{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T12:23:33Z","timestamp":1782908613399,"version":"3.54.5"},"publisher-location":"Cham","reference-count":27,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783031923685","type":"print"},{"value":"9783031923692","type":"electronic"}],"license":[{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"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":[],"published-print":{"date-parts":[[2025]]},"DOI":"10.1007\/978-3-031-92369-2_23","type":"book-chapter","created":{"date-parts":[[2025,5,16]],"date-time":"2025-05-16T09:17:09Z","timestamp":1747387029000},"page":"298-310","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["An Approximated $$L_{1}$$ Curvature-Based Method for\u00a0Implicit Surface Reconstruction from\u00a0Point Cloud"],"prefix":"10.1007","author":[{"given":"Ho","family":"Law","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sung Ha","family":"Kang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wei","family":"Zhu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2025,5,17]]},"reference":[{"issue":"1","key":"23_CR1","doi-asserted-by":"publisher","first-page":"1","DOI":"10.3934\/ipi.2017001","volume":"11","author":"E Bae","year":"2017","unstructured":"Bae, E., Tai, X.C., Zhu, W.: Augmented Lagrangian method for an Euler\u2019s elastica based segmentation model that promotes convex contours. Inverse Probl. Imaging 11(1), 1\u201323 (2017)","journal-title":"Inverse Probl. Imaging"},{"issue":"1","key":"23_CR2","doi-asserted-by":"publisher","first-page":"566","DOI":"10.1137\/130939493","volume":"47","author":"K Bredies","year":"2015","unstructured":"Bredies, K., Pock, T., Wirth, B.: A convex, lower semicontinuous approximation of Euler\u2019s elastica energy. SIAM J. Math. Anal. 47(1), 566\u2013613 (2015)","journal-title":"SIAM J. Math. Anal."},{"issue":"1","key":"23_CR3","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1023\/A:1007979827043","volume":"22","author":"V Caselles","year":"1997","unstructured":"Caselles, V., Kimmel, R., Sapiro, G.: Geodesic active contours. Int. J. Comput. Vision 22(1), 61\u201379 (1997)","journal-title":"Int. J. Comput. Vision"},{"key":"23_CR4","doi-asserted-by":"crossref","unstructured":"Cui, G., Law, H., Kang, S.H.: Surface reconstruction from noisy point cloud using directional G-norm, pp. 94\u2013106 (2023)","DOI":"10.1007\/978-3-031-31975-4_8"},{"issue":"2","key":"23_CR5","doi-asserted-by":"publisher","first-page":"1190","DOI":"10.1137\/18M1226361","volume":"12","author":"LJ Deng","year":"2019","unstructured":"Deng, L.J., Glowinski, R., Tai, X.C.: A new operator splitting method for the Euler elastica model for image smoothing. SIAM J. Imag. Sci. 12(2), 1190\u20131230 (2019)","journal-title":"SIAM J. Imag. Sci."},{"key":"23_CR6","doi-asserted-by":"crossref","unstructured":"Guillard, B., Stella, F., Fua, P.: MeshUDF: fast and differentiable meshing of unsigned distance field networks. In: European Conference on Computer Vision (2022)","DOI":"10.1007\/978-3-031-20062-5_33"},{"issue":"4","key":"23_CR7","doi-asserted-by":"publisher","first-page":"1834","DOI":"10.1137\/20M1314525","volume":"13","author":"Y He","year":"2020","unstructured":"He, Y., Kang, S.H., Liu, H.: Curvature regularized surface reconstruction from point clouds. SIAM J. Imag. Sci. 13(4), 1834\u20131859 (2020)","journal-title":"SIAM J. Imag. Sci."},{"key":"23_CR8","doi-asserted-by":"crossref","unstructured":"Hoppe, H., DeRose, T., Duchamp, T., McDonald, J., Stuetzle, W.: Surface reconstruction from unorganized points. In: Proceedings of the 19th Annual Conference on Computer Graphics and Interactive Techniques, pp. 71\u201378 (1992)","DOI":"10.1145\/133994.134011"},{"key":"23_CR9","doi-asserted-by":"crossref","unstructured":"Krishnamurthy, V., Levoy, M.: Fitting smooth surfaces to dense polygon meshes. In: Proceedings of the 23rd Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 1996, pp. 313\u2013324. Association for Computing Machinery, New York (1996)","DOI":"10.1145\/237170.237270"},{"issue":"2","key":"23_CR10","doi-asserted-by":"publisher","first-page":"A675","DOI":"10.1137\/110846634","volume":"35","author":"R Lai","year":"2013","unstructured":"Lai, R., Tai, X.C., Chan, T.F.: A ridge and corner preserving model for surface restoration. SIAM J. Sci. Comput. 