Targeted Iterative Filtering

Freddie Åström; Michael Felsberg; George Baravdish; Claes Lundström

cs.CVAug 23, 2026

Targeted Iterative Filtering

Authors: Freddie Åström, Michael Felsberg, George Baravdish, Claes Lundström

Organizations: Computer Vision Laboratory, Linköping University, Sweden · Center for Medical Image Science and Visualization, Linköping University, Sweden · Department of Science and Technology, Linköping University, Sweden · Sectra AB, Sweden

Abstract

The assessment of image denoising results depends on the respective application area, i.e. image compression, still-image acquisition, and medical images require entirely different behavior of the applied denoising method. In this paper we propose a novel, nonlinear diffusion scheme that is derived from a linear diffusion process in a value space determined by the application. We show that application-driven linear diffusion in the transformed space compares favorably with existing nonlinear diffusion techniques.

Figures & tables

Figure 1: Example of mapping function

	$\sigma$	$\hat{\sigma}_{m}$	LD	PM	TF	AD
SSIM	5	51.19	0.89 $\pm$ 0.005	0.92 $\pm$ 0.004	0.93 $\pm$ 0.003	0.94 $\pm$ 0.003
	10	102.38	0.84 $\pm$ 0.004	0.87 $\pm$ 0.005	0.89 $\pm$ 0.005	0.87 $\pm$ 0.006
	15	153.56	0.82 $\pm$ 0.006	0.83 $\pm$ 0.005	0.86 $\pm$ 0.006	0.82 $\pm$ 0.005
PSNR	5	51.19	28.44 $\pm$ 0.37	30.82 $\pm$ 0.56	30.76 $\pm$ 0.51	32.18 $\pm$ 0.72
	10	102.38	25.92 $\pm$ 0.45	27.68 $\pm$ 0.49	28.13 $\pm$ 0.53	27.88 $\pm$ 0.49
	15	153.56	24.81 $\pm$ 0.54	25.74 $\pm$ 0.53	26.82 $\pm$ 0.59	25.38 $\pm$ 0.51

Table 1: SSIM and PSNR values.

\hat{\sigma}_{m}

was computed according to ( 13 ).

Panel of Figure 2 — Figure 2: Slice 250. Noise level $\sigma=5$ . Details best viewed on monitor

Panel of Figure 3 — Figure 3: Slice 350. Noise level $\sigma=10$ . Details best viewed on monitor

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Apr 23, 2026, cs.CVJ/K move · Enter open · S save

Pre-process for segmentation task with nonlinear diffusion filters

Javier Sanguino, Carlos Platero, Olga Velasco

Health Science Technology Group, Technical University of Madrid, Ronda de Valencia 3, 28012, Madrid, Spain.

Image Segmentation Diffusion Models

Open paper AskPDF arXiv

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.

Abstract

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