{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T09:14:26Z","timestamp":1760346866097},"reference-count":37,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2020,4,10]],"date-time":"2020-04-10T00:00:00Z","timestamp":1586476800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,4,10]],"date-time":"2020-04-10T00:00:00Z","timestamp":1586476800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"name":"The National Science Fund of China","award":["No.61702262","No. U1713208"],"award-info":[{"award-number":["No.61702262","No. U1713208"]}]},{"name":"Funds for International Cooperation and Exchange of the National Natural Science Foundation of China","award":["No.61861136011"],"award-info":[{"award-number":["No.61861136011"]}]},{"name":"Natural Science Foundation of Jiangsu Province, China","award":["No.BK20181299"],"award-info":[{"award-number":["No.BK20181299"]}]},{"name":"The Fundamental Research Funds for the Central Universities","award":["No.30918011322"],"award-info":[{"award-number":["No.30918011322"]}]},{"name":"CCF-Tencent Open Fund","award":["RAGR20180113"],"award-info":[{"award-number":["RAGR20180113"]}]},{"name":"Young Elite Scientists Sponsorship Program by CAST","award":["2018QNRC001"],"award-info":[{"award-number":["2018QNRC001"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Pattern Anal Applic"],"published-print":{"date-parts":[[2020,11]]},"DOI":"10.1007\/s10044-020-00877-6","type":"journal-article","created":{"date-parts":[[2020,4,10]],"date-time":"2020-04-10T19:02:35Z","timestamp":1586545355000},"page":"1551-1567","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Accurate quaternion radial harmonic Fourier moments for color image reconstruction and object recognition"],"prefix":"10.1007","volume":"23","author":[{"given":"Yunan","family":"Liu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shanshan","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guangyu","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Houjun","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jian","family":"Yang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,4,10]]},"reference":[{"issue":"7","key":"877_CR1","doi-asserted-by":"publisher","first-page":"1002","DOI":"10.1016\/j.jvcir.2013.06.017","volume":"24","author":"B Xiao","year":"2013","unstructured":"Xiao B, Wang G (2013) Generic radial orthogonal moment invariant for invariant image recognition. J Vis Commun Image Represent 24(7):1002\u20131008","journal-title":"J Vis Commun Image Represent"},{"key":"877_CR2","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1016\/j.ins.2018.03.040","volume":"450","author":"C Wang","year":"2018","unstructured":"Wang C, Wang X, Li Y, Xia Z, Zhang C (2018) Quaternion polar harmonic Fourier moments for color images. Inf Sci 450:141\u2013156","journal-title":"Inf Sci"},{"issue":"5","key":"877_CR3","doi-asserted-by":"publisher","first-page":"489","DOI":"10.1109\/34.55109","volume":"12","author":"A Khotanzad","year":"1990","unstructured":"Khotanzad A, Hong Y (1990) Invariant image recognition by Zernike moments. IEEE Trans Pattern Anal Mach Intell 12(5):489\u2013497","journal-title":"IEEE Trans Pattern Anal Mach Intell"},{"issue":"1","key":"877_CR4","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1016\/j.patcog.2003.06.003","volume":"37","author":"C Chong","year":"2004","unstructured":"Chong C, Raveendran P, Mukundan R (2004) Translation and scale invariants of Legendre moments. Pattern Recognit 37(1):119\u2013129","journal-title":"Pattern Recognit"},{"issue":"2","key":"877_CR5","doi-asserted-by":"publisher","first-page":"1037","DOI":"10.1109\/TAES.2018.2856321","volume":"55","author":"S Gishkori","year":"2018","unstructured":"Gishkori S, Mulgrew B (2018) Pseudo-Zernike moments based sparse representations for SAR image classification. IEEE Trans Aerosp Electron Syst 55(2):1037\u20131044","journal-title":"IEEE Trans Aerosp Electron Syst"},{"key":"877_CR6","doi-asserted-by":"publisher","first-page":"30","DOI":"10.1016\/j.ipl.2017.09.010","volume":"130","author":"R