{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T18:37:01Z","timestamp":1776710221460,"version":"3.51.2"},"reference-count":35,"publisher":"Springer Science and Business Media LLC","issue":"1-3","license":[{"start":{"date-parts":[[2008,2,29]],"date-time":"2008-02-29T00:00:00Z","timestamp":1204243200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2008,7]]},"DOI":"10.1007\/s11075-008-9183-x","type":"journal-article","created":{"date-parts":[[2008,2,29]],"date-time":"2008-02-29T15:49:51Z","timestamp":1204300191000},"page":"189-211","source":"Crossref","is-referenced-by-count":41,"title":["Generalized fast marching method: applications to image segmentation"],"prefix":"10.1007","volume":"48","author":[{"given":"Nicolas","family":"Forcadel","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Carole","family":"Le Guyader","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Christian","family":"Gout","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2008,2,29]]},"reference":[{"key":"9183_CR1","doi-asserted-by":"crossref","unstructured":"Aubert, G., Kornprobst, P.: Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations. Springer Verlag (2002)","DOI":"10.1007\/b97428"},{"key":"9183_CR2","unstructured":"Baerentzen, J.A.: On the implementation of fast marching methods for 3D lattices. Technical Report, Informatics and Mathematical Modelling, Technical University of Denmark, DTU (2001)"},{"key":"9183_CR3","volume-title":"Solutions de Viscosit\u00e9 des \u00c9quations de Hamilton-Jacobi, vol.\u00a017 of Math\u00e9matiques & Applications (Berlin) [Mathematics & Applications]","author":"G. Barles","year":"1994","unstructured":"Barles, G.: Solutions de Viscosit\u00e9 des \u00c9quations de Hamilton-Jacobi, vol.\u00a017 of Math\u00e9matiques & Applications (Berlin) [Mathematics & Applications]. Springer-Verlag, Paris (1994)"},{"issue":"2","key":"9183_CR4","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1007\/s10851-007-0002-0","volume":"28","author":"X. Bresson","year":"2007","unstructured":"Bresson, X., Esedoglu, S., Vandergheynst, P., Thiran, J., Osher, S.: Fast global minimization of the active contour\/snake models. J. Math. Imaging Vis. 28(2), 151\u2013167 (2007)","journal-title":"J. Math. Imaging Vis."},{"key":"9183_CR5","unstructured":"Carlini, E., Cristiani, E., Forcadel, N.: A non-monotone fast marching scheme for a Hamilton-jacobi equation modeling dislocation dynamics. ENUMATH 2005, Santiago de Compostela (Spain) (2007)"},{"issue":"1","key":"9183_CR6","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1023\/A:1007979827043","volume":"22","author":"V. Caselles","year":"1993","unstructured":"Caselles, V., Kimmel, R., Sapiro, G.: Geodesic active contours. Int. J. Comput. Vis. 22(1), 61\u201387 (1993)","journal-title":"Int. J. Comput. Vis."},{"issue":"2","key":"9183_CR7","doi-asserted-by":"crossref","first-page":"266","DOI":"10.1109\/83.902291","volume":"10","author":"T. Chan","year":"2001","unstructured":"Chan, T., Vese, L.: Active contours without edges. IEEE Trans. Image Process. 10(2), 266\u2013277 (2001)","journal-title":"IEEE Trans. Image Process."},{"issue":"5","key":"9183_CR8","doi-asserted-by":"crossref","first-page":"1632","DOI":"10.1137\/040615286","volume":"66","author":"T.F. Chan","year":"2006","unstructured":"Chan, T.F., Esedoglu, S., Nikolova, M.: Algorithms for finding global minimizers of image segmentation and denoising models. SIAM J. Appl. Math. 66(5), 1632\u20131648 (2006)","journal-title":"SIAM J. Appl. Math."},{"key":"9183_CR9","unstructured":"Chung, J.T., Vese, L.: Image segmentation using a multilayer level-set approach. EMMCVPR 2005, 439\u2013455 (2005)"},{"issue":"2","key":"9183_CR10","first-page":"211","volume":"52","author":"L.D. Cohen","year":"1991","unstructured":"Cohen, L.D.: On active contour models and balloons. Comput. Vision Graphics Image Processing: Image Understanding 52(2), 211\u2013218 (1991)","journal-title":"Vision Graphics Image Processing: Image Understanding"},{"key":"9183_CR11","unstructured":"Epstein, C.L., Gage, M.: The curve shortening flow. In: Chorin, A., Majda, A. (eds.) Wave Motion: Theory, Modelling and Computation (1997)"},{"issue":"4","key":"9183_CR12","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1007\/s10596-006-9029-3","volume":"10","author":"C. Gout","year":"2006","unstructured":"Gout, C., Le\u00a0Guyader, C.: Segmentation of complex geophysical structures with well data. Comput. Geosci. 