35(2), A675\u2013A695 (2013)","journal-title":"SIAM J. Sci. Comput."},{"issue":"2","key":"23_CR11","doi-asserted-by":"publisher","first-page":"577","DOI":"10.1007\/s10915-012-9674-8","volume":"54","author":"J Liang","year":"2013","unstructured":"Liang, J., Park, F., Zhao, H.: Robust and efficient implicit surface reconstruction for point clouds based on convexified image segmentation. J. Sci. Comput. 54(2), 577\u2013602 (2013)","journal-title":"J. Sci. Comput."},{"issue":"1","key":"23_CR12","doi-asserted-by":"publisher","first-page":"A290","DOI":"10.1137\/23M1552772","volume":"46","author":"Z Liu","year":"2024","unstructured":"Liu, Z., Sun, B., Tai, X.C., Wang, Q., Chang, H.: A fast minimization algorithm for the Euler elastica model based on a bilinear decomposition. SIAM J. Sci. Comput. 46(1), A290\u2013A312 (2024)","journal-title":"SIAM J. Sci. Comput."},{"issue":"1","key":"23_CR13","doi-asserted-by":"publisher","first-page":"12","DOI":"10.1016\/0021-9991(88)90002-2","volume":"79","author":"S Osher","year":"1988","unstructured":"Osher, S., Sethian, J.A.: Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations. J. Comput. Phys. 79(1), 12\u201349 (1988)","journal-title":"J. Comput. Phys."},{"key":"23_CR14","doi-asserted-by":"crossref","unstructured":"Ren, S., Hou, J., Chen, X., He, Y., Wang, W.: GeoUDF: surface reconstruction from 3D point clouds via geometry-guided distance representation. In: Proceedings of the IEEE\/CVF International Conference on Computer Vision, pp. 14214\u201314224 (2023)","DOI":"10.1109\/ICCV51070.2023.01307"},{"issue":"4","key":"23_CR15","doi-asserted-by":"publisher","first-page":"2665","DOI":"10.1137\/17M1162354","volume":"11","author":"T Ringholm","year":"2018","unstructured":"Ringholm, T., Lazi\u0107, J., Sch\u00f6nlieb, C.B.: Variational image regularization with Euler\u2019s elastica using a discrete gradient scheme. SIAM J. Imag. Sci. 11(4), 2665\u20132691 (2018)","journal-title":"SIAM J. Imag. Sci."},{"issue":"4","key":"23_CR16","doi-asserted-by":"publisher","first-page":"1165","DOI":"10.1137\/S1064827596298245","volume":"20","author":"M Sussman","year":"1999","unstructured":"Sussman, M., Fatemi, E.: An efficient, interface-preserving level set redistancing algorithm and its application to interfacial incompressible fluid flow. SIAM J. Sci. Comput. 20(4), 1165\u20131191 (1999)","journal-title":"SIAM J. Sci. Comput."},{"issue":"1","key":"23_CR17","doi-asserted-by":"publisher","first-page":"146","DOI":"10.1006\/jcph.1994.1155","volume":"114","author":"M Sussman","year":"1994","unstructured":"Sussman, M., Smereka, P., Osher, S.: A level set approach for computing solutions to incompressible two-phase flow. J. Comput. Phys. 114(1), 146\u2013159 (1994)","journal-title":"J. Comput. Phys."},{"issue":"1","key":"23_CR18","doi-asserted-by":"publisher","first-page":"313","DOI":"10.1137\/100803730","volume":"4","author":"XC Tai","year":"2011","unstructured":"Tai, X.C., Hahn, J., Chung, G.J.: A fast algorithm for Euler\u2019s elastica model using augmented Lagrangian method. SIAM J. Imag. Sci. 4(1), 313\u2013344 (2011)","journal-title":"SIAM J. Imag. Sci."},{"key":"23_CR19","doi-asserted-by":"publisher","first-page":"1552","DOI":"10.1137\/16M1063757","volume":"9","author":"M Yashtini","year":"2016","unstructured":"Yashtini, M., Kang, S.H.: A fast relaxed normal two split method and an effective weighted tv approach for Euler\u2019s elastica image inpainting. SIAM J. Imaging Sci. 9, 1552\u20131581 (2016)","journal-title":"SIAM J. Imaging Sci."