Zhi","year":"2018","unstructured":"Zhi R, Cao L, Cao G (2018) Translation and scale invariants of Krawtchouk moments. Inf Process Lett 130:30\u201335","journal-title":"Inf Process Lett"},{"issue":"9","key":"877_CR7","doi-asserted-by":"publisher","first-page":"1748","DOI":"10.1364\/JOSAA.19.001748","volume":"19","author":"Z Ping","year":"2002","unstructured":"Ping Z, Wu R, Sheng Y (2002) Image description with Chebyshev\u2013Fourier moments. J Opt Soc Am A 19(9):1748\u20131754","journal-title":"J Opt Soc Am A"},{"issue":"8","key":"877_CR8","doi-asserted-by":"publisher","first-page":"2620","DOI":"10.1016\/j.patcog.2010.03.013","volume":"43","author":"B Xiao","year":"2010","unstructured":"Xiao B, Ma J, Wang X (2010) Image analysis by Bessel\u2013Fourier moments. Pattern Recognit 43(8):2620\u20132629","journal-title":"Pattern Recognit"},{"issue":"6","key":"877_CR9","doi-asserted-by":"publisher","first-page":"1748","DOI":"10.1364\/JOSAA.11.001748","volume":"11","author":"YL Sheng","year":"1994","unstructured":"Sheng YL, Shen LX (1994) Orthogonal Fourier\u2013Mellin moments for invariant pattern recognition. J Opt Soc Am A 11(6):1748\u20131757","journal-title":"J Opt Soc Am A"},{"issue":"8","key":"877_CR10","doi-asserted-by":"publisher","first-page":"2596","DOI":"10.1016\/j.patcog.2014.02.014","volume":"47","author":"H Hu","year":"2014","unstructured":"Hu H, Zhang Y, Shao C, Ju Q (2014) Orthogonal moments based on exponent functions: exponent Fourier moments. Pattern Recognit 47(8):2596\u20132606","journal-title":"Pattern Recognit"},{"key":"877_CR11","doi-asserted-by":"publisher","first-page":"623","DOI":"10.1016\/j.ijleo.2017.12.058","volume":"158","author":"R Upneja","year":"2018","unstructured":"Upneja R, Pawlak M, Sahan A (2018) An accurate approach for the computation of polar harmonic transforms. Optik 158:623\u2013633","journal-title":"Optik"},{"issue":"4","key":"877_CR12","doi-asserted-by":"publisher","first-page":"631","DOI":"10.1364\/JOSAA.20.000631","volume":"20","author":"H Ren","year":"2003","unstructured":"Ren H, Ping Z, Bo W, Wu W, Sheng Y (2003) Multidistortion-invariant image recognition with radial harmonic Fourier moments. J Opt Soc Am A 20(4):631\u2013637","journal-title":"J Opt Soc Am A"},{"key":"877_CR13","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1016\/j.ins.2018.08.028","volume":"470","author":"C Wang","year":"2019","unstructured":"Wang C, Wang X, Xia Z, Zhang C (2019) Ternary radial harmonic Fourier moments based robust stereo image zero-watermarking algorithm. Inf Sci 470:109\u2013120","journal-title":"Inf Sci"},{"key":"877_CR14","unstructured":"Singh C, Upneja R (2012) A computational model for enhanced accuracy of radial harmonic Fourier moments. In: World congress of engineering, London, UK, pp 1189\u20131194"},{"issue":"5","key":"877_CR15","doi-asserted-by":"publisher","first-page":"1470","DOI":"10.1016\/j.dsp.2013.05.006","volume":"23","author":"C Singh","year":"2013","unstructured":"Singh C, Ranade S (2013) A high capacity image adaptive watermarking scheme with radial harmonic Fourier moments. Dig Signal Process 23(5):1470\u20131482","journal-title":"Dig Signal Process"},{"key":"877_CR16","doi-asserted-by":"publisher","first-page":"10","DOI":"10.1016\/j.image.2016.04.005","volume":"45","author":"C Wang","year":"2016","unstructured":"Wang C, Wang X, Xia Z (2016) Geometrically invariant image watermarking based on fast radial harmonic Fourier moments. Signal Process Image Commun 45:10\u201323","journal-title":"Signal Process Image Commun"},{"key":"877_CR17","doi-asserted-by":"publisher","first-page":"16","DOI":"10.1016\/j.patcog.2016.02.014","volume":"56","author":"A Deng","year":"2016","unstructured":"Deng A, Wei C, Gwo C (2016) Stable, fast computation of high-order Zernike moments using a recursive method. Pattern Recognit 56:16\u201325","journal-title":"Pattern