Abstract
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 often 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 nonlinear local contrast enhancement and colour image Daltonisation illustrate the behaviour of the method.
Highlights
Introduction and BackgroundIn 2002, Fattal et al [1] introduced the method of gradient-domain high-dynamicrange compression
For the applications to linear and nonlinear local contrast enhancement and colour image Daltonisation, we show that the two approaches gives very similar results
In order to demonstrate the usefulness of the proposed method, we apply it to three example problems: linear local contrast enhancement, nonlinear local contrast enhancement, and colour image Daltonisation
Summary
In 2002, Fattal et al [1] introduced the method of gradient-domain high-dynamicrange compression. Imaging 2021, 7, 196 and the corresponding eigenvectors θ± of the structure tensor as a basis for constructing the diffusion equations In terms of these eigenvalues, an alternative to the colour total variation by Blomgren and Chan [5] can be obtained by the functional. For other application of Poission image editing, i.e., applications of Equation (2) where G = 0, extensions to anisotropic and edge-preserving methods have been obtained by ad hoc modifications of Equation (2) This has been done for e.g., colour gamut mapping [11], colour image demosaicing [12], colour-to-greyscale conversion [13], and colour image Daltonisation [10]. For the applications to linear and nonlinear local contrast enhancement and colour image Daltonisation, we show that the two approaches gives very similar results
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