contribution

A novel diffusivity function based on backward diffusion techniques is proposed, satisfying scale-space requirements and improving image segmentation preprocessing.

Findings

Filters produce piecewise constant images with preserved edges.

Theoretical framework ensures well-posedness of the diffusion process.

Code implementation is available at the provided GitHub repository.

Abstract

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.