{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T20:18:08Z","timestamp":1777666688164,"version":"3.51.4"},"reference-count":38,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2012,10,19]],"date-time":"2012-10-19T00:00:00Z","timestamp":1350604800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Med Biol Eng Comput"],"published-print":{"date-parts":[[2013,2]]},"DOI":"10.1007\/s11517-012-0972-y","type":"journal-article","created":{"date-parts":[[2012,10,18]],"date-time":"2012-10-18T12:46:09Z","timestamp":1350564369000},"page":"89-101","source":"Crossref","is-referenced-by-count":7,"title":["Using three-dimensional multigrid-based snake and multiresolution image registration for reconstruction of cranial defect"],"prefix":"10.1007","volume":"51","author":[{"given":"Yuan-Lin","family":"Liao","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chia-Feng","family":"Lu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chieh-Tsai","family":"Wu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiann-Der","family":"Lee","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shih-Tseng","family":"Lee","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yung-Nien","family":"Sun","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yu-Te","family":"Wu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2012,10,19]]},"reference":[{"key":"972_CR1","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1055\/s-2008-1058580","volume":"8","author":"C Agner","year":"1998","unstructured":"Agner C, Dujovny M, Evenhouse R, Charbel FT, Sadler L (1998) Stereolithography for posterior fossa cranioplasty. Skull Base Surg 8:81\u201386","journal-title":"Skull Base Surg"},{"key":"972_CR2","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611971538","volume-title":"Templates for the solution of linear systems: building blocks for iterative methods","author":"R Barrett","year":"1994","unstructured":"Barrett R (1994) Templates for the solution of linear systems: building blocks for iterative methods. Society for Industrial and Applied Mathematics, Philadelphia"},{"key":"972_CR3","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898719505","volume-title":"A multigrid tutorial","author":"WL Briggs","year":"2000","unstructured":"Briggs WL, Henson VE, McCormick SF (2000) A multigrid tutorial, 2nd edn. Society for Industrial and Applied Mathematics, Philadelphia","edition":"2"},{"key":"972_CR4","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1002\/nla.475","volume":"13","author":"MM Bronstein","year":"2006","unstructured":"Bronstein MM, Bronstein AM, Kimmel R, Yavneh I (2006) Multigrid multidimensional scaling. Numer Linear Algebr Appl 13:149\u2013171","journal-title":"Numer Linear Algebr Appl"},{"key":"972_CR5","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1109\/42.552059","volume":"16","author":"JC Carr","year":"1997","unstructured":"Carr JC, Fright WR, Beatson RK (1997) Surface interpolation with radial basis functions for medical imaging. IEEE Trans Med Imaging 16:96\u2013107","journal-title":"IEEE Trans Med Imaging"},{"key":"972_CR6","doi-asserted-by":"crossref","first-page":"344","DOI":"10.1097\/00001665-200603000-00024","volume":"17","author":"CS Chong","year":"2006","unstructured":"Chong CS, Lee HP, Kumar AS (2006) Automatic hole repairing for cranioplasty using Bezier surface approximation. J Craniofac Surg 17:344\u2013352","journal-title":"J Craniofac Surg"},{"key":"972_CR7","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1023\/A:1020826424915","volume":"50","author":"D Cremers","year":"2002","unstructured":"Cremers D, Tischh\u00e4user F, Weickert J, Schn\u00f6rr C (2002) Diffusion snakes: introducing statistical shape knowledge into the Mumford\u2013Shah functional. Int J Comput Vis 50:295\u2013313","journal-title":"Int J Comput Vis"},{"key":"972_CR8","doi-asserted-by":"crossref","first-page":"710","DOI":"10.1016\/S0531-5131(03)00514-4","volume":"1256","author":"D