Fractional Calculus In Image Processing: A Review

TL;DR

This review paper discusses how fractional calculus, with its extra degree of freedom, has been successfully applied across various image processing tasks over the past decade.

Contribution

It provides a comprehensive overview of recent studies on fractional calculus applications in ten key image processing sub-fields.

Findings

Fractional derivatives improve image enhancement and denoising.

Fractional calculus enhances edge detection and segmentation.

Fractional methods are effective in image encryption and restoration.

Abstract

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.