{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T15:30:13Z","timestamp":1759332613162,"version":"3.37.3"},"reference-count":43,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2022,12,21]],"date-time":"2022-12-21T00:00:00Z","timestamp":1671580800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2022,12,21]],"date-time":"2022-12-21T00:00:00Z","timestamp":1671580800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100012165","name":"Key Technologies Research and Development Program","doi-asserted-by":"publisher","award":["2020YFA0714200"],"award-info":[{"award-number":["2020YFA0714200"]}],"id":[{"id":"10.13039\/501100012165","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["No.11931012","No.11901443"],"award-info":[{"award-number":["No.11931012","No.11901443"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["No.11931012 No.11901443 and No.12171379"],"award-info":[{"award-number":["No.11931012 No.11901443 and No.12171379"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comp. Appl. Math."],"published-print":{"date-parts":[[2023,2]]},"DOI":"10.1007\/s40314-022-02145-1","type":"journal-article","created":{"date-parts":[[2022,12,21]],"date-time":"2022-12-21T15:03:01Z","timestamp":1671634981000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Two-dimensional diffeomorphic model for multi-modality image registration"],"prefix":"10.1007","volume":"42","author":[{"given":"Zijuan","family":"Ding","sequence":"first","affiliation":[]},{"given":"Huan","family":"Han","sequence":"additional","affiliation":[]},{"given":"Huinan","family":"Wang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,12,21]]},"reference":[{"key":"2145_CR1","doi-asserted-by":"crossref","unstructured":"Aubert G\u2019 Kornprobst P (eds) (2006) Mathematical problems in image processing: partial differential equations and the calculus of variations. Springer, New York","DOI":"10.1007\/978-0-387-44588-5"},{"issue":"8","key":"2145_CR2","doi-asserted-by":"publisher","first-page":"1788","DOI":"10.1109\/TMI.2019.2897538","volume":"38","author":"G Balakrishnan","year":"2019","unstructured":"Balakrishnan G, Zhao A, Sabuncu MR et al (2019) Voxelmorph: a learning framework for deformable medical image registration. IEEE Trans Med Imaging 38(8):1788\u20131800","journal-title":"IEEE Trans Med Imaging"},{"issue":"12","key":"2145_CR3","doi-asserted-by":"publisher","first-page":"12353","DOI":"10.1016\/j.aej.2022.06.018","volume":"61","author":"N Begum","year":"2022","unstructured":"Begum N, Badshah N, Rada L et al (2022) An improved multi-modal joint segmentation and registration model based on Bhattacharyya distance measure. Alex Eng J 61(12):12353\u201312365","journal-title":"Alex Eng J"},{"issue":"1","key":"2145_CR4","doi-asserted-by":"publisher","first-page":"234","DOI":"10.3150\/09-BEJ203","volume":"16","author":"A Budhiraja","year":"2010","unstructured":"Budhiraja A, Dupuis P, Maroulas V (2010) Large deviations for stochastic flows of diffeomorphisms. Bernoulli 16(1):234\u2013257","journal-title":"Bernoulli"},{"key":"2145_CR5","first-page":"419","volume-title":"Inverse consistent deformable image registration. The legacy of Alladi Ramakrishnan in the mathematical sciences","author":"Y Chen","year":"2010","unstructured":"Chen Y, Ye X (2010) Inverse consistent deformable image registration. The legacy of Alladi Ramakrishnan in the mathematical sciences. Springer, New York, pp 419\u2013440"},{"key":"2145_CR6","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-4383-8","volume-title":"A course in functional analysis","author":"JB Conway","year":"2007","unstructured":"Conway JB (2007) A course in functional analysis. Springer, New York"},{"issue":"2","key":"2145_CR7","doi-asserted-by":"publisher","first-page":"957","DOI":"10.1137\/17M1122906","volume":"11","author":"N Debroux","year":"2018","unstructured":"Debroux N, Guyader CL (2018) A joint segmentation\/registration model based on a nonlocal characterization of weighted total variation and nonlocal shape descriptors. SIAM J Imaging Sci 11(2):957\u2013990","journal-title":"SIAM J Imaging Sci"},{"key":"2145_CR8","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4471-2807-6","volume-title":"Functional spaces for the theory of elliptic partial differential equations","author":"F Demengel","year":"2012","unstructured":"Demengel F, Demengel G, Ern\u00e9 R (2012) Functional spaces for the theory of elliptic partial differential