10(4), 361\u2013372 (2006)","journal-title":"Comput. Geosci."},{"issue":"1,3","key":"9183_CR13","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1007\/s11075-004-3627-8","volume":"39","author":"C. Gout","year":"2005","unstructured":"Gout, C., Le\u00a0Guyader, C., Vese, L.: Segmentation under geometrical conditions using geodesic active contours and interpolation using level set methods. Numer. Algoirthms 39(1,3), 155\u2013173 (2005)","journal-title":"Numer. Algoirthms"},{"key":"9183_CR15","unstructured":"Kass, M., Witkin, A., Terzopoulos, D.: Snakes: active contour models in proceeding. First International Conference on Computer Vision, London, England, IEEE, Piscataway NJ, pp.\u00a0259\u2013268 (1987)"},{"key":"9183_CR16","doi-asserted-by":"crossref","unstructured":"Kichenassamy, S., Kumar, A., Olver, P., Tannenbaum, A., Yezzi, A.: Gradient flows and geometric active contour models. In: Proceedings, Fifth International Conference on Computer Vision, pp.\u00a0810\u2013815 (1995)","DOI":"10.1109\/ICCV.1995.466855"},{"issue":"1\u20133","key":"9183_CR18","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1007\/s11075-004-3631-z","volume":"39","author":"C. Guyader Le","year":"2005","unstructured":"Le\u00a0Guyader, C., Apprato, D., Gout, C.: The level set methods and image segmentation under interpolation conditions. Numer. Algorithms 39(1\u20133), 221\u2013235 (2005)","journal-title":"Numer. Algorithms"},{"key":"9183_CR19","doi-asserted-by":"crossref","first-page":"9389","DOI":"10.1073\/pnas.93.18.9389","volume":"93","author":"R. Malladi","year":"1996","unstructured":"Malladi, R., Sethian, J.A.: An $\\mathcal{O}\\left( {n\\,\\text{log}n} \\right)$ algorithm for shape modeling. Proc. Natl. Acad. Sci. 93, 9389\u20139392 (1996)","journal-title":"Proc. Natl. Acad. Sci."},{"key":"9183_CR20","doi-asserted-by":"crossref","unstructured":"Malladi, R., Sethian, J.A., Vemuri, B.: Evolutionary fronts for topology-independent shape modeling and recovery. In: Proceedings of Third European Conference on Computer Vision, pp.\u00a03\u201313 (1994)","DOI":"10.1007\/3-540-57956-7_1"},{"key":"9183_CR21","unstructured":"Merriman, B., Bence, J., Osher, S.: Diffusion generated motion by mean curvature. In: Taylor, J.E. (ed.) Proceedings of the Computational Crystal Growers Workshop, American Mathematical Society, Providence, Rhode Island, pp.\u00a073\u201383 (1992)"},{"key":"9183_CR22","doi-asserted-by":"crossref","first-page":"577","DOI":"10.1002\/cpa.3160420503","volume":"42","author":"D. Mumford","year":"1989","unstructured":"Mumford, D., Shah, J.: Optimal approximation by piecewise smooth functions and associated variational problems. Commun. Pure Appl. Math. 42, 577\u2013685 (1989)","journal-title":"Commun. Pure Appl. Math."},{"key":"9183_CR23","doi-asserted-by":"crossref","unstructured":"Osher, S., Fedkiw, R.: Level Set Methods and Dynamic Implicit Surfaces. Springer Verlag (2003)","DOI":"10.1007\/b98879"},{"key":"9183_CR24","doi-asserted-by":"crossref","unstructured":"Osher, S., Paragios, N.: Geometric Level Set Methods in Imaging, Vision, and Graphics. Springer Verlag (2003)","DOI":"10.1007\/b97541"},{"key":"9183_CR25","doi-asserted-by":"crossref","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, 12\u201349 (1988)","journal-title":"J. Comput. Phys."},{"issue":"3","key":"9183_CR26","doi-asserted-by":"crossref","first-page":"867","DOI":"10.1137\/0729053","volume":"29","author":"V. Rouy","year":"1992","unstructured":"Rouy, V., Tourin, F.: A viscosity solutions approach to shape-from-shading. SIAM J. Num. Anal. 29(3), 867\u2013884 (1992)","journal-title":"SIAM J. Num. Anal."},{"key":"9183_CR27","doi-asserted-by":"crossref","first-page":"131","DOI":"10.4310\/jdg\/1214444092","volume":"31","author":"J.A. Sethian","year":"1989","unstructured":"Sethian, J.A.: A review of recent numerical algorithms for hypersurfaces moving with curvature dependent flows. J. Differ. Geom. 31, 131\u2013161 (1989)","journal-title":"J. Differ. Geom."