{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T10:18:50Z","timestamp":1777457930081,"version":"3.51.4"},"reference-count":42,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2019,7,27]],"date-time":"2019-07-27T00:00:00Z","timestamp":1564185600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2019,7,27]],"date-time":"2019-07-27T00:00:00Z","timestamp":1564185600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61601311"],"award-info":[{"award-number":["61601311"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004480","name":"Natural Science Foundation of Shanxi Province","doi-asserted-by":"publisher","award":["201801D221186"],"award-info":[{"award-number":["201801D221186"]}],"id":[{"id":"10.13039\/501100004480","id-type":"DOI","asserted-by":"publisher"}]},{"name":"School Foundation of Taiyuan University of Technology","award":["2017QN12"],"award-info":[{"award-number":["2017QN12"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Pattern Anal Applic"],"published-print":{"date-parts":[[2020,5]]},"DOI":"10.1007\/s10044-019-00840-0","type":"journal-article","created":{"date-parts":[[2019,7,27]],"date-time":"2019-07-27T17:02:41Z","timestamp":1564246961000},"page":"785-795","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["The modified generic polar harmonic transforms for image representation"],"prefix":"10.1007","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1136-6783","authenticated-orcid":false,"given":"Xilin","family":"Liu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yongfei","family":"Wu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhuhong","family":"Shao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiasong","family":"Wu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2019,7,27]]},"reference":[{"issue":"12","key":"840_CR1","doi-asserted-by":"publisher","first-page":"3784","DOI":"10.1109\/TIP.2006.884913","volume":"15","author":"J Flusser","year":"2006","unstructured":"Flusser J, Suk T (2006) Rotation moment invariants for recognition of symmetric objects. IEEE Trans Image Process 15(12):3784\u20133790","journal-title":"IEEE Trans Image Process"},{"key":"840_CR2","doi-asserted-by":"crossref","unstructured":"J. Flusser, T. Suk, B. Zitova (2009) Moments and moments invariants in pattern recognition. Wiley, Hoboken","DOI":"10.1002\/9780470684757"},{"issue":"1","key":"840_CR3","doi-asserted-by":"publisher","first-page":"167","DOI":"10.1016\/0031-3203(93)90098-H","volume":"26","author":"J Flusser","year":"1993","unstructured":"Flusser J, Suk T (1993) Pattern recognition by affine moment invariants. Pattern Recogn 26(1):167\u2013174","journal-title":"Pattern Recogn"},{"issue":"5","key":"840_CR4","doi-asserted-by":"publisher","first-page":"70","DOI":"10.1109\/EMB.2007.906026","volume":"26","author":"HZ Shu","year":"2007","unstructured":"Shu HZ, Luo LM, Coatrieux JL (2007) Moment-based approaches in imaging part 1, basic features. IEEE Eng Med Biol Mag 26(5):70\u201374","journal-title":"IEEE Eng Med Biol Mag"},{"key":"840_CR5","doi-asserted-by":"publisher","DOI":"10.1142\/3838","volume-title":"Moment functions in image analysis-theory and applications","author":"R Mukundan","year":"1998","unstructured":"Mukundan R, Ramakrishnan KR (1998) Moment functions in image analysis-theory and applications. World Scientific, Singapore"},{"issue":"2","key":"840_CR6","first-page":"691","volume":"40","author":"B Fu","year":"2007","unstructured":"Fu B, Zhou JZ, Li YH, Zhang GJ, Wang C (2007) Image analysis by modified Legendre moments 40(2):691\u2013704","journal-title":"Image analysis by modified Legendre moments"},{"issue":"9","key":"840_CR7","doi-asserted-by":"publisher","first-page":"1357","DOI":"10.1109\/83.941859","volume":"10","author":"R Mukundan","year":"2001","unstructured":"Mukundan R, Ong SH, Lee PA (2001) Image analysis by Tchebichef moments. IEEE Trans Image Process 10(9):1357\u20131364","journal-title":"IEEE Trans Image Process"},{"issue":"8","key":"840_CR8","doi-asserted-by":"publisher","first-page":"920","DOI":"10.1364\/JOSA.70.000920","volume":"70","author":"MR