Targeted Iterative Filtering

Abstract

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.

Mapping-Based Image Diffusion

“…In our previous work [4] we proposed to filter certain value ranges of the image data, i.e., an image value range adaptive filter. In a related work, [5], we interpret the image data as observations from a stochastic process and use an oversegmentation of the input image to define the mapping function.…”

“…The basic approach is to describe each locally homogeneous region using first and second statistical moments to drive a nonlinear filtering process. In this work we combine the mapping function [4,5] and the tensor-based method [2], leading to novel results.…”

“…Application areas where a mapping function has shown beneficial are visualization of medical images [4] and colour-image denoising [5]. In the present work, we further study this approach by considering a wide range of applications: denoising overexposed images, targeted filtering and denoising of natural images.…”

“…An alternative to using the negative exponential function as the diffusivity function is to let the problem define which edge-stopping function is suitable. In the work on targeted iterative filtering [4] we let the mapping be defined by a user selected sigmoidal function, that compresses the value range of 12-bit image data for the purpose of medical visualization. The regularization term introduced in [4] is defined as…”

“…Depending on the definition of m the function can be understood as the diffusivity function g in (11). Note that the PDE (13) is equivalent to the formulation in [4] due to the novel Lemma 2 in Section 4.2.…”