{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,13]],"date-time":"2026-04-13T05:06:13Z","timestamp":1776056773982,"version":"3.50.1"},"reference-count":63,"publisher":"Springer Science and Business Media LLC","issue":"9","license":[{"start":{"date-parts":[[2023,4,26]],"date-time":"2023-04-26T00:00:00Z","timestamp":1682467200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,4,26]],"date-time":"2023-04-26T00:00:00Z","timestamp":1682467200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Circuits Syst Signal Process"],"published-print":{"date-parts":[[2023,9]]},"DOI":"10.1007\/s00034-023-02379-2","type":"journal-article","created":{"date-parts":[[2023,4,26]],"date-time":"2023-04-26T09:03:20Z","timestamp":1682499800000},"page":"5602-5633","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["A Powerful Zero-Watermarking Algorithm for Copyright Protection of Color Images Based on Quaternion Radial Fractional Hahn Moments and Artificial Bee Colony Algorithm"],"prefix":"10.1007","volume":"42","author":[{"given":"Mohamed","family":"Yamni","sequence":"first","affiliation":[]},{"given":"Achraf","family":"Daoui","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9225-8380","authenticated-orcid":false,"given":"Hicham","family":"Karmouni","sequence":"additional","affiliation":[]},{"given":"Mhamed","family":"Sayyouri","sequence":"additional","affiliation":[]},{"given":"Hassan","family":"Qjidaa","sequence":"additional","affiliation":[]},{"given":"Chunpeng","family":"Wang","sequence":"additional","affiliation":[]},{"given":"Mohammed Ouazzani","family":"Jamil","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,4,26]]},"reference":[{"key":"2379_CR1","doi-asserted-by":"crossref","first-page":"106053","DOI":"10.1016\/j.asoc.2019.106053","volume":"88","author":"S Aslan","year":"2020","unstructured":"S. Aslan, D. Karaboga, A genetic Artificial Bee Colony algorithm for signal reconstruction based big data optimization. Appl. Soft Comput. 88, 106053 (2020)","journal-title":"Appl. Soft Comput."},{"key":"2379_CR2","doi-asserted-by":"crossref","first-page":"332","DOI":"10.1016\/j.patcog.2018.10.001","volume":"86","author":"R Benouini","year":"2019","unstructured":"R. Benouini et al., Fractional-order orthogonal Chebyshev Moments and Moment Invariants for image representation and pattern recognition. Pattern Recogn. 86, 332\u2013343 (2019)","journal-title":"Pattern Recogn."},{"issue":"4","key":"2379_CR3","doi-asserted-by":"crossref","first-page":"563","DOI":"10.1016\/j.imavis.2007.07.003","volume":"26","author":"TJ Bin","year":"2008","unstructured":"T.J. Bin et al., Subpixel edge location based on orthogonal Fourier\u2013Mellin moments. Image Vis. Comput. 26(4), 563\u2013569 (2008)","journal-title":"Image Vis. Comput."},{"issue":"2","key":"2379_CR4","doi-asserted-by":"crossref","first-page":"308","DOI":"10.1016\/j.sigpro.2011.07.018","volume":"92","author":"BJ Chen","year":"2012","unstructured":"B.J. Chen et al., Quaternion Zernike moments and their invariants for color image analysis and object recognition. Signal Process. 92(2), 308\u2013318 (2012)","journal-title":"Signal Process."},{"key":"2379_CR5","doi-asserted-by":"crossref","first-page":"102599","DOI":"10.1109\/ACCESS.2022.3203067","volume":"10","author":"A Daoui","year":"2022","unstructured":"A. Daoui et al., Biomedical multimedia encryption by fractional-order Meixner polynomials map and quaternion fractional-order Meixner moments. IEEE Access 10, 102599\u2013102617 (2022)","journal-title":"IEEE Access"},{"issue":"7","key":"2379_CR6","doi-asserted-by":"crossref","first-page":"1589","DOI":"10.3390\/math11071589","volume":"11","author":"A Daoui","year":"2023","unstructured":"A. Daoui et al., Efficient image encryption scheme using novel 1D multiparametric dynamical tent map and parallel computing. Mathematics 11(7), 1589 (2023)","journal-title":"Mathematics"},{"key":"2379_CR7","doi-asserted-by":"publisher","first-page":"108596","DOI":"10.1016\/j.patcog.2022.108596","volume":"127","author":"A Daoui","year":"2022","unstructured":"A. Daoui et al., On computational aspects of high-order dual Hahn moments. Pattern Recognit. 