## 1. Introduction and Background

## 2. Variational Anisotropic Gradient-Domain Formulation

## 3. Results and Discussion

#### 3.1. Implementation

#### 3.2. The Diffusion Tensor

#### 3.3. Linear Local Contrast Enhancement

#### 3.4. Nonlinear Local Contrast Enhancement

#### 3.5. Colour Image Daltonisation

## 4. Conclusions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**The diffusion coefficients $2\partial {\psi}^{\prime}/\partial {\lambda}_{+}^{\prime}$ (

**left**) and $2\partial {\psi}^{\prime}/\partial {\lambda}_{-}^{\prime}$ (

**right**) for one of the test images.

**Figure 3.**Example results for linear contrast enhancement with $a=2$. Original images in the first column, Poisson solution in the second, ad hoc anisotropic diffusion with $K={10}^{-3}$ in the third, and the proposed variational with $K=3\times {10}^{-4}$ in the fourth. All images are available under the CC0 licence.

**Figure 4.**Example results for gamma contrast enhancement with $\gamma =0.7$. Original images in the first column, Poisson solution in the second, ad hoc anisotropic diffusion with $K={10}^{-3}$ in the third, and the proposed variational with $K=0.3\times {10}^{-4}$ in the fourth. All images are available under the CC0 licence.

**Figure 5.**Example of colour image Daltonisation by the proposed method. Colour images in the left column, and corresponding colour–vision–deficiency simulations in the right. Top to bottom: original image, simple global Daltonisation, ad hoc anisotropic gradient domain Daltonisation, and the proposed variational gradient-domain solution.

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