},{"key":"23_CR20","doi-asserted-by":"crossref","unstructured":"Ye, J., Yanovsky, I., Dong, B., Gandlin, R., Brandt, A., Osher, S.: Multigrid narrow band surface reconstruction via level set functions. In: Bebis, G., et al. (eds.) Advances in Visual Computing, pp. 61\u201370. Springer, Heidelberg (2012)","DOI":"10.1007\/978-3-642-33179-4_7"},{"key":"23_CR21","doi-asserted-by":"crossref","unstructured":"Ye, J., Chen, Y., Wang, N., Wang, X.: GIFS: neural implicit function for general shape representation. In: Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition (2022)","DOI":"10.1109\/CVPR52688.2022.01249"},{"key":"23_CR22","doi-asserted-by":"crossref","unstructured":"Zhang, C., Heeren, B., Rumpf, M., Smith, W.A.P.: Shell PCA: statistical shape modelling in shell space. In: Proceedings of the IEEE International Conference on Computer Vision (ICCV) (2015)","DOI":"10.1109\/ICCV.2015.195"},{"issue":"250","key":"23_CR23","doi-asserted-by":"publisher","first-page":"603","DOI":"10.1090\/S0025-5718-04-01678-3","volume":"74","author":"HK Zhao","year":"2005","unstructured":"Zhao, H.K.: A fast sweeping method for Eikonal equations. Math. Comput. 74(250), 603\u2013627 (2005)","journal-title":"Math. Comput."},{"key":"23_CR24","unstructured":"Zhao, H.K., Osher, S., Fedkiw, R.: Fast surface reconstruction using the level set method. In: Proceedings IEEE Workshop on Variational and Level Set Methods in Computer Vision, pp. 194\u2013201 (2001)"},{"issue":"3","key":"23_CR25","doi-asserted-by":"publisher","first-page":"295","DOI":"10.1006\/cviu.2000.0875","volume":"80","author":"HK Zhao","year":"2000","unstructured":"Zhao, H.K., Osher, S., Merriman, B., Kang, M.: Implicit and nonparametric shape reconstruction from unorganized data using a variational level set method. Comput. Vis. Image Underst. 80(3), 295\u2013314 (2000)","journal-title":"Comput. Vis. Image Underst."},{"key":"23_CR26","doi-asserted-by":"crossref","unstructured":"Zhu, W., Chan, T., Esedo$$\\bar{\\rm g}$$lu, S.: Segmentation with depth: a level set approach. SIAM J. Sci. Comput. 28(5), 1957\u20131973 (2006)","DOI":"10.1137\/050622213"},{"issue":"4","key":"23_CR27","doi-asserted-by":"publisher","first-page":"1409","DOI":"10.3934\/ipi.2013.7.1409","volume":"7","author":"W Zhu","year":"2013","unstructured":"Zhu, W., Tai, X.C., Chan, T.: Augmented Lagrangian method for a mean curvature based image denoising model. Inverse Probl. Imaging 7(4), 1409\u20131432 (2013)","journal-title":"Inverse Probl. Imaging"}],"container-title":["Lecture Notes in Computer Science","Scale Space and Variational Methods in Computer Vision"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-92369-2_23","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,16]],"date-time":"2025-05-16T11:52:52Z","timestamp":1747396372000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-92369-2_23"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025]]},"ISBN":["9783031923685","9783031923692"],"references-count":27,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-92369-2_23","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025]]},"assertion":[{"value":"17 May 2025","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"SSVM","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Scale Space and Variational Methods in Computer Vision","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Dartington","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"United Kingdom","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2025","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"18 May 2025","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"22 May 2025","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"10","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"scalespace2025","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}