Recognit"},{"issue":"19","key":"877_CR18","doi-asserted-by":"publisher","first-page":"7925","DOI":"10.1016\/j.ijleo.2016.05.097","volume":"127","author":"R Upneja","year":"2016","unstructured":"Upneja R (2016) Accurate and fast Jacobi\u2013Fourier moments for invariant image recognition. Optik 127(19):7925\u20137940","journal-title":"Optik"},{"issue":"6","key":"877_CR19","doi-asserted-by":"publisher","first-page":"e0199430","DOI":"10.1371\/journal.pone.0199430","volume":"13","author":"C Li","year":"2018","unstructured":"Li C, Li Y, Yuan Y, Wu X, Sang Q (2018) Quaternion wavelet transform based full reference image quality assessment for multiply distorted images. PLoS ONE 13(6):e0199430","journal-title":"PLoS ONE"},{"issue":"18","key":"877_CR20","doi-asserted-by":"publisher","first-page":"23483","DOI":"10.1007\/s11042-018-5652-y","volume":"77","author":"F Liu","year":"2018","unstructured":"Liu F, Ma L, Liu C, Lu Z (2018) Optimal blind watermarking for color images based on the U matrix of quaternion singular value decomposition. Multimed Tools Appl 77(18):23483\u201323500","journal-title":"Multimed Tools Appl"},{"key":"877_CR21","doi-asserted-by":"publisher","first-page":"197","DOI":"10.1016\/j.sigpro.2016.12.010","volume":"134","author":"C Wang","year":"2017","unstructured":"Wang C, Wang X, Zhang C, Xia Z (2017) Geometric correction based color image watermarking using fuzzy least squares support vector machine and Bessel K form distribution. Signal Process 134:197\u2013208","journal-title":"Signal Process"},{"key":"877_CR22","doi-asserted-by":"publisher","first-page":"108","DOI":"10.1016\/j.sigpro.2018.11.011","volume":"157","author":"Z Xia","year":"2019","unstructured":"Xia Z, Wang X, Zhou W, Li R, Wang C, Zhang C (2019) Color medical image lossless watermarking using chaotic system and accurate quaternion polar harmonic transforms. Signal Process 157:108\u2013118","journal-title":"Signal Process"},{"issue":"2","key":"877_CR23","doi-asserted-by":"publisher","first-page":"187","DOI":"10.1016\/j.patcog.2010.08.017","volume":"44","author":"L Guo","year":"2011","unstructured":"Guo L, Zhu M (2011) Quaternion Fourier\u2013Mellin moments for color images. Pattern Recognit 44(2):187\u2013195","journal-title":"Pattern Recognit"},{"issue":"2","key":"877_CR24","doi-asserted-by":"publisher","first-page":"308","DOI":"10.1016\/j.sigpro.2011.07.018","volume":"92","author":"B Chen","year":"2012","unstructured":"Chen B, Shu H, Zhang H, Chen G, Tounoulin C, Dillenseger JL, Luo LM (2012) Quaternion Zernike moments and their invariant for color image analysis and object recognition. Signal Process 92(2):308\u2013318","journal-title":"Signal Process"},{"key":"877_CR25","doi-asserted-by":"publisher","first-page":"132","DOI":"10.1016\/j.ins.2014.03.037","volume":"273","author":"LQ Guo","year":"2014","unstructured":"Guo LQ, Dai M, Zhu M (2014) Quaternion moment and its invariant for color object classification. Inf Sci 273:132\u2013143","journal-title":"Inf Sci"},{"issue":"2","key":"877_CR26","doi-asserted-by":"publisher","first-page":"603","DOI":"10.1016\/j.patcog.2013.08.016","volume":"47","author":"Z Shao","year":"2014","unstructured":"Shao Z, Shu H, Wu J, Chen B, Coatrieux J (2014) Quaternion Bessel\u2013Fourier moments and their invariant descriptors for object reconstruction and recognition. Pattern Recognit 47(2):603\u2013611","journal-title":"Pattern Recognit"},{"issue":"1","key":"877_CR27","doi-asserted-by":"publisher","first-page":"124","DOI":"10.1007\/s10851-014-0511-6","volume":"51","author":"B Chen","year":"2015","unstructured":"Chen B, Shu H, Coatrieux G, Chen G, Sun X, Coatrieux JL (2015) Color image analysis by quaternion-type moments. J Math Imaging Vis 51(1):124\u2013144","journal-title":"J Math Imaging Vis"},{"key":"877_CR28","doi-asserted-by":"publisher","first-page":"247","DOI":"10.1016\/j.jvcir.2016.10.004","volume":"41","author":"C Wang","year":"2016","unstructured":"Wang C, Wang X, Xia Z, Zhang C, Chen X (2016) Geometrically resilient color image zero-watermarking algorithm