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Firstly, the proposed QFr-GLMs are directly constructed in Cartesian coordinate space, avoiding the need for conversion between Cartesian and polar coordinates; therefore, they are better image descriptors than circularly orthogonal moments constructed in polar coordinates. Moreover, unlike the latest Zernike moments based on quaternion and fractional-order transformations, which extract only the global features from color images, our proposed QFr-GLMs can extract both the global and local color features. This paper also derives a new set of invariant color-image descriptors by QFr-GLMs, enabling geometric-invariant pattern recognition in color images. Finally, the performances of our proposed QFr-GLMs and moment invariants were evaluated in simulation experiments of correlated color images. Both theoretical analysis and experimental results demonstrate the value of the proposed QFr-GLMs and their geometric invariants in the representation and recognition of color images.<\/jats:p>","DOI":"10.1186\/s13640-021-00553-7","type":"journal-article","created":{"date-parts":[[2021,5,17]],"date-time":"2021-05-17T08:02:40Z","timestamp":1621238560000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Quaternion fractional-order color orthogonal moment-based image representation and recognition"],"prefix":"10.1186","volume":"2021","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7667-9617","authenticated-orcid":false,"given":"Bing","family":"He","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jun","family":"Liu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tengfei","family":"Yang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bin","family":"Xiao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yanguo","family":"Peng","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,5,17]]},"reference":[{"issue":"3","key":"553_CR1","doi-asserted-by":"publisher","first-page":"1105","DOI":"10.1007\/s10044-018-0740-1","volume":"22","author":"K Hosny","year":"2019","unstructured":"K. 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