Dean","year":"2003","unstructured":"Dean D, Min K-J (2003) Deformable templates for preoperative computer-aided design and fabrication of large cranial implants. Int Congr Ser 1256:710\u2013715","journal-title":"Int Congr Ser"},{"key":"972_CR9","doi-asserted-by":"crossref","first-page":"200","DOI":"10.1054\/bjps.1999.3268","volume":"53","author":"PS D\u2019Urso","year":"2000","unstructured":"D\u2019Urso PS, Effeney DJ, Earwaker WJ, Barker TM, Redmond MJ, Thompson RG, Tomlinson FH (2000) Custom cranioplasty using stereolithography and acrylic. Br J Plast Surg 53:200\u2013204","journal-title":"Br J Plast Surg"},{"key":"972_CR10","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1007\/s00791-004-0150-3","volume":"7","author":"C Frohn-Schauf","year":"2004","unstructured":"Frohn-Schauf C, Henn S, Witsch K (2004) Nonlinear multigrid methods for total variation image denoising. Comput Vis Sci 7:199\u2013206","journal-title":"Comput Vis Sci"},{"key":"972_CR11","first-page":"209","volume-title":"Proceedings of the 24th annual conference on computer graphics and interactive techniques, Los Angeles","author":"M Garland","year":"1997","unstructured":"Garland M, Heckbert PS (1997) Surface simplification using quadric error metrics. In: Owen GS, Whitted T, Mones-Hattal B (eds) Proceedings of the 24th annual conference on computer graphics and interactive techniques, Los Angeles. ACM Press\/Addison-Wesley Publishing Co., New York, pp 209\u2013216"},{"key":"972_CR12","volume-title":"Digital image processing","author":"RC Gonzalez","year":"2008","unstructured":"Gonzalez RC, Woods RE (2008) Digital image processing. Pearson\/Prentice Hall, Upper Saddle River"},{"key":"972_CR13","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1108\/13552540410539030","volume":"10","author":"S Gopakumar","year":"2004","unstructured":"Gopakumar S (2004) RP in medicine: a case study in cranial reconstructive surgery. Rapid Prototyp J 10:207\u2013221","journal-title":"Rapid Prototyp J"},{"key":"972_CR14","doi-asserted-by":"crossref","first-page":"1594","DOI":"10.1137\/040608106","volume":"27","author":"E Haber","year":"2006","unstructured":"Haber E, Modersitzki J (2006) A multilevel method for image registration. SIAM J Sci Comput 27:1594\u20131607","journal-title":"SIAM J Sci Comput"},{"key":"972_CR15","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1049\/iet-ipr:20050225","volume":"1","author":"X Han","year":"2007","unstructured":"Han X, Xu C, Prince JL (2007) Fast numerical scheme for gradient vector flow computation using a multigrid method. IET Image Process 1:48\u201355","journal-title":"IET Image Process"},{"key":"972_CR16","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1007\/BF00133570","volume":"1","author":"M Kass","year":"1987","unstructured":"Kass M, Witkin A, Terzopoulos D (1987) Snakes: active contour models. Int J Comput Vis 1:321\u2013331","journal-title":"Int J Comput Vis"},{"key":"972_CR17","doi-asserted-by":"crossref","first-page":"162","DOI":"10.4103\/0976-3147.83584","volume":"2","author":"B Kucukyuruk","year":"2011","unstructured":"Kucukyuruk B, Abuzayed B, Sanus G, Aydin S, Aydin S (2011) Cranioplasty: review of materials and techniques. J Neurosci Rural Pract 2:162\u2013167","journal-title":"J Neurosci Rural Pract"},{"key":"972_CR18","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1016\/j.jocn.2008.04.001","volume":"16","author":"S-C Lee","year":"2009","unstructured":"Lee S-C, Wu C-T, Lee S-T, Chen P-J (2009) Cranioplasty using polymethyl methacrylate prostheses. J Clin Neurosci 16:56\u201363","journal-title":"J Clin Neurosci"},{"key":"972_CR19","first-page":"269","volume-title":"Proceeding of the 2nd international con-ference on bioinformatics and biomedical technology (ICBBT)","author":"Y-L Liao","year":"2010","unstructured":"Liao Y-L, Sun Y-N, Lu C-F, Wu Y-T, Wu C-T, Lee