Fractional Calculus in Image Processing: A Review

• Published in: Fractional calculus & applied analysis Vol. 19; no. 5; pp. 1222 - 1249
• Main Authors: Yang, Qi, Chen, Dali, Zhao, Tiebiao, Chen, YangQuan
• Format: Journal Article
• Language: English
• Published: Warsaw Versita 01.10.2016; De Gruyter; Nature Publishing Group
• Subjects: 34K37; 35R11; Abstract Harmonic Analysis; Analysis; Calculus; Computer vision; Derivatives; Edge detection; Fractional calculus; fractional-order derivative; Functional Analysis; Image compression; Image detection; Image enhancement; Image processing; Image registration; Image restoration; Image segmentation; Integral Transforms; Mathematical analysis; Mathematical models; Mathematics; Object recognition; Operational Calculus; Optimization; Primary 26A33; Secondary 34A08; Survey Paper; fractional-order derivative; image processing; fractional calculus; Primary 26A33; 35R11; 34K37; Secondary 34A08
• ISSN: 1311-0454; 1314-2224
• DOI: 10.1515/fca-2016-0063

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 a, 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.