Density Driven Diffusion

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 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.…”

“…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.…”

“…We define the tensor W and the mapping in functional (28) to describe isotropic diffusion (ISO), isotropic diffusion with a mapping function (ISOm) [5], total variation (TV) [50], total variation with a mapping function (TVm), see (52), gradient energy tensor total variation (GETV) [2] and GETV with a mapping function (GETVm), see (65). The definitions of these methods are outlined in Table 2.…”

“…The introduction of a mapping into the diffusion framework was first presented in [5]. In this work we extend the initial formulation to include a tensor component, this is enabled by the functional in Theorem 1.…”