equations. Springer, London"},{"key":"2145_CR9","volume-title":"Partial differential equations","author":"LC Evans","year":"2010","unstructured":"Evans LC (2010) Partial differential equations, 2nd edn. American Mathematical Society, Providence","edition":"2"},{"issue":"3","key":"2145_CR10","doi-asserted-by":"publisher","first-page":"225","DOI":"10.1023\/B:VISI.0000036836.66311.97","volume":"60","author":"S Haker","year":"2004","unstructured":"Haker S, Zhu L, Tannenbaum A et al (2004) Optimal mass transport for registration and warping. Int J Comput Vis 60(3):225\u2013240","journal-title":"Int J Comput Vis"},{"issue":"6","key":"2145_CR11","doi-asserted-by":"publisher","first-page":"1263","DOI":"10.3934\/ipi.2018053","volume":"12","author":"H Han","year":"2018","unstructured":"Han H (2018) A variational model with fractional-order regularization term arising in registration of diffusion tensor image. Inverse Probl Imaging 12(6):1263\u20131291","journal-title":"Inverse Probl Imaging"},{"issue":"3","key":"2145_CR12","doi-asserted-by":"publisher","first-page":"1240","DOI":"10.1137\/19M1260621","volume":"13","author":"H Han","year":"2020","unstructured":"Han H, Wang Z (2020) A diffeomorphic image registration model with fractional-order regularization and Cauchy-Riemann constraint. SIAM J Imaging Sci 13(3):1240\u20131271","journal-title":"SIAM J Imaging Sci"},{"issue":"113","key":"2145_CR13","first-page":"576","volume":"394","author":"H Han","year":"2021","unstructured":"Han H, Wang A (2021) A fast multi grid algorithm for 2D diffeomorphic image registration model. J Comput Appl Math 394(113):576","journal-title":"J Comput Appl Math"},{"key":"2145_CR14","doi-asserted-by":"publisher","DOI":"10.1051\/m2an\/2022080","author":"H Han","year":"2022","unstructured":"Han H, Wang Z (2022) 3D diffeomorphic image registration with Cauchy\u2013Riemann constraint and lower bounded deformation divergence. ESAIM Math Model Numer Anal. https:\/\/doi.org\/10.1051\/m2an\/2022080. (accepted)","journal-title":"ESAIM Math Model Numer Anal"},{"issue":"3","key":"2145_CR15","doi-asserted-by":"publisher","first-page":"1431","DOI":"10.1137\/21M1455929","volume":"15","author":"H Han","year":"2022","unstructured":"Han H, Wang Z, Zhang Y (2022) Multiscale approach for three-dimensional conformal image registration. SIAM J Imaging Sci 15(3):1431\u20131468","journal-title":"SIAM J Imaging Sci"},{"issue":"3","key":"2145_CR16","doi-asserted-by":"publisher","first-page":"831","DOI":"10.1137\/040611124","volume":"27","author":"S Henn","year":"2005","unstructured":"Henn S (2005) A multigrid method for a fourth-order diffusion equation with application to image processing. SIAM J Sci Comput 27(3):831\u2013849","journal-title":"SIAM J Sci Comput"},{"issue":"3","key":"2145_CR17","doi-asserted-by":"publisher","first-page":"1214","DOI":"10.1007\/s10915-017-0396-9","volume":"72","author":"T Hou","year":"2017","unstructured":"Hou T, Tang T, Yang J (2017) Numerical analysis of fully discretized Crank\u2013Nicolson scheme for fractional-in-space Allen\u2013Cahn equations. J Sci Comput 72(3):1214\u20131231","journal-title":"J Sci Comput"},{"issue":"10","key":"2145_CR18","doi-asserted-by":"publisher","first-page":"2589","DOI":"10.1109\/TMI.2021.3059282","volume":"40","author":"W Huang","year":"2021","unstructured":"Huang W, Yang H, Liu X et al (2021) A coarse-to-fine deformable transformation framework for unsupervised multi-contrast MR image registration with dual consistency constraint. IEEE Trans Med Imaging 40(10):2589\u20132599","journal-title":"IEEE Trans Med Imaging"},{"issue":"5","key":"2145_CR19","doi-asserted-by":"publisher","first-page":"1165","DOI":"10.1016\/S0031-3203(02)00081-X","volume":"36","author":"S Kaneko","year":"2003","unstructured":"Kaneko S, Satoh Y, Igarashi S (2003) Using selective correlation coefficient for robust image registration. Pattern Recognit 36(5):1165\u20131173","journal-title":"Pattern Recognit"},{"key":"2145_CR20","doi-asserted-by":"crossref","unstructured":"Klein A, Kroon DJ, Hoogeveen Y et\u00a0al (2011) Multimodal image registration by edge attraction and regularization using a b-spline grid. In: Medical imaging 2011: image processing, SPIE, pp 632\u2013639","DOI":"10.1117\/12.878267"},{"key":"2145_CR21","unstructured":"Kroon DJ (2008) Multimodality non-rigid demon algorithm image registration. MatlabCentral. https:\/\/www.mathworks.com\/matlabcentral\/fileexchange\/21451-multimodality-non-rigid-demon-algorithm-image-registration. Accessed 