{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,5]],"date-time":"2026-06-05T01:06:44Z","timestamp":1780621604039,"version":"3.54.1"},"reference-count":19,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2019,1,1]],"date-time":"2019-01-01T00:00:00Z","timestamp":1546300800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"crossref","award":["2017YFC0601801"],"award-info":[{"award-number":["2017YFC0601801"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11871298"],"award-info":[{"award-number":["11871298"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2019,5]]},"DOI":"10.1007\/s10915-018-00899-7","type":"journal-article","created":{"date-parts":[[2018,12,31]],"date-time":"2018-12-31T22:57:45Z","timestamp":1546297065000},"page":"1057-1077","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["Image Segmentation Using the Cahn\u2013Hilliard Equation"],"prefix":"10.1007","volume":"79","author":[{"given":"Wenli","family":"Yang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5623-4864","authenticated-orcid":false,"given":"Zhongyi","family":"Huang","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":[[2019,1,1]]},"reference":[{"issue":"1","key":"899_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"},{"key":"899_CR2","unstructured":"Bertozzi, A., Esedo\n                    \n                      \n                    \n                    $$\\bar{\\rm g}$$\n                    \n                      \n                        \n                          \n                            g\n                          \n                          \n                            \u00af\n                          \n                        \n                      \n                    \n                  lu, S., Gillette, A.: Analysis of a two-scale Cahn\u2013Hilliard model for binary image inpainting. Multiscale Model. Simul. 6(3), 913\u2013936 (2007)"},{"issue":"1","key":"899_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. Vis. 22(1), 61\u201379 (1997)","journal-title":"Int. J. Comput. Vis."},{"issue":"2","key":"899_CR4","doi-asserted-by":"publisher","first-page":"266","DOI":"10.1109\/83.902291","volume":"10","author":"TF Chan","year":"2001","unstructured":"Chan, T.F., Vese, L.A.: Active contours without edges. IEEE Trans. Image Process. 10(2), 266\u2013277 (2001)","journal-title":"IEEE Trans. Image Process."},{"issue":"3","key":"899_CR5","doi-asserted-by":"publisher","first-page":"315","DOI":"10.1023\/A:1020878408985","volume":"50","author":"Y Chen","year":"2002","unstructured":"Chen, Y., Tagare, H.D., Thiruvenkadam, S.: Using prior shapes in geometric active contours in a variational framework. Int. J. Comput. Vis. 50(3), 315\u2013328 (2002)","journal-title":"Int. J. Comput. Vis."},{"issue":"1","key":"899_CR6","doi-asserted-by":"publisher","first-page":"575","DOI":"10.1137\/15M1040177","volume":"15","author":"L Cherfils","year":"2017","unstructured":"Cherfils, L., Fakih, H., Miranville, A.: A complex version of the Cahn\u2013Hilliard equation for grayscale image inpainting. Multiscale Model. Simul. 15(1), 575\u2013605 (2017)","journal-title":"Multiscale Model. Simul."},{"issue":"2","key":"899_CR7","doi-asserted-by":"publisher","first-page":"243","DOI":"10.1007\/s10915-008-9187-7","volume":"36","author":"H Han","year":"2008","unstructured":"Han, H., Huang, Z., Kellogg, R.B.: A tailored finite point method for a singular perturbation problem on an unbounded domain. J. Sci. Comput. 36(2), 243\u2013261 (2008)","journal-title":"J. Sci. Comput."},{"issue":"2","key":"899_CR8","doi-asserted-by":"publisher","first-page":"659","DOI":"10.1007\/s10543-015-0573-x","volume":"56","author":"Z Huang","year":"2016","unstructured":"Huang, Z., Li, Y.: Monotone finite point method foe non-equilibrium radiation diffusion equations. BIT Numer. Math. 56(2), 659\u2013679 (2016)","journal-title":"BIT Numer. Math."},{"issue":"4","key":"899_CR9","doi-asserted-by":"publisher","first-page":"321","DOI":"10.1007\/BF00133570","volume":"1","author":"M Kass","year":"1988","unstructured":"Kass, M., Witkin, A., Terzopoulos, D.: Snakes: active contour models. Int. J Comput. Vis. 1(4), 321\u2013331 (1988)","journal-title":"Int. J Comput. Vis."