Non-uniformly lighted image enhancement exploiting the Atangana–Baleanu fractional integral and the Sobel filter

Improving the quality of non-uniformly lighted images is particularly hard because these images contain regions with different brightness, thus needing a different level of enhancement. Recently, this problem has been addressed by combining the input image with a new version where the input brightness is linearly up-scaled by a parameter, which is estimated without supervision by segmenting the image into dark and bright regions and comparing their brightness. This estimate represents a pitfall because it makes the algorithm performance dependent on the segmentation accuracy and cannot be applied to images whose bright regions are almost white. To overcome these issues, the present work introduces a new image-aware estimate of the brightness up-scaling parameter, which exploits edge information extracted by the Sobel filter and by the first derivative of the Atangana-Baleanu fractional integral. The joint use of integer- and fractional-order calculus proposed here represents the main contribution of this work and, as proved by the experiments, enables us to reach a good level of enhancement surpassing other cutting-edge techniques, particularly in terms of reduced artifact production.