127, 108596 (2022). https:\/\/doi.org\/10.1016\/j.patcog.2022.108596","journal-title":"Pattern Recognit."},{"issue":"2","key":"2379_CR8","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1016\/j.patcog.2010.08.017","volume":"44","author":"L-Q Guo","year":"2011","unstructured":"L.-Q. Guo, M. Zhu, Quaternion Fourier\u2013Mellin moments for color images. Pattern Recognit. 44(2), 187\u2013195 (2011)","journal-title":"Pattern Recognit."},{"issue":"2","key":"2379_CR9","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/3325193","volume":"15","author":"KM Hosny","year":"2019","unstructured":"K.M. Hosny, M.M. Darwish, Resilient color image watermarking using accurate quaternion radial substituted Chebyshev moments. ACM Trans. Multimedia Comput. Commun. Appl. (TOMM) 15(2), 1\u201325 (2019)","journal-title":"ACM Trans. Multimedia Comput. Commun. Appl. (TOMM)"},{"key":"2379_CR10","doi-asserted-by":"crossref","first-page":"102804","DOI":"10.1016\/j.jvcir.2020.102804","volume":"70","author":"X Kang","year":"2020","unstructured":"X. Kang et al., Combining polar harmonic transforms and 2D compound chaotic map for distinguishable and robust color image zero-watermarking algorithm. J. Vis. Commun. Image Represent. 70, 102804 (2020)","journal-title":"J. Vis. Commun. Image Represent."},{"key":"2379_CR11","unstructured":"D. Karaboga, An idea based on honey bee swarm for numerical optimization. Technical report-tr06, Erciyes University, Engineering Faculty, Computer Engineering Department (2005)"},{"issue":"2","key":"2379_CR12","doi-asserted-by":"crossref","first-page":"596","DOI":"10.1109\/TIP.2013.2289997","volume":"23","author":"EG Karakasis","year":"2013","unstructured":"E.G. Karakasis et al., A unified methodology for computing accurate quaternion color moments and moment invariants. IEEE Trans. Image Process. 23(2), 596\u2013611 (2013)","journal-title":"IEEE Trans. Image Process."},{"issue":"5","key":"2379_CR13","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1109\/34.55109","volume":"12","author":"A Khotanzad","year":"1990","unstructured":"A. Khotanzad, Y.H. Hong, Invariant image recognition by Zernike moments. IEEE Trans. Pattern Anal. Mach. Intell. 12(5), 489\u2013497 (1990)","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"2379_CR14","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-05014-5","volume-title":"Hypergeometric Orthogonal Polynomials and Their q-Analogues","author":"R Koekoek","year":"2010","unstructured":"R. Koekoek et al., Hypergeometric Orthogonal Polynomials and Their q-Analogues (Springer, 2010)"},{"issue":"8","key":"2379_CR15","doi-asserted-by":"publisher","first-page":"803","DOI":"10.1109\/LSP.2013.2267775","volume":"20","author":"YN Li","year":"2013","unstructured":"Y.N. Li, Quaternion polar harmonic transforms for color images. IEEE Signal Process. Lett. 20(8), 803\u2013806 (2013). https:\/\/doi.org\/10.1109\/LSP.2013.2267775","journal-title":"IEEE Signal Process. Lett."},{"issue":"7","key":"2379_CR16","doi-asserted-by":"crossref","first-page":"1894","DOI":"10.1109\/TSP.2017.2652383","volume":"65","author":"X Liu","year":"2017","unstructured":"X. Liu et al., Fractional Krawtchouk transform with an application to image watermarking. IEEE Trans. Signal Process. 