S-T, Lee J-D (2010) Skull-based registration of intra-subject CT images: the effects of different resolutions and partial contents. In: Mahadevan V, Zhou J (eds) Proceeding of the 2nd international con-ference on bioinformatics and biomedical technology (ICBBT). Research Publishing Services, Singapore, pp 269\u2013272"},{"key":"972_CR20","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1007\/s11517-010-0720-0","volume":"49","author":"Y-L Liao","year":"2011","unstructured":"Liao Y-L, Lu C-F, Sun Y-N, Wu C-T, Lee J-D, Lee S-T, Wu Y-T (2011) Three-dimensional reconstruction of cranial defect using active contour model and image registration. Med Biol Eng Comput 49:203\u2013211","journal-title":"Med Biol Eng Comput"},{"key":"972_CR21","doi-asserted-by":"crossref","first-page":"671","DOI":"10.1007\/s11517-010-0724-9","volume":"49","author":"Y-L Liao","year":"2011","unstructured":"Liao Y-L, Sun Y-N, Guo W-Y, Chou Y-H, Hsieh J-C, Wu Y-T (2011) A hybrid strategy to integrate surface-based and mutual-information-based methods for co-registering brain SPECT and MR images. Med Biol Eng Comput 49:671\u2013685","journal-title":"Med Biol Eng Comput"},{"key":"972_CR22","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1145\/37402.37422","volume":"21","author":"WE Lorensen","year":"1987","unstructured":"Lorensen WE, Cline HE (1987) Marching cubes: a high resolution 3D surface construction algorithm. ACM SIGGRAPH Comput Graph\u00a021:163\u2013169","journal-title":"ACM SIGGRAPH Comput Graph"},{"key":"972_CR23","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1109\/38.920624","volume":"21","author":"DP Luebke","year":"2001","unstructured":"Luebke DP (2001) A developer\u2019s survey of polygonal simplification algorithms. IEEE Comput Graph Appl 21:24\u201335","journal-title":"IEEE Comput Graph Appl"},{"key":"972_CR24","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1016\/S1361-8415(99)80030-9","volume":"3","author":"F Maes","year":"1999","unstructured":"Maes F, Vandermeulen D, Suetens P (1999) Comparative evaluation of multiresolution optimization strategies for multimodality image registration by maximization of mutual information. Med Image Anal 3:373\u2013386","journal-title":"Med Image Anal"},{"key":"972_CR25","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1080\/03091900600700749","volume":"32","author":"E Maravelakis","year":"2008","unstructured":"Maravelakis E, David K, Antoniadis A, Manios A, Bilalis N, Papaharilaou Y (2008) Reverse engineering techniques for cranioplasty: a case study. J Med Eng Technol 32:115\u2013121","journal-title":"J Med Eng Technol"},{"key":"972_CR26","first-page":"44","volume":"5","author":"S Melax","year":"1998","unstructured":"Melax S (1998) A simple, fast, and effective polygon reduction algorithm. Game Dev 5:44\u201349","journal-title":"Game Dev"},{"key":"972_CR27","doi-asserted-by":"crossref","first-page":"202","DOI":"10.1097\/01.prs.0000187152.48402.17","volume":"117","author":"K Movassaghi","year":"2006","unstructured":"Movassaghi K, Ver Halen J, Ganchi P, Amin-Hanjani S, Mesa J, Yaremchuk MJ (2006) Cranioplasty with subcutaneously preserved autologous bone grafts. Plast Reconstr Surg 117:202\u2013206","journal-title":"Plast Reconstr Surg"},{"key":"972_CR28","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1109\/TIP.2006.884952","volume":"16","author":"G Papandreou","year":"2007","unstructured":"Papandreou G, Maragos P (2007) Multigrid geometric active contour models. IEEE Trans Image Process 16:229\u2013240","journal-title":"IEEE Trans Image Process"},{"key":"972_CR29","doi-asserted-by":"crossref","first-page":"737","DOI":"10.1109\/42.802752","volume":"18","author":"DL Pham","year":"1999","unstructured":"Pham DL, Prince JL (1999) Adaptive fuzzy segmentation of magnetic resonance images. IEEE Trans Med Imaging 18:737\u2013752","journal-title":"IEEE Trans Med