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Fractional Calculus in Image Processing: A Review

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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 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.

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Authors and Affiliations

  1. School of Mechanical Engineering, ShenYang LiGong University, Shenyang, 110159, China

    Qi Yang

  2. College of Information Science and Technology, Northeastern University, Shenyang, 110819, China

    Dali Chen

  3. School of Engineering, University of California Merced, 5200 N. Lake Road, Merced, CA, 95343, USA

    Tiebiao Zhao & YangQuan Chen

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  1. Qi Yang
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  2. Dali Chen
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Correspondence to Qi Yang.

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Yang, Q., Chen, D., Zhao, T. et al. Fractional Calculus in Image Processing: A Review. FCAA 19, 1222–1249 (2016). https://doi.org/10.1515/fca-2016-0063

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