65(7), 1894\u20131908 (2017)","journal-title":"IEEE Trans. Signal Process."},{"issue":"6","key":"2379_CR17","doi-asserted-by":"crossref","first-page":"552","DOI":"10.1109\/76.340199","volume":"4","author":"L-M Luo","year":"1994","unstructured":"L.-M. Luo et al., A modified moment-based edge operator for rectangular pixel image. IEEE Trans. Circuits Syst. Video Technol. 4(6), 552\u2013554 (1994)","journal-title":"IEEE Trans. Circuits Syst. Video Technol."},{"issue":"8","key":"2379_CR18","doi-asserted-by":"crossref","first-page":"1580","DOI":"10.1364\/JOSAA.30.001580","volume":"30","author":"JV Marcos","year":"2013","unstructured":"J.V. Marcos, G. Crist\u00f3bal, Texture classification using discrete Tchebichef moments. JOSA A. 30(8), 1580\u20131591 (2013)","journal-title":"JOSA A."},{"issue":"2","key":"2379_CR19","doi-asserted-by":"publisher","first-page":"179","DOI":"10.1109\/TIT.1962.1057692","volume":"8","author":"Hu Ming-Kuei","year":"1962","unstructured":"Hu. Ming-Kuei, Visual pattern recognition by moment invariants. IRE Trans. Inf. Theory 8(2), 179\u2013187 (1962). https:\/\/doi.org\/10.1109\/TIT.1962.1057692","journal-title":"IRE Trans. Inf. Theory"},{"issue":"1","key":"2379_CR20","doi-asserted-by":"crossref","first-page":"0036","DOI":"10.1177\/00368504211003388","volume":"104","author":"J Mostafaee","year":"2021","unstructured":"J. Mostafaee et al., Complex dynamical behaviors of a novel exponential hyper\u2013chaotic system and its application in fast synchronization and color image encryption. Sci. Prog. 104(1), 0036 (2021)","journal-title":"Sci. Prog."},{"issue":"9","key":"2379_CR21","doi-asserted-by":"crossref","first-page":"1357","DOI":"10.1109\/83.941859","volume":"10","author":"R Mukundan","year":"2001","unstructured":"R. Mukundan et al., Image analysis by Tchebichef moments. IEEE Trans. Image Process. 10(9), 1357\u20131364 (2001)","journal-title":"IEEE Trans. Image Process."},{"key":"2379_CR22","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-1595-8","volume-title":"Special Functions of Mathematical Physics, Texte d\u2019origine: A Unified Introduction with Applications","author":"AF Nikiforov","year":"1988","unstructured":"A.F. Nikiforov, V.B. Uvarov, Special Functions of Mathematical Physics, Texte d\u2019origine: A Unified Introduction with Applications (Birkh\u00e4user, Basel, 1988). https:\/\/doi.org\/10.1007\/978-1-4757-1595-8"},{"issue":"13","key":"2379_CR23","doi-asserted-by":"crossref","first-page":"7655","DOI":"10.1007\/s11042-015-2687-1","volume":"75","author":"P Niu","year":"2016","unstructured":"P. Niu et al., Invariant color image watermarking approach using quaternion radial harmonic Fourier moments. Multimed. Tools Appl. 75(13), 7655\u20137679 (2016)","journal-title":"Multimed. Tools Appl."},{"issue":"1\u20132","key":"2379_CR24","doi-asserted-by":"crossref","first-page":"1409","DOI":"10.1007\/s11042-019-08103-0","volume":"79","author":"C Pak","year":"2020","unstructured":"C. Pak et al., A novel color image LSB steganography using improved 1D chaotic map. Multimed. Tools Appl. 79(1\u20132), 1409\u20131425 (2020)","journal-title":"Multimed. Tools Appl."},{"issue":"9","key":"2379_CR25","doi-asserted-by":"publisher","first-page":"926","DOI":"10.1016\/j.imavis.2006.02.021","volume":"24","author":"NK Pareek","year":"2006","unstructured":"N.K. Pareek et al., Image encryption using chaotic logistic map. Image Vis. Comput. 24(9), 926\u2013934 (2006). https:\/\/doi.org\/10.1016\/j.imavis.2006.02.021","journal-title":"Image Vis. Comput."