🤖 AI Summary
This work addresses the challenge of obtaining piecewise-constant images with sharp edges and homogeneous interior intensities for image segmentation preprocessing. To this end, a novel method based on nonlinear diffusion filtering is proposed. By constructing a new family of diffusion coefficients that satisfy scale-space theory, the approach integrates a semi-implicit numerical scheme within a forward nonlinear diffusion framework. This formulation effectively preserves edges while homogenizing intensities within regions, and it guarantees well-posedness in both semi-discrete and fully discrete scale-space settings. Experimental results demonstrate that the method efficiently produces high-quality piecewise-constant images, significantly enhancing the performance of subsequent segmentation tasks.
📝 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.