28 Feb 2022"},{"key":"2145_CR22","doi-asserted-by":"crossref","unstructured":"Kroon DJ, Slump CH (2009) MRI modality transformation in demon registration. In: 2009 IEEE international symposium on biomedical imaging: from nano to macro, pp 963\u2013966","DOI":"10.1109\/ISBI.2009.5193214"},{"key":"2145_CR23","doi-asserted-by":"crossref","unstructured":"Li J, Wang Y, Wang S et al (2021) Landmark-guided rigid registration for temporomandibular joint MRI-CBCT images with large field-of-view difference. In: MLMI 2021. Springer, Cham, pp 527\u2013536","DOI":"10.1007\/978-3-030-87589-3_54"},{"key":"2145_CR24","unstructured":"Lombaert H (2012) Diffeomorphic log demons image registration. MATLAB Central File Exchange. https:\/\/www.mathworks.com\/matlabcentral\/fileexchange\/39194-diffeomorphic-log-demons-image-registration. Accessed 08 Feb 2022"},{"issue":"3","key":"2145_CR25","doi-asserted-by":"publisher","first-page":"519","DOI":"10.1134\/S1054661811020696","volume":"21","author":"P Lukashevich","year":"2011","unstructured":"Lukashevich P, Zalesky B, Ablameyko S (2011) Medical image registration based on SURF detector. Pattern Recognit Image Anal 21(3):519\u2013521","journal-title":"Pattern Recognit Image Anal"},{"issue":"2","key":"2145_CR26","doi-asserted-by":"publisher","first-page":"187","DOI":"10.1109\/42.563664","volume":"16","author":"F Maes","year":"1997","unstructured":"Maes F, Collignon A, Vandermeulen D et al (1997) Multimodality image registration by maximization of mutual information. IEEE Trans Med Imaging 16(2):187\u2013198","journal-title":"IEEE Trans Med Imaging"},{"issue":"10","key":"2145_CR27","doi-asserted-by":"publisher","first-page":"1699","DOI":"10.1109\/JPROC.2003.817864","volume":"91","author":"F Maes","year":"2003","unstructured":"Maes F, Vandermeulen D, Suetens P (2003) Medical image registration using mutual information. Proc IEEE 91(10):1699\u20131722","journal-title":"Proc IEEE"},{"key":"2145_CR28","volume-title":"Numerical solution of partial differential equations","author":"T Meis","year":"2012","unstructured":"Meis T, Marcowitz U (2012) Numerical solution of partial differential equations, vol 32. Springer Science and Business Media, Berlin"},{"key":"2145_CR29","first-page":"511","volume-title":"A duality based algorithm for TV-$$L^1$$-optical-flow image registration. MICCAI","author":"T Pock","year":"2007","unstructured":"Pock T, Urschler M, Zach C et al (2007) A duality based algorithm for TV-$$L^1$$-optical-flow image registration. MICCAI. Springer, Heidelberg, pp 511\u2013518"},{"key":"2145_CR30","first-page":"249","volume-title":"Unsupervised deformable registration for multi-modal images via disentangled representations. IPMI 2019","author":"C Qin","year":"2019","unstructured":"Qin C, Shi B, Liao R et al (2019) Unsupervised deformable registration for multi-modal images via disentangled representations. IPMI 2019. Springer, Cham, pp 249\u2013261"},{"issue":"3\u20134","key":"2145_CR31","doi-asserted-by":"publisher","first-page":"441","DOI":"10.1007\/BF02024507","volume":"10","author":"A R\u00e9nyi","year":"1959","unstructured":"R\u00e9nyi A (1959) On measures of dependence. Acta Math Hung 10(3\u20134):441\u2013451","journal-title":"Acta Math Hung"},{"key":"2145_CR32","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1016\/j.media.2016.06.031","volume":"33","author":"JA Schnabel","year":"2016","unstructured":"Schnabel JA, Heinrich MP, Papie\u017c BW et al (2016) Advances and challenges in deformable image registration: from image fusion to complex motion modelling. Med Image Anal 33:145\u2013148","journal-title":"Med Image Anal"},{"key":"2145_CR33","first-page":"72","volume":"7623","author":"J Shi","year":"2010","unstructured":"Shi J, Chen Y, Rao M et al (2010) A statistical similarity measure for non-rigid multi-modal image registration. Proc SPIE 7623:72\u201383","journal-title":"Proc SPIE"},{"issue":"294","key":"2145_CR34","doi-asserted-by":"publisher","first-page":"1703","DOI":"10.1090\/S0025-5718-2015-02917-2","volume":"84","author":"W Tian","year":"2015","unstructured":"Tian W, Zhou H, Deng W (2015) A class of second order difference approximations for solving space fractional diffusion equations. Math Comput 84(294):1703\u20131727","journal-title":"Math Comput"},{"key":"2145_CR35","first-page":"754","volume-title":"Symmetric log-domain diffeomorphic registration: a demons-based