Pre-process for segmentation task with nonlinear diffusion filters

arXiv cs.CV / 4/24/2026

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Key Points

The paper proposes using nonlinear diffusion filters as a preprocessing step to produce piecewise constant images for subsequent segmentation methods.
It introduces an intrinsic formulation of the nonlinear diffusion equation to derive design conditions and proposes a new family of diffusivities connected to backward diffusion.
The approach aims to partition images into closed contours with homogenized intensities inside regions while avoiding blurred edges.
The authors prove the filters meet key scale-space requirements (well-posedness in semi-discrete and full discrete settings) and show semi-implicit schemes solve a forward nonlinear diffusion problem for edge preservation.
Experiments on real images and released code demonstrate that, with appropriate diffusivity conditions and an early stopping criterion, the method achieves piecewise constant outputs with low computational cost.

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.