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aim to extract meaningful information from images but often depend on manual feature engineering, making it difficult to handle complex real-world scenarios. Fractional calculus (FC), which extends derivatives to non-integer orders, provides a flexible way to model systems with memory effects and long-term dependencies, making it a powerful tool for capturing fractional rates of variation. Recently, neural networks (NNs) have demonstrated remarkable capabilities in learning complex patterns directly from raw data, automating computer vision tasks and enhancing performance. Therefore, the use of fractional calculus in neural network-based computer vision is a powerful method to address existing challenges by effectively capturing complex spatial and temporal relationships in images and videos. This paper presents a survey of fractional calculus neural network-based (FC NN-based) computer vision techniques for denoising, enhancement, object detection, segmentation, restoration, and NN compression. This survey compiles existing FFC NN-based approaches, elucidates underlying concepts, and identifies open questions and research directions. By leveraging FC\u2019s properties, FC NN-based approaches offer a novel way to improve the robustness and efficiency of computer vision systems.<\/jats:p>","DOI":"10.3390\/ai5030067","type":"journal-article","created":{"date-parts":[[2024,8,10]],"date-time":"2024-08-10T06:25:24Z","timestamp":1723271124000},"page":"1391-1426","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["Fractional Calculus Meets Neural Networks for Computer Vision: A Survey"],"prefix":"10.3390","volume":"5","author":[{"ORCID":"https:\/\/orcid.org\/0009-0009-4502-937X","authenticated-orcid":false,"given":"Cec\u00edlia","family":"Coelho","sequence":"first","affiliation":[{"name":"Centre of Mathematics (CMAT), University of Minho, 4710-057 Braga, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6235-286X","authenticated-orcid":false,"given":"M. Fernanda P.","family":"Costa","sequence":"additional","affiliation":[{"name":"Centre of Mathematics (CMAT), University of Minho, 4710-057 Braga, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5477-3226","authenticated-orcid":false,"given":"Lu\u00eds L.","family":"Ferr\u00e1s","sequence":"additional","affiliation":[{"name":"Centre of Mathematics (CMAT), University of Minho, 4710-057 Braga, Portugal"},{"name":"Department of Mechanical Engineering (Section of Mathematics) and CEFT\u2014Centro de Estudos de Fen\u00f3menos de Transporte\u2014FEUP, University of Porto, 4200-465 Porto, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2024,8,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Szeliski, R. (2022). Computer Vision: Algorithms and Applications, Springer Nature.","DOI":"10.1007\/978-3-030-34372-9"},{"key":"ref_2","unstructured":"Dey, S. (2018). 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