# Fractional Calculus In Image Processing: A Review

arXiv: https://arxiv.org/abs/1608.03240 · HTML: https://mlsanity.com/paper/1608.03240/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Aug 2016.

## Built on by (most cited first, 3 of 3)

- [KANtrol: A Physics-Informed Kolmogorov-Arnold Network Framework for Solving Multi-Dimensional and Fractional Optimal Control Problems](https://mlsanity.com/paper/2409.06649/) (2024)
- [A Fractional Variational Approach to Spectral Filtering Using the Fourier Transform](https://mlsanity.com/paper/2511.20675/) (2025)
- [Fractional-Order Adaptive Motion Magnification: Phase-Reliability Weighting for Noise-Constrained Video Amplification](https://mlsanity.com/paper/2609.04502/) (2026)

## Abstract (arXiv)

Over the last decade, it has been demonstrated that many systems in science and engineering can be modeled more accurately by fractional-order than integer-order derivatives, and many methods are developed to solve the problem of fractional systems. Due to the extra free parameter order, fractional-order based methods provide additional degree of freedom in optimization performance. Not surprisingly, many fractional-order based methods have been used in image processing field. Herein recent studies are reviewed in ten sub-fields, which include image enhancement, image denoising, image edge detection, image segmentation, image registration, image recognition, image fusion, image encryption, image compression and image restoration. In sum, it is well proved that as a fundamental mathematic tool, fractional-order derivative shows great success in image processing.