Imaging"},{"key":"972_CR30","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1016\/S0262-8856(00)00054-8","volume":"19","author":"JPW Pluim","year":"2001","unstructured":"Pluim JPW, Maintz JBA, Viergever MA (2001) Mutual information matching in multiresolution contexts. Image Vis Comput 19:45\u201352","journal-title":"Image Vis Comput"},{"key":"972_CR31","volume-title":"Numerical recipes in C: the art of scientific computing","author":"WH Press","year":"1992","unstructured":"Press WH (1992) Numerical recipes in C: the art of scientific computing. Cambridge University Press, Cambridge"},{"key":"972_CR32","doi-asserted-by":"crossref","first-page":"1108","DOI":"10.1145\/1141911.1142001","volume":"25","author":"L Shi","year":"2006","unstructured":"Shi L, Yu Y, Bell N, Feng W-W (2006) A fast multigrid algorithm for mesh deformation. ACM Trans Graph\u00a025:1108\u20131117","journal-title":"ACM Trans Graph"},{"key":"972_CR33","doi-asserted-by":"crossref","first-page":"1233","DOI":"10.1097\/01.PRS.0000046048.77472.23","volume":"111","author":"PJ Taub","year":"2003","unstructured":"Taub PJ, Rudkin GH, Clearihue WJ, Miller TA (2003) Prefabricated alloplastic implants for cranial defects. Plast Reconstr Surg 111:1233\u20131240","journal-title":"Plast Reconstr Surg"},{"key":"972_CR34","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1109\/TPAMI.1986.4767767","volume":"8","author":"D Terzopoulos","year":"1986","unstructured":"Terzopoulos D (1986) Image analysis using multigrid relaxation methods. IEEE Trans Pattern Anal Mach Intell 8:129\u2013139","journal-title":"IEEE Trans Pattern Anal Mach Intell"},{"key":"972_CR35","volume-title":"An Introduction to Multigrid Methods","author":"P Wesseling","year":"2004","unstructured":"Wesseling P (2004) An Introduction to Multigrid Methods. R.T. Edwards, Philadelphia"},{"key":"972_CR36","first-page":"9","volume-title":"9th international conference on medical image computing and computer assisted intervention (MICCAI), LNCS 4190","author":"T Wu","year":"2006","unstructured":"Wu T, Engelhardt M, Fieten L, Popovic A, Radermacher K (2006) Anatomically constrained deformation for design of cranial implant: methodology and validation. In: Larsen R, Nielsen M, Sporring J (eds) 9th international conference on medical image computing and computer assisted intervention (MICCAI), LNCS 4190. Springer, Berlin, pp 9\u201316"},{"key":"972_CR37","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1177\/0983911509102348","volume":"24","author":"WZ Wu","year":"2009","unstructured":"Wu WZ, Zhang Y, Li H, Wang WS (2009) Fabrication of repairing skull bone defects based on the rapid prototyping. J Bioact Compat Polym 24:125\u2013136","journal-title":"J Bioact Compat Polym"},{"key":"972_CR38","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1007\/BF01456175","volume":"96","author":"T Yamashima","year":"1989","unstructured":"Yamashima T (1989) Cranioplasty with hydroxylapatite ceramic plates that can easily be trimmed during surgery. Acta Neurochir 96:149\u2013453","journal-title":"Acta Neurochir"}],"container-title":["Medical & Biological Engineering & Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11517-012-0972-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11517-012-0972-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11517-012-0972-y","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,1]],"date-time":"2019-06-01T12:10:09Z","timestamp":1559391009000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11517-012-0972-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,10,19]]},"references-count":38,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2013,2]]}},"alternative-id":["972"],"URL":"https:\/\/doi.org\/10.1007\/s11517-012-0972-y","relation":{},"ISSN":["0140-0118","1741-0444"],"issn-type":[{"value":"0140-0118","type":"print"},{"value":"1741-0444","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,10,19]]}}}