},{"issue":"5","key":"899_CR10","doi-asserted-by":"publisher","first-page":"577","DOI":"10.1002\/cpa.3160420503","volume":"42","author":"D Mumford","year":"1989","unstructured":"Mumford, D., Shah, J.: Optimal approximations by piecewise smooth functions and associated variational problems. Commun. Pure Appl. Math. 42(5), 577\u2013685 (1989)","journal-title":"Commun. Pure Appl. Math."},{"key":"899_CR11","doi-asserted-by":"crossref","unstructured":"Nitzberg, M., Mumford, D., Shiota, T.: Filtering, segmentation and depth. Lecture Notes in Computer Science. Springer (1993)","DOI":"10.1007\/3-540-56484-5"},{"issue":"1","key":"899_CR12","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\u2013Jacobi formulations. J. Comput. Phys. 79(1), 12\u201349 (1988)","journal-title":"J. Comput. Phys."},{"issue":"1\u20134","key":"899_CR13","doi-asserted-by":"publisher","first-page":"259","DOI":"10.1016\/0167-2789(92)90242-F","volume":"60","author":"LI Rudin","year":"1992","unstructured":"Rudin, L.I., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Physica D 60(1\u20134), 259\u2013268 (1992)","journal-title":"Physica D"},{"issue":"2","key":"899_CR14","doi-asserted-by":"publisher","first-page":"564","DOI":"10.1137\/S0036139901390088","volume":"63","author":"J Shen","year":"2003","unstructured":"Shen, J., Kang, S.H., Chan, T.F.: Euler\u2019s elastica and curvature-based inpainting. SIAM J. Appl. Math. 63(2), 564\u2013592 (2003)","journal-title":"SIAM J. Appl. Math."},{"issue":"1","key":"899_CR15","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. Imaging Sci. 4(1), 313\u2013344 (2011)","journal-title":"SIAM J. Imaging Sci."},{"issue":"1","key":"899_CR16","doi-asserted-by":"publisher","first-page":"183","DOI":"10.1007\/BF02186838","volume":"77","author":"JE Taylor","year":"1994","unstructured":"Taylor, J.E., Cahn, J.W.: Linking anisotropic sharp and diffuse surface motion laws via gradient flows. J. Stat. Phys. 77(1), 183\u2013197 (1994)","journal-title":"J. Stat. Phys."},{"issue":"3","key":"899_CR17","doi-asserted-by":"publisher","first-page":"271","DOI":"10.1023\/A:1020874308076","volume":"50","author":"LA Vese","year":"2002","unstructured":"Vese, L.A., Chan, T.F.: A multiphase level set framework for image segmentation using the Mumford and Shah model. Int. J. Comput. Vis. 50(3), 271\u2013293 (2002)","journal-title":"Int. J. Comput. Vis."},{"issue":"4","key":"899_CR18","doi-asserted-by":"publisher","first-page":"1169","DOI":"10.4208\/cicp.2018.hh80.03","volume":"24","author":"W Yang","year":"2018","unstructured":"Yang, W., Huang, Z., Zhu, W.: An efficient tailored finite point method for Rician denoising and deblurring. Commun. Comput. Phys. 24(4), 1169\u20131195 (2018)","journal-title":"Commun. Comput. Phys."},{"issue":"2","key":"899_CR19","doi-asserted-by":"publisher","first-page":"414","DOI":"10.1007\/s10915-013-9710-3","volume":"57","author":"W Zhu","year":"2013","unstructured":"Zhu, W., Tai, X.C., Chan, T.: Image segmentation using Euler\u2019s elastica as the regularization. J. Sci. Comput. 57(2), 414\u2013438 (2013)","journal-title":"J. Sci. Comput."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-018-00899-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10915-018-00899-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-018-00899-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,1]],"date-time":"2020-01-01T00:46:53Z","timestamp":1577839613000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-018-00899-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1,1]]},"references-count":19,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2019,5]]}},"alternative-id":["899"],"URL":"https:\/\/doi.org\/10.1007\/s10915-018-00899-7","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,1,1]]},"assertion":[{"value":"25 April 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 October 2018","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 December 2018","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 January 2019","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}