Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Variational Anisotropic Gradient-Domain Image Processing

Version 1 : Received: 27 August 2021 / Approved: 31 August 2021 / Online: 31 August 2021 (12:44:20 CEST)
Version 2 : Received: 23 September 2021 / Approved: 24 September 2021 / Online: 24 September 2021 (10:24:26 CEST)

A peer-reviewed article of this Preprint also exists.

Farup, I. Variational Anisotropic Gradient-Domain Image Processing. J. Imaging 2021, 7, 196. Farup, I. Variational Anisotropic Gradient-Domain Image Processing. J. Imaging 2021, 7, 196.


Gradient-domain image processing is a technique where, instead of operating directly on the image pixel values, the gradient of the image is computed and processed. The resulting image is obtained by reintegrating the processed gradient. This is normally done by solving the Poisson equation, most oftenly by means of a finite difference implementation of the gradient descent method. However, this technique in some cases lead to severe haloing artefacts in the resulting image. To deal with this, local or anisotropic diffusion has been added as an ad-hoc modification of the Poisson equation. In this paper, we show that a version of anisotropic gradient-domain image processing can result from a more general variational formulation through the minimisation of an action potential formulated in terms of the eigenvalues of the structure tensor of the differences between the processed gradient and the gradient of the original image. An example application of local contrast enhancement illustrates the behaviour of the method.


variational methods; anisotropic diffusion; gradient-domain image processing; local contrast enhancement


Computer Science and Mathematics, Signal Processing

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