Teague","year":"1980","unstructured":"Teague MR (1980) Image analysis via the general theory of moments. J Opt Soc Am 70(8):920\u2013930","journal-title":"J Opt Soc Am"},{"issue":"5","key":"840_CR9","doi-asserted-by":"publisher","first-page":"489","DOI":"10.1109\/34.55109","volume":"12","author":"A Khotanzad","year":"1990","unstructured":"Khotanzad A, Hong YH (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":"6","key":"840_CR10","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. JOSA A 11(6):1748\u20131757","journal-title":"JOSA A"},{"issue":"4","key":"840_CR11","doi-asserted-by":"publisher","first-page":"389","DOI":"10.1109\/34.491620","volume":"18","author":"RR Bailey","year":"1996","unstructured":"Bailey RR, Srinath M (1996) Orthogonal moment features for use with parametric and non-parametric classifiers. IEEE Trans Pattern Anal Mach Intell 18(4):389\u2013399","journal-title":"IEEE Trans Pattern Anal Mach Intell"},{"key":"840_CR12","unstructured":"Ananthraj P, Venkataramana A (2007) Radial Krawtchouk moments for rotational invariant pattern recognition. In: 6th International conference on information, communications and signal processing, pp 1\u20135"},{"issue":"2","key":"840_CR13","doi-asserted-by":"publisher","first-page":"381","DOI":"10.1016\/j.jvcir.2011.11.008","volume":"23","author":"B Xiao","year":"2012","unstructured":"Xiao B, Ma JF, Cui JT (2012) Radial Tchebichef moment invariants for image recognition. J Vis Commun Image Represent 23(2):381\u2013386","journal-title":"J Vis Commun Image Represent"},{"issue":"12","key":"840_CR14","doi-asserted-by":"publisher","first-page":"994","DOI":"10.1016\/j.imavis.2014.09.002","volume":"32","author":"B Xiao","year":"2014","unstructured":"Xiao B, Wang GY, Li WS (2014) Radial shifted Legendre moments for image analysis and invariant image recognition. Image Vis Comput 32(12):994\u20131006","journal-title":"Image Vis Comput"},{"issue":"8","key":"840_CR15","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 JF, Wang X (2010) Image analysis by Bessel\u2013Fourier moments. Pattern Recogn 43(8):2620\u20132629","journal-title":"Pattern Recogn"},{"issue":"9","key":"840_CR16","doi-asserted-by":"publisher","first-page":"1748","DOI":"10.1364\/JOSAA.19.001748","volume":"19","author":"ZL Ping","year":"2002","unstructured":"Ping ZL, Wu RG, Sheng YL (2002) Image description with Chebyshev\u2013Fourier moments. J Opt Soc Am A Opt Image Sci Vis 19(9):1748\u20131754","journal-title":"J Opt Soc Am A Opt Image Sci Vis"},{"issue":"4","key":"840_CR17","doi-asserted-by":"publisher","first-page":"1245","DOI":"10.1016\/j.patcog.2006.07.016","volume":"40","author":"ZL Ping","year":"2007","unstructured":"Ping ZL, Ren HP, Zou J, Sheng YL, Bo W (2007) Generic orthogonal moments: Jacobi\u2013Fourier moments for invariant image description. Pattern Recogn 40(4):1245\u20131254","journal-title":"Pattern Recogn"},{"key":"840_CR18","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.patcog.2015.09.018","volume":"51","author":"HQ Zhu","year":"2016","unstructured":"Zhu HQ, Yang Y, Gui ZG, Zhu Y, Chen ZH (2016) Image analysis by generalized Chebyshev\u2013Fourier and generalized pseudo-Jacobi\u2013Fourier moments. Pattern Recogn 51:1\u201311","journal-title":"Pattern Recogn"},{"issue":"1","key":"840_CR19","doi-asserted-by":"publisher","first-page":"50","DOI":"10.1364\/JOSAA.24.000050","volume":"24","author":"T Xia","year":"2007","unstructured":"Xia T, Zhu HQ, Shu HS, Haigron P, Luo LM (2007) Image description with generalized pseudo-Zernike moments. J Opt Soc Am A Opt Image Sci Vis 24(1):50\u201359","journal-title":"J Opt Soc Am A Opt Image Sci Vis"},{"issue":"12","key":"840_CR20","doi-asserted-by":"publisher","first-page":"5455","DOI":"10.1109\/TIP.2014.2365353","volume":"23","author":"HQ Zhu","year":"2014","unstructured":"Zhu HQ, Yang Y, Zhu XL, Gui ZG, Shu HZ (2014) General form for obtaining unit disc-based generalized orthogonal moments. IEEE Trans Image Process 23(12):5455\u20135469","journal-title":"IEEE Trans Image