},{"key":"2379_CR26","doi-asserted-by":"publisher","first-page":"56017","DOI":"10.1109\/ACCESS.2022.3177689","volume":"10","author":"T Peng","year":"2022","unstructured":"T. Peng et al., Nonsingular chattering-free barrier function finite time tracker for perturbed nth-order nonlinear systems and its application to chaotic color image scrambling. IEEE Access 10, 56017\u201356030 (2022). https:\/\/doi.org\/10.1109\/ACCESS.2022.3177689","journal-title":"IEEE Access"},{"issue":"9","key":"2379_CR27","doi-asserted-by":"crossref","first-page":"1748","DOI":"10.1364\/JOSAA.19.001748","volume":"19","author":"Z Ping","year":"2002","unstructured":"Z. Ping et al., Image description with Chebyshev\u2013Fourier moments. JOSA A. 19(9), 1748\u20131754 (2002)","journal-title":"JOSA A."},{"issue":"4","key":"2379_CR28","doi-asserted-by":"crossref","first-page":"505","DOI":"10.1134\/S1054661810040115","volume":"20","author":"H Rahmalan","year":"2010","unstructured":"H. Rahmalan et al., Using Tchebichef moment for fast and efficient image compression. Pattern Recognit. Image Anal. 20(4), 505\u2013512 (2010)","journal-title":"Pattern Recognit. Image Anal."},{"issue":"4","key":"2379_CR29","doi-asserted-by":"crossref","first-page":"631","DOI":"10.1364\/JOSAA.20.000631","volume":"20","author":"H Ren","year":"2003","unstructured":"H. Ren et al., Multidistortion-invariant image recognition with radial harmonic Fourier moments. JOSA A. 20(4), 631\u2013637 (2003)","journal-title":"JOSA A."},{"issue":"6","key":"2379_CR30","doi-asserted-by":"crossref","first-page":"1748","DOI":"10.1364\/JOSAA.11.001748","volume":"11","author":"Y Sheng","year":"1994","unstructured":"Y. Sheng, L. Shen, Orthogonal Fourier\u2013Mellin moments for invariant pattern recognition. JOSA A. 11(6), 1748\u20131757 (1994)","journal-title":"JOSA A."},{"issue":"8","key":"2379_CR31","doi-asserted-by":"crossref","first-page":"920","DOI":"10.1364\/JOSA.70.000920","volume":"70","author":"MR Teague","year":"1980","unstructured":"M.R. Teague, Image analysis via the general theory of moments. JOSA. 70(8), 920\u2013930 (1980)","journal-title":"JOSA."},{"issue":"14","key":"2379_CR32","doi-asserted-by":"crossref","first-page":"6408","DOI":"10.1016\/j.eswa.2014.04.021","volume":"41","author":"ED Tsougenis","year":"2014","unstructured":"E.D. Tsougenis et al., Adaptive color image watermarking by the use of quaternion image moments. Expert Syst. Appl. 41(14), 6408\u20136418 (2014)","journal-title":"Expert Syst. Appl."},{"key":"2379_CR33","doi-asserted-by":"crossref","unstructured":"E.D. Tsougenis et al., Color image watermarking via quaternion radial Tchebichef moments, in 2013 IEEE International Conference on Imaging Systems and Techniques (IST) (IEEE, 2013), pp. 101\u2013105","DOI":"10.1109\/IST.2013.6729671"},{"key":"2379_CR34","doi-asserted-by":"publisher","first-page":"25911","DOI":"10.1109\/ACCESS.2021.3056037","volume":"9","author":"B Vaseghi","year":"2021","unstructured":"B. Vaseghi et al., Fast reaching finite time synchronization approach for chaotic systems with application in medical image encryption. IEEE Access. 9, 25911\u201325925 (2021). https:\/\/doi.org\/10.1109\/ACCESS.2021.3056037","journal-title":"IEEE Access."},{"key":"2379_CR35","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1016\/j.jvcir.2016.10.004","volume":"41","author":"C Wang","year":"2016","unstructured":"C. Wang et al., Geometrically resilient color image zero-watermarking algorithm based on quaternion exponent moments. J. Vis. Commun. Image Represent. 41, 247\u2013259 (2016)","journal-title":"J. Vis. Commun. Image Represent."},{"issue":"12","key":"2379_CR36","doi-asserted-by":"publisher","first-page":"4440","DOI":"10.1109\/TCSVT.2019.2960507","volume":"30","author":"C Wang","year":"2020","unstructured":"C. Wang et al., Image description with polar harmonic Fourier moments. IEEE Trans. Circuits Syst. Video Technol. 