Pre-process for segmentation task with nonlinear diffusion filters

Fuente: arXiv
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Hauptverfasser: Sanguino, Javier, Platero, Carlos, Velasco, Olga
Format: Preprint
Veröffentlicht: 2026
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author Sanguino, Javier
Platero, Carlos
Velasco, Olga
author_facet Sanguino, Javier
Platero, Carlos
Velasco, Olga
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2604_21422
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Pre-process for segmentation task with nonlinear diffusion filters
Sanguino, Javier
Platero, Carlos
Velasco, Olga
Computer Vision and Pattern Recognition
68U10 (Image processing), 68T45 (Machine vision and scene understanding), 65M06 (Finite difference methods)
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.
title Pre-process for segmentation task with nonlinear diffusion filters
topic Computer Vision and Pattern Recognition
68U10 (Image processing), 68T45 (Machine vision and scene understanding), 65M06 (Finite difference methods)
url https://arxiv.org/abs/2604.21422