Process"},{"issue":"7","key":"840_CR21","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 GY (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":"840_CR22","doi-asserted-by":"publisher","first-page":"90","DOI":"10.1007\/978-3-642-36669-7_12","volume":"7751","author":"XB Dai","year":"2013","unstructured":"Dai XB, Liu TL, Shu HZ, Luo LM (2013) Pseudo-Zernike moments invariants to blur degradation and their use in image recognition. Lect Notes Comput Sci 7751:90\u201397","journal-title":"Lect Notes Comput Sci"},{"key":"840_CR23","doi-asserted-by":"publisher","first-page":"522","DOI":"10.1016\/j.sigpro.2015.10.005","volume":"120","author":"ZH Shao","year":"2016","unstructured":"Shao ZH, Shang YY, Zhang Y, Liu X, Guo G (2016) Robust watermarking using orthogonal Fourier\u2013Mellin moments and chaotic map for double images. Sig Process 120:522\u2013531","journal-title":"Sig Process"},{"issue":"2","key":"840_CR24","doi-asserted-by":"publisher","first-page":"345","DOI":"10.1109\/TIP.2010.2062195","volume":"20","author":"BJ Chen","year":"2011","unstructured":"Chen BJ, Shu HZ, Zhang H, Goatrieux G, Luo LM, Coatrieux JL (2011) Combined invariants to similarity transformation and to blur using orthogonal Zernike moments. IEEE Trans Image Process 20(2):345\u2013360","journal-title":"IEEE Trans Image Process"},{"issue":"4","key":"840_CR25","doi-asserted-by":"publisher","first-page":"631","DOI":"10.1364\/JOSAA.20.000631","volume":"20","author":"HP Ren","year":"2003","unstructured":"Ren HP, Ping ZL, Bo W, Wu WK, Sheng YL (2003) Multidistortion-invariant image recognition with radial harmonic Fourier moments. J Opt Soc Am A Opt Image Sci Vis 20(4):631\u2013637","journal-title":"J Opt Soc Am A Opt Image Sci Vis"},{"issue":"7","key":"840_CR26","doi-asserted-by":"publisher","first-page":"1259","DOI":"10.1109\/TPAMI.2009.119","volume":"32","author":"PT Yap","year":"2010","unstructured":"Yap PT, Jiang XD, Kot AC (2010) Two-dimensional polar harmonic transforms for invariant image representation. IEEE Trans Pattern Anal Mach Intell 32(7):1259\u20131270","journal-title":"IEEE Trans Pattern Anal Mach Intell"},{"issue":"8","key":"840_CR27","doi-asserted-by":"publisher","first-page":"2596","DOI":"10.1016\/j.patcog.2014.02.014","volume":"47","author":"HT Hu","year":"2014","unstructured":"Hu HT, Zhang YD, Shao C, Ju Q (2014) Orthogonal moments based on exponent functions: exponent\u2013Fourier moments. Pattern Recogn 47(8):2596\u20132606","journal-title":"Pattern Recogn"},{"key":"840_CR28","unstructured":"Hoang TV, Tabbone S (2011) Generic polar harmonic transform for invariant image description. In: Proceedings of 18th IEEE international conference on image processing, pp 829\u2013832"},{"key":"840_CR29","doi-asserted-by":"publisher","first-page":"10","DOI":"10.1016\/j.image.2016.04.005","volume":"45","author":"CP Wang","year":"2016","unstructured":"Wang CP, Wang XY, Xia ZQ (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":"840_CR30","doi-asserted-by":"publisher","first-page":"627","DOI":"10.1016\/j.neucom.2015.09.082","volume":"174","author":"XY Wang","year":"2016","unstructured":"Wang XY, Liu YN, Li S, Yang HY, Niu PP (2016) Robust image watermarking approach using polar harmonic transforms based geometric correction. Neurocomputing 174:627\u2013642","journal-title":"Neurocomputing"},{"key":"840_CR31","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.ins.2012.02.062","volume":"199","author":"LD Li","year":"2012","unstructured":"Li LD, Li SS, Abraham A, Pan JS (2012) Geometrically invariant image watermarking using polar harmonic transforms. Inf Sci 199:1\u201319","journal-title":"Inf Sci"},{"issue":"14","key":"840_CR32","doi-asserted-by":"publisher","first-page":"1540018-1","DOI":"10.1142\/S0218127415400180","volume":"25","author":"YF Gan","year":"2015","unstructured":"Gan YF (2015) Research on copy-move image forgery detection using features of discrete polar complex exponent transform. Int J Bifurc Chaos 25(14):1540018-1\u20131540018-15","journal-title":"Int J Bifurc