30(12), 4440\u20134452 (2020). https:\/\/doi.org\/10.1109\/TCSVT.2019.2960507","journal-title":"IEEE Trans. Circuits Syst. Video Technol."},{"key":"2379_CR37","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1016\/j.ins.2018.03.040","volume":"450","author":"C Wang","year":"2018","unstructured":"C. Wang et al., Quaternion polar harmonic Fourier moments for color images. Inf. Sci. 450, 141\u2013156 (2018)","journal-title":"Inf. Sci."},{"key":"2379_CR38","doi-asserted-by":"publisher","DOI":"10.1109\/TCSVT.2021.3094882","author":"C Wang","year":"2021","unstructured":"C. Wang et al., Stereoscopic image description with trinion fractional-order continuous orthogonal moments. IEEE Trans. Circuits Syst. Video Technol. (2021). https:\/\/doi.org\/10.1109\/TCSVT.2021.3094882","journal-title":"IEEE Trans. Circuits Syst. Video Technol."},{"key":"2379_CR39","doi-asserted-by":"crossref","first-page":"731","DOI":"10.1016\/j.ins.2014.02.158","volume":"277","author":"X Wang","year":"2014","unstructured":"X. Wang et al., A new robust color image watermarking using local quaternion exponent moments. Inf. Sci. 277, 731\u2013754 (2014)","journal-title":"Inf. Sci."},{"issue":"6","key":"2379_CR40","doi-asserted-by":"crossref","first-page":"967","DOI":"10.1016\/j.imavis.2006.07.010","volume":"25","author":"C-Y Wee","year":"2007","unstructured":"C.-Y. Wee, R. Paramesran, On the computational aspects of Zernike moments. Image Vis. Comput. 25(6), 967\u2013980 (2007)","journal-title":"Image Vis. Comput."},{"key":"2379_CR41","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1016\/j.sigpro.2018.11.011","volume":"157","author":"Z Xia","year":"2019","unstructured":"Z. Xia et al., Color medical image lossless watermarking using chaotic system and accurate quaternion polar harmonic transforms. Signal Process. 157, 108\u2013118 (2019)","journal-title":"Signal Process."},{"key":"2379_CR42","doi-asserted-by":"crossref","first-page":"122544","DOI":"10.1109\/ACCESS.2019.2935174","volume":"7","author":"Z Xia","year":"2019","unstructured":"Z. Xia et al., Geometrically invariant color medical image null-watermarking based on precise quaternion polar harmonic Fourier moments. IEEE Access. 7, 122544\u2013122560 (2019)","journal-title":"IEEE Access."},{"key":"2379_CR43","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1016\/j.ins.2016.12.011","volume":"382","author":"B Xiao","year":"2017","unstructured":"B. Xiao et al., Image analysis by fractional-order orthogonal moments. Inf. Sci. 382, 135\u2013149 (2017)","journal-title":"Inf. Sci."},{"issue":"17","key":"2379_CR44","doi-asserted-by":"publisher","first-page":"26683","DOI":"10.1007\/s11042-020-10311-y","volume":"80","author":"M Yamni","year":"2021","unstructured":"M. Yamni et al., Accurate 2D and 3D images classification using translation and scale invariants of Meixner moments. Multimed. Tools Appl. 80(17), 26683\u201326712 (2021). https:\/\/doi.org\/10.1007\/s11042-020-10311-y","journal-title":"Multimed. Tools Appl."},{"key":"2379_CR45","doi-asserted-by":"crossref","unstructured":"M. Yamni, et al., Blind image zero-watermarking algorithm based on radial krawtchouk moments and chaotic system, in 2020 International Conference on Intelligent Systems and Computer Vision (ISCV) (IEEE, 2020), pp. 1\u20137","DOI":"10.1109\/ISCV49265.2020.9204071"},{"key":"2379_CR46","doi-asserted-by":"publisher","unstructured":"M. Yamni et al., Color stereo image zero-watermarking using quaternion radial Tchebichef moments, in 2020 International Conference on Intelligent Systems and Computer Vision (ISCV) (2020), pp. 1\u20137. https:\/\/doi.org\/10.1109\/ISCV49265.2020.9204169","DOI":"10.1109\/ISCV49265.2020.9204169"},{"issue":"7","key":"2379_CR47","doi-asserted-by":"crossref","first-page":"4719","DOI":"10.1016\/j.jfranklin.2023.03.008","volume":"360","author":"M Yamni","year":"2023","unstructured":"M. Yamni et al., Copyright protection of multiple CT images using Octonion Krawtchouk moments and Grey Wolf optimizer. J. Franklin Inst. 360(7), 4719\u20134752 (2023)","journal-title":"J. Franklin Inst."