based on quaternion exponent moments. J Vis Commun Image Represent 41:247\u2013259","journal-title":"J Vis Commun Image Represent"},{"issue":"2","key":"877_CR29","doi-asserted-by":"publisher","first-page":"451","DOI":"10.1007\/s10044-016-0588-1","volume":"21","author":"X Wang","year":"2018","unstructured":"Wang X, Liu Y, Xu H, Wang P, Yang H (2018) Robust copy\u2013move forgery detection using quaternion exponent moments. Pattern Anal Appl 21(2):451\u2013467","journal-title":"Pattern Anal Appl"},{"key":"877_CR30","doi-asserted-by":"publisher","first-page":"78","DOI":"10.1016\/j.optlastec.2014.08.009","volume":"66","author":"X Wang","year":"2015","unstructured":"Wang X, Li W, Yang H, Niu P, Li Y (2015) Invariant quaternion radial harmonic Fourier moments for color image retrieval. Opt Laser Technol 66:78\u201388","journal-title":"Opt Laser Technol"},{"key":"877_CR31","doi-asserted-by":"publisher","first-page":"368","DOI":"10.1016\/j.sigpro.2019.06.025","volume":"164","author":"Z Xia","year":"2019","unstructured":"Xia Z, Wang X, Li X, Wang M, Zhao T (2019) Efficient copyright protection for three CT images based on quaternion polar harmonic Fourier moments. Signal Process 164:368\u2013379","journal-title":"Signal Process"},{"key":"877_CR32","doi-asserted-by":"publisher","first-page":"388","DOI":"10.1016\/j.ins.2019.07.089","volume":"505","author":"T Yang","year":"2019","unstructured":"Yang T, Ma J, Miao Y, Wang X, Xiao B, He B, Meng Q (2019) Quaternion weighted spherical Bessel\u2013Fourier moment and its invariant for color image reconstruction and object recognition. Inf Sci 505:388\u2013405","journal-title":"Inf Sci"},{"issue":"3","key":"877_CR33","doi-asserted-by":"publisher","first-page":"1105","DOI":"10.1007\/s10044-018-0740-1","volume":"22","author":"K Hosny","year":"2019","unstructured":"Hosny K, Darwish M (2019) Invariant color images representation using accurate quaternion Legendre\u2013Fourier moments. Pattern Anal Appl 22(3):1105\u20131122","journal-title":"Pattern Anal Appl"},{"key":"877_CR34","unstructured":"https:\/\/www.cs.columbia.edu\/CAVE\/software\/softlib\/coil-100.php"},{"issue":"8","key":"877_CR35","doi-asserted-by":"publisher","first-page":"2060","DOI":"10.1016\/j.patcog.2010.03.013","volume":"43","author":"B Xiao","year":"2010","unstructured":"Xiao B, Ma JF, Wang X (2010) Image analysis by Bessel\u2013Fourier moments. Pattern Recognit 43(8):2060\u20132629","journal-title":"Pattern Recognit"},{"issue":"7","key":"877_CR36","doi-asserted-by":"publisher","first-page":"1002","DOI":"10.1016\/j.jvcir.2013.06.017","volume":"24","author":"B Xiao","year":"2013","unstructured":"Xiao B, Wang G (2013) Generic radial orthogonal moment invariants for invariant image recognition. J Vis Commun Image Represent 24(7):1002\u20131008","journal-title":"J Vis Commun Image Represent"},{"key":"877_CR37","unstructured":"https:\/\/cswww.essex.ac.uk\/mv\/allfaces\/index.html"}],"container-title":["Pattern Analysis and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10044-020-00877-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10044-020-00877-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10044-020-00877-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,9]],"date-time":"2021-04-09T23:35:26Z","timestamp":1618011326000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10044-020-00877-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,4,10]]},"references-count":37,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2020,11]]}},"alternative-id":["877"],"URL":"https:\/\/doi.org\/10.1007\/s10044-020-00877-6","relation":{},"ISSN":["1433-7541","1433-755X"],"issn-type":[{"value":"1433-7541","type":"print"},{"value":"1433-755X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,4,10]]},"assertion":[{"value":"20 September 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"30 March 2020","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 April 2020","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}