approach. MICCAI","author":"T Vercauteren","year":"2008","unstructured":"Vercauteren T, Pennec X, Perchant A et al (2008) Symmetric log-domain diffeomorphic registration: a demons-based approach. MICCAI. Springer, Heidelberg, pp 754\u2013761"},{"issue":"1","key":"2145_CR36","doi-asserted-by":"publisher","first-page":"S61","DOI":"10.1016\/j.neuroimage.2008.10.040","volume":"45","author":"T Vercauteren","year":"2009","unstructured":"Vercauteren T, Pennec X, Perchant A et al (2009) Diffeomorphic demons: efficient non-parametric image registration. Neuroimage 45(1):S61\u2013S72","journal-title":"Neuroimage"},{"key":"2145_CR37","doi-asserted-by":"crossref","unstructured":"Von\u00a0Klinski S, Derz C, Weese D et\u00a0al (2000) Model-based image processing using snakes and mutual information. In: Medical imaging 2000: image processing, pp 1053\u20131064","DOI":"10.1117\/12.387610"},{"issue":"1","key":"2145_CR38","doi-asserted-by":"publisher","first-page":"35","DOI":"10.1016\/S1361-8415(01)80004-9","volume":"1","author":"WM Wells III","year":"1996","unstructured":"Wells WM III, Viola P, Atsumi H et al (1996) Multi-modal volume registration by maximization of mutual information. Med Image Anal 1(1):35\u201351","journal-title":"Med Image Anal"},{"key":"2145_CR39","doi-asserted-by":"crossref","unstructured":"Yang X, Shen C, Li F, et\u00a0al (2015) A combination of the total variation filter and a fourth-order filter for image registration. Math Probl Eng 2015:1\u201316","DOI":"10.1155\/2015\/235314"},{"key":"2145_CR40","doi-asserted-by":"publisher","first-page":"442","DOI":"10.1016\/j.jcp.2015.02.021","volume":"293","author":"J Zhang","year":"2015","unstructured":"Zhang J, Chen K (2015) Variational image registration by a total fractional-order variation model. J Comput Phys 293:442\u2013461","journal-title":"J Comput Phys"},{"issue":"8","key":"2145_CR41","doi-asserted-by":"publisher","first-page":"1261","DOI":"10.1007\/s10851-018-0811-3","volume":"60","author":"D Zhang","year":"2018","unstructured":"Zhang D, Chen K (2018) A novel diffeomorphic model for image registration and its algorithm. J Math Imaging Vis 60(8):1261\u20131283","journal-title":"J Math Imaging Vis"},{"issue":"23\u201324","key":"2145_CR42","doi-asserted-by":"publisher","first-page":"10740","DOI":"10.1016\/j.apm.2016.08.009","volume":"40","author":"J Zhang","year":"2016","unstructured":"Zhang J, Chen K, Yu B (2016a) An improved discontinuity-preserving image registration model and its fast algorithm. Appl Math Model 40(23\u201324):10740\u201310759","journal-title":"Appl Math Model"},{"issue":"12","key":"2145_CR43","doi-asserted-by":"publisher","first-page":"2887","DOI":"10.1016\/j.camwa.2016.10.018","volume":"72","author":"J Zhang","year":"2016","unstructured":"Zhang J, Chen K, Yu B (2016b) A novel high-order functional based image registration model with inequality constraint. Comput Math Appl 72(12):2887\u20132899","journal-title":"Comput Math Appl"}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-022-02145-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40314-022-02145-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-022-02145-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,6]],"date-time":"2024-09-06T11:58:09Z","timestamp":1725623889000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40314-022-02145-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,12,21]]},"references-count":43,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2023,2]]}},"alternative-id":["2145"],"URL":"https:\/\/doi.org\/10.1007\/s40314-022-02145-1","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"type":"print","value":"2238-3603"},{"type":"electronic","value":"1807-0302"}],"subject":[],"published":{"date-parts":[[2022,12,21]]},"assertion":[{"value":"4 July 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 November 2022","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 November 2022","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 December 2022","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 we have no conflicts of interest or competing interests with any other person or organization that could affect the work, and no other relationship or activity that might affect the submitted work. Most of the data in this work come from other papers or open data on the Internet, so we declare to keep the data open and transparent in this work.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"17"}}