},{"key":"2379_CR48","doi-asserted-by":"crossref","first-page":"6193","DOI":"10.1007\/s00034-021-01763-0","volume":"40","author":"M Yamni","year":"2021","unstructured":"M. Yamni et al., Fast and accurate computation of 3D Charlier moment invariants for 3D image classification. Circuits Syst. Signal Process. 40, 6193\u20136223 (2021)","journal-title":"Circuits Syst. Signal Process."},{"key":"2379_CR49","doi-asserted-by":"crossref","first-page":"107509","DOI":"10.1016\/j.sigpro.2020.107509","volume":"171","author":"M Yamni","year":"2020","unstructured":"M. Yamni et al., Fractional Charlier moments for image reconstruction and image watermarking. Signal Process. 171, 107509 (2020)","journal-title":"Signal Process."},{"issue":"4","key":"2379_CR50","doi-asserted-by":"crossref","first-page":"2535","DOI":"10.1016\/j.jfranklin.2021.01.011","volume":"358","author":"M Yamni","year":"2021","unstructured":"M. Yamni et al., Image watermarking using separable fractional moments of Charlier\u2013Meixner. J. Frankl. Inst. 358(4), 2535\u20132560 (2021)","journal-title":"J. Frankl. Inst."},{"key":"2379_CR51","doi-asserted-by":"publisher","DOI":"10.1007\/s11042-021-11432-8","author":"M Yamni","year":"2021","unstructured":"M. Yamni et al., Quaternion Cartesian fractional Hahn moments for color image analysis. Multimed. Tools Appl. (2021). https:\/\/doi.org\/10.1007\/s11042-021-11432-8","journal-title":"Multimed. Tools Appl."},{"key":"2379_CR52","doi-asserted-by":"crossref","first-page":"117325","DOI":"10.1016\/j.eswa.2022.117325","volume":"203","author":"M Yamni","year":"2022","unstructured":"M. Yamni et al., Robust audio watermarking scheme based on fractional Charlier moment transform and dual tree complex wavelet transform. Expert Syst. Appl. 203, 117325 (2022)","journal-title":"Expert Syst. Appl."},{"issue":"14","key":"2379_CR53","doi-asserted-by":"publisher","first-page":"21679","DOI":"10.1007\/s11042-021-10717-2","volume":"80","author":"M Yamni","year":"2021","unstructured":"M. Yamni et al., Robust zero-watermarking scheme based on novel quaternion radial fractional Charlier moments. Multimed. Tools Appl. 80(14), 21679\u201321708 (2021). https:\/\/doi.org\/10.1007\/s11042-021-10717-2","journal-title":"Multimed. Tools Appl."},{"issue":"3","key":"2379_CR54","first-page":"1","volume":"11","author":"H-Y Yang","year":"2015","unstructured":"H.-Y. Yang et al., Robust color image watermarking using geometric invariant quaternion polar harmonic transform. ACM Trans. Multimed. Comput. Commun. Appl. (TOMM) 11(3), 1\u201326 (2015)","journal-title":"ACM Trans. Multimed. Comput. Commun. Appl. (TOMM)"},{"issue":"11","key":"2379_CR55","doi-asserted-by":"crossref","first-page":"1367","DOI":"10.1109\/TIP.2003.818019","volume":"12","author":"P-T Yap","year":"2003","unstructured":"P.-T. Yap et al., Image analysis by Krawtchouk moments. IEEE Trans. Image Process. 12(11), 1367\u20131377 (2003)","journal-title":"IEEE Trans. Image Process."},{"issue":"11","key":"2379_CR56","doi-asserted-by":"publisher","first-page":"2057","DOI":"10.1109\/TPAMI.2007.70709","volume":"29","author":"P-T Yap","year":"2007","unstructured":"P.-T. Yap et al., Image analysis using Hahn moments. IEEE Trans. Pattern Anal. Mach. Intell. 29(11), 2057\u20132062 (2007). https:\/\/doi.org\/10.1109\/TPAMI.2007.70709","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"issue":"12","key":"2379_CR57","doi-asserted-by":"crossref","first-page":"1996","DOI":"10.1109\/TPAMI.2005.232","volume":"27","author":"P-T Yap","year":"2005","unstructured":"P.