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This paper introduces a novel family of nonlinear diffusion filters designed to generate piecewise constant images as a preprocessing step for segmentation. The key innovation lies in a new diffusivity function, derived from nonlinear diffusion techniques and related to backward diffusion, which aims to create images with homogenized grey intensity inside closed contours and sharp edges. The authors demonstrate that their filters satisfy well-posedness requirements in both semi-discrete and fully discrete scale-space settings, and validate their approach on real images, achieving piecewise constant images with low computational cost.
Achieve sharper image segmentations faster by preprocessing with a new family of nonlinear diffusion filters that create piecewise constant images with distinct, non-blurred edges.
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.