Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed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.

Journal reference: J. Imaging 2021, 7, 196
DOI: 10.3390/jimaging7100196


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 a functional formulated in terms of the eigenvalues of the structure tensor of the differences between the processed gradient and the gradient of the original image. Example applications of linear and non-linear local contrast enhancement and colour image daltonisation illustrate the behaviour of the method.


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



Comments (1)

Comment 1
Received: 24 September 2021
Commenter: Ivar Farup
Commenter's Conflict of Interests: Author
Comment: The mathematical notation has been changed from component notation to vector notation throughout, and the result chapter has been extended with two more applications showing the suitability of the proposed method.
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