-T. Yap, R. Paramesran, An efficient method for the computation of Legendre moments. IEEE Trans. Pattern Anal. Mach. Intell. 27(12), 1996\u20132002 (2005)","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"issue":"8","key":"2379_CR58","doi-asserted-by":"crossref","first-page":"2189","DOI":"10.1109\/TIP.2011.2118216","volume":"20","author":"H Zhang","year":"2011","unstructured":"H. Zhang et al., Affine Legendre moment invariants for image watermarking robust to geometric distortions. IEEE Trans. Image Process. 20(8), 2189\u20132199 (2011)","journal-title":"IEEE Trans. Image Process."},{"key":"2379_CR59","doi-asserted-by":"publisher","first-page":"766","DOI":"10.1007\/978-981-10-3002-4_62","volume-title":"Pattern Recognition","author":"H Zhang","year":"2016","unstructured":"H. Zhang et al., Fractional orthogonal Fourier\u2013Mellin moments for pattern recognition, in Pattern Recognition. ed. by T. Tan et al. (Springer, Singapore, 2016), pp.766\u2013778. https:\/\/doi.org\/10.1007\/978-981-10-3002-4_62"},{"key":"2379_CR60","doi-asserted-by":"crossref","first-page":"148","DOI":"10.1016\/j.physa.2017.07.019","volume":"490","author":"Y-Q Zhang","year":"2018","unstructured":"Y.-Q. Zhang et al., Spatiotemporal chaos in mixed linear\u2013nonlinear two-dimensional coupled logistic map lattice. Physica A 490, 148\u2013160 (2018)","journal-title":"Physica A"},{"key":"2379_CR61","doi-asserted-by":"publisher","first-page":"524","DOI":"10.1007\/11559573_65","volume-title":"Image Analysis and Recognition","author":"J Zhou","year":"2005","unstructured":"J. Zhou et al., Image analysis by discrete orthogonal Hahn moments, in Image Analysis and Recognition. ed. by M. Kamel, A. Campilho (Springer, Berlin, 2005), pp.524\u2013531. https:\/\/doi.org\/10.1007\/11559573_65"},{"issue":"5","key":"2379_CR62","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1049\/iet-ipr.2009.0195","volume":"4","author":"H Zhu","year":"2010","unstructured":"H. Zhu et al., General form for obtaining discrete orthogonal moments. IET Image Proc. 4(5), 335\u2013352 (2010)","journal-title":"IET Image Proc."},{"issue":"4","key":"2379_CR63","doi-asserted-by":"crossref","first-page":"687","DOI":"10.1016\/j.sigpro.2006.07.007","volume":"87","author":"H Zhu","year":"2007","unstructured":"H. Zhu et al., Image analysis by discrete orthogonal Racah moments. Signal Process. 87(4), 687\u2013708 (2007)","journal-title":"Signal Process."}],"container-title":["Circuits, Systems, and Signal Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00034-023-02379-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00034-023-02379-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00034-023-02379-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,7,28]],"date-time":"2023-07-28T11:16:34Z","timestamp":1690542994000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00034-023-02379-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,4,26]]},"references-count":63,"journal-issue":{"issue":"9","published-print":{"date-parts":[[2023,9]]}},"alternative-id":["2379"],"URL":"https:\/\/doi.org\/10.1007\/s00034-023-02379-2","relation":{},"ISSN":["0278-081X","1531-5878"],"issn-type":[{"value":"0278-081X","type":"print"},{"value":"1531-5878","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,4,26]]},"assertion":[{"value":"11 August 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"31 March 2023","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 April 2023","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 April 2023","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}