{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,7]],"date-time":"2026-04-07T06:20:05Z","timestamp":1775542805279,"version":"3.50.1"},"reference-count":19,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2021,2,24]],"date-time":"2021-02-24T00:00:00Z","timestamp":1614124800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["UID\/EMS\/50022\/2020"],"award-info":[{"award-number":["UID\/EMS\/50022\/2020"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematics"],"abstract":"<jats:p>Many image processing algorithms make use of derivatives. In such cases, fractional derivatives allow an extra degree of freedom, which can be used to obtain better results in applications such as edge detection. Published literature concentrates on grey-scale images; in this paper, algorithms of six fractional detectors for colour images are implemented, and their performance is illustrated. The algorithms are: Canny, Sobel, Roberts, Laplacian of Gaussian, CRONE, and fractional derivative.<\/jats:p>","DOI":"10.3390\/math9050457","type":"journal-article","created":{"date-parts":[[2021,2,25]],"date-time":"2021-02-25T02:36:13Z","timestamp":1614220573000},"page":"457","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":20,"title":["Fractional-Order Colour Image Processing"],"prefix":"10.3390","volume":"9","author":[{"given":"Manuel","family":"Henriques","sequence":"first","affiliation":[{"name":"IDMEC, Instituto Superior T\u00e9cnico, Universidade de Lisboa, Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9388-4308","authenticated-orcid":false,"given":"Duarte","family":"Val\u00e9rio","sequence":"additional","affiliation":[{"name":"IDMEC, Instituto Superior T\u00e9cnico, Universidade de Lisboa, Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6861-8446","authenticated-orcid":false,"given":"Paulo","family":"Gordo","sequence":"additional","affiliation":[{"name":"CENTRA, Faculdade de Ci\u00eancias, Universidade de Lisboa, Campo Grande, 1749-016 Lisboa, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1081-2729","authenticated-orcid":false,"given":"Rui","family":"Melicio","sequence":"additional","affiliation":[{"name":"IDMEC, Instituto Superior T\u00e9cnico, Universidade de Lisboa, Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal"},{"name":"ICT, Universidade de \u00c9vora, Rua Rom\u00e3o Ramalho 59, 7000-671 \u00c9vora, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2021,2,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2421","DOI":"10.1016\/S0165-1684(03)00194-4","article-title":"Fractional differentiation for edge detection","volume":"83","author":"Mathieu","year":"2003","journal-title":"Signal Process."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Yaacoub, C., and Zeid Daou, R.A. (2019, January 6\u20139). Fractional Order Sobel Edge Detector. Proceedings of the 2019 Ninth International Conference on Image Processing Theory, Tools and Applications (IPTA), Istanbul, Turkey.","DOI":"10.1109\/IPTA.2019.8936101"},{"key":"ref_3","unstructured":"Chen, X., and Fei, X. (2012, January 25\u201326). Improving edge-detection algorithm based on fractional differential approach. Proceedings of the 2012 International Conference on Image, Vision and Computing, Shanghai, China."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"55","DOI":"10.4028\/www.scientific.net\/AMM.536-537.55","article-title":"A Fractional-Order Laplacian Operator for Image Edge Detection","volume":"536\u2013537","author":"Tian","year":"2014","journal-title":"Appl. Mech. Mater."},{"key":"ref_5","unstructured":"Kanade, T. (1987). Image Understanding Research at Carnegie Mellon. Proceedings of a Workshop on Image Understanding Workshop, Morgan Kaufmann Publishers Inc."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1016\/1049-9652(91)90018-F","article-title":"Edge detection in multispectral images","volume":"53","author":"Cumani","year":"1991","journal-title":"CVGIP Graph. Model. 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Pattern Anal. Mach. Intell., 679\u2013698.","DOI":"10.1109\/TPAMI.1986.4767851"},{"key":"ref_12","unstructured":"CVonline (2020, July 31). Edges: The Canny Edge Detector. Available online: http:\/\/homepages.inf.ed.ac.uk\/rbf\/CVonline\/LOCAL_COPIES\/MARBLE\/low\/edges\/canny.htm."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1109\/MSP.2005.1407716","article-title":"Detection and classification of edges in color images","volume":"22","author":"Koschan","year":"2005","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_14","unstructured":"Fisher, R., Perkins, S., Walker, A., and Wolfart, E. (2021, January 15). Image Processing Learning Resources. Available online: http:\/\/homepages.inf.ed.ac.uk\/rbf\/HIPR2\/."},{"key":"ref_15","unstructured":"Roberts, L. (1963). Machine Perception of 3-D Solids. [Ph.D. Thesis, Massachusetts Institute of Technology]."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Pratt, W.K. (2007). Second-Order Derivative Edge Detection. Digital Image Processing, John Wiley & Sons, Inc.","DOI":"10.1002\/9780470097434.ch15"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"612","DOI":"10.1117\/1.602105","article-title":"Comprehensive analysis of edge detection in color image processing","volume":"38","author":"Zhu","year":"1999","journal-title":"Opt. Eng."},{"key":"ref_18","unstructured":"ESA (2020, March 31). Copernicus Open Access Hub. Available online: https:\/\/scihub.copernicus.eu\/."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"181","DOI":"10.5890\/JAND.2017.06.005","article-title":"Fractional order image processing of medical images","volume":"6","author":"Bento","year":"2017","journal-title":"J. Appl. Nonlinear Dyn."}],"container-title":["Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2227-7390\/9\/5\/457\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:27:31Z","timestamp":1760160451000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2227-7390\/9\/5\/457"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,2,24]]},"references-count":19,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2021,3]]}},"alternative-id":["math9050457"],"URL":"https:\/\/doi.org\/10.3390\/math9050457","relation":{},"ISSN":["2227-7390"],"issn-type":[{"value":"2227-7390","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,2,24]]}}}