Chaos"},{"key":"840_CR33","doi-asserted-by":"publisher","first-page":"59","DOI":"10.1016\/j.forsciint.2012.10.031","volume":"224","author":"YN Li","year":"2013","unstructured":"Li YN (2013) Image copy-move forgery detection based on polar cosine transform and approximate nearest neighbor searching. Forensic Sci Int 224:59\u201367","journal-title":"Forensic Sci Int"},{"issue":"8","key":"840_CR34","doi-asserted-by":"publisher","first-page":"497","DOI":"10.1016\/j.imavis.2014.04.016","volume":"32","author":"TV Hoang","year":"2014","unstructured":"Hoang TV, Tabbone S (2014) Generic polar harmonic transforms for invariant image representation. Image Vis Comput 32(8):497\u2013509","journal-title":"Image Vis Comput"},{"issue":"6","key":"840_CR35","doi-asserted-by":"publisher","first-page":"698","DOI":"10.1109\/TPAMI.1984.4767594","volume":"6","author":"YS Abu-Mostafa","year":"1984","unstructured":"Abu-Mostafa YS, Psaltis D (1984) Recognitive aspects of moment invariants. IEEE Trans Pattern Anal Mach Intell 6(6):698\u2013706","journal-title":"IEEE Trans Pattern Anal Mach Intell"},{"key":"840_CR36","doi-asserted-by":"publisher","first-page":"471","DOI":"10.1016\/j.patcog.2015.10.005","volume":"52","author":"HT Hu","year":"2016","unstructured":"Hu HT, Ju Q, Shao C (2016) Errata and comments on \u201cErrata and Comments on orthogonal moments based on exponent functions: exponent\u2013Fourier moments\u201d. Pattern Recogn 52:471\u2013476","journal-title":"Pattern Recogn"},{"issue":"4","key":"840_CR37","doi-asserted-by":"publisher","first-page":"1571","DOI":"10.1016\/j.patcog.2014.10.030","volume":"48","author":"B Xiao","year":"2015","unstructured":"Xiao B, Li WS, Wang GY (2015) Errata and comments on \u201cOrthogonal moments based on exponent functions: exponent\u2013Fourier moments\u201d. Pattern Recogn 48(4):1571\u20131573","journal-title":"Pattern Recogn"},{"key":"840_CR38","unstructured":"https:\/\/www1.cs.columbia.edu\/CAVE\/\/software\/softlib\/coil-20.php"},{"key":"840_CR39","unstructured":"https:\/\/www.fileformat.info\/info\/unicode\/font\/arial_bold"},{"issue":"2","key":"840_CR40","doi-asserted-by":"publisher","first-page":"311","DOI":"10.1007\/s10044-012-0273-y","volume":"17","author":"XB Dai","year":"2014","unstructured":"Dai XB, Zhang H, Liu TL, Shu HZ, Luo LM (2014) Legendre moment invariants to blur and affine transformation and their use in image recognition. Pattern Anal Appl 17(2):311\u2013326","journal-title":"Pattern Anal Appl"},{"key":"840_CR41","doi-asserted-by":"crossref","unstructured":"Vedaldi A, Lenc K (2015) MatConvNet\u2014convolutional neural networks for MATLAB. In: Proceedings of the ACM international conference on multimedia","DOI":"10.1145\/2733373.2807412"},{"issue":"4","key":"840_CR42","doi-asserted-by":"publisher","first-page":"496","DOI":"10.1109\/34.3913","volume":"20","author":"CH Teh","year":"1988","unstructured":"Teh CH, Chin RT (1988) On image analysis by the methods of moments. IEEE Trans Pattern Anal Mach Intell 20(4):496\u2013513","journal-title":"IEEE Trans Pattern Anal Mach Intell"}],"container-title":["Pattern Analysis and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10044-019-00840-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10044-019-00840-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10044-019-00840-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,7,25]],"date-time":"2020-07-25T23:21:16Z","timestamp":1595719276000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10044-019-00840-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,7,27]]},"references-count":42,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2020,5]]}},"alternative-id":["840"],"URL":"https:\/\/doi.org\/10.1007\/s10044-019-00840-0","relation":{},"ISSN":["1433-7541","1433-755X"],"issn-type":[{"value":"1433-7541","type":"print"},{"value":"1433-755X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,7,27]]},"assertion":[{"value":"29 December 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 July 2019","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 July 2019","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}