},{"key":"9183_CR28","doi-asserted-by":"crossref","first-page":"1591","DOI":"10.1073\/pnas.93.4.1591","volume":"93","author":"J.A. Sethian","year":"1996","unstructured":"Sethian, J.A.: A fast marching level set method for monotonically advancing fronts. Proc. Natl. Acad. Sci. 93, 1591\u20131595 (1996)","journal-title":"Proc. Natl. Acad. Sci."},{"key":"9183_CR29","volume-title":"Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision and Material Science","author":"J.A. Sethian","year":"1999","unstructured":"Sethian, J.A.: Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision and Material Science. Cambridge University Press, Londres (1999)"},{"issue":"2","key":"9183_CR30","doi-asserted-by":"crossref","first-page":"503","DOI":"10.1006\/jcph.2000.6657","volume":"169","author":"J.A. Sethian","year":"2001","unstructured":"Sethian, J.A.: Evolution, implementation and application of level set and fast marching methods for advancing fronts. J. Comput. Phys. 169(2), 503\u2013555 (2001)","journal-title":"J. Comput. Phys."},{"issue":"2","key":"9183_CR31","doi-asserted-by":"crossref","first-page":"673","DOI":"10.1137\/S0036142901396533","volume":"41","author":"Y.R. Tsai","year":"2002","unstructured":"Tsai, Y.R., Cheng, L.T., Osher, S., Zhao, H.K.: Fast sweeping algorithms for a class of Hamilton-Jacobi equations. SIAM J. Numer. Anal. 41(2), 673\u2013694 (2002)","journal-title":"SIAM J. Numer. Anal."},{"key":"9183_CR32","doi-asserted-by":"crossref","first-page":"1528","DOI":"10.1109\/9.412624","volume":"40","author":"N. Tsitsiklis","year":"1995","unstructured":"Tsitsiklis, N.: Efficient algorithms for globally optimal trajectories. IEEE Tran. Automatic. Control 40, 1528\u20131538 (1995)","journal-title":"IEEE Tran. Automatic. Control"},{"issue":"3","key":"9183_CR33","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1023\/A:1020874308076","volume":"50","author":"L. Vese","year":"2002","unstructured":"Vese, L., Chan, T.: 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":"3","key":"9183_CR34","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1109\/83.661186","volume":"7","author":"C. Xu","year":"1998","unstructured":"Xu, C., Prince, J.L.: Snakes, shapes, and gradient vector flow. IEEE Trans. Image Process. 7(3), 359\u2013369 (1998)","journal-title":"IEEE Trans. Image Process."},{"issue":"2","key":"9183_CR35","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1016\/j.jcp.2005.08.005","volume":"212","author":"L. Yatziv","year":"2006","unstructured":"Yatziv, L., Bartesaghi, A., Sapiro, G.: $\\mathcal{O}\\left( n \\right)$ implementation of the fast marching algorithm. J. Comput. Phys. 212(2), 393\u2013399 (2006)","journal-title":"J. Comput. Phys."},{"key":"9183_CR36","doi-asserted-by":"crossref","first-page":"603","DOI":"10.1090\/S0025-5718-04-01678-3","volume":"74","author":"H.-K. Zhao","year":"2004","unstructured":"Zhao, H.-K.: Fast sweeping method for Eikonal equations. Math. Comput. 74, 603\u2013627 (2004)","journal-title":"Math. Comput."},{"key":"9183_CR37","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1006\/jcph.1996.0167","volume":"127","author":"H.-K. Zhao","year":"1996","unstructured":"Zhao, H.-K., Chan, T., Merriman, B., Osher, S.: A variational level set approach to multiphase motion. J. Comput. Phys. 127, 179\u2013195 (1996)","journal-title":"J. Comput. Phys."}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-008-9183-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11075-008-9183-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-008-9183-x","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,2]],"date-time":"2020-05-02T12:15:12Z","timestamp":1588421712000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11075-008-9183-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,2,29]]},"references-count":35,"journal-issue":{"issue":"1-3","published-print":{"date-parts":[[2008,7]]}},"alternative-id":["9183"],"URL":"https:\/\/doi.org\/10.1007\/s11075-008-9183-x","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,2,29]]}}}