{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T16:32:14Z","timestamp":1772296334803,"version":"3.50.1"},"reference-count":38,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2006,7,1]],"date-time":"2006-07-01T00:00:00Z","timestamp":1151712000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int J Comput Vision"],"published-print":{"date-parts":[[2007,6]]},"DOI":"10.1007\/s11263-006-9140-x","type":"journal-article","created":{"date-parts":[[2006,7,10]],"date-time":"2006-07-10T15:10:15Z","timestamp":1152544215000},"page":"61-76","source":"Crossref","is-referenced-by-count":50,"title":["Image Segmentation Using Some Piecewise Constant Level Set Methods with MBO Type of Projection"],"prefix":"10.1007","volume":"73","author":[{"given":"Xue-Cheng","family":"Tai","sequence":"first","affiliation":[]},{"given":"Oddvar","family":"Christiansen","sequence":"additional","affiliation":[]},{"given":"Ping","family":"Lin","sequence":"additional","affiliation":[]},{"given":"Inge","family":"Skj\u00c6laaen","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2006,7,1]]},"reference":[{"issue":"8","key":"9140_CR1","doi-asserted-by":"crossref","first-page":"999","DOI":"10.1002\/cpa.3160430805","volume":"43","author":"L. Ambrosio","year":"1990","unstructured":"Ambrosio, L. and Tortorelli, V. M. 1990. Approximation of fun-ctionals depending on jumps by elliptic functionals via \u0393-conver-gence. Comm. Pure Appl. Math., 43(8):999\u20131036.","journal-title":"Comm. Pure Appl. Math."},{"key":"9140_CR2","doi-asserted-by":"crossref","unstructured":"Aubert, G. and Kornprobst, P. 2002. Mathematical problems in image processing, volume 147 of Applied Mathematical Sciences. Springer-Verlag, New York. Partial differential equations and the calculus of variations, With a foreword by Olivier Faugeras.","DOI":"10.1007\/b97428"},{"issue":"1","key":"9140_CR3","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1023\/A:1024484920022","volume":"19","author":"D. Barash","year":"2003","unstructured":"Barash, D., Schlick, T., Israeli, M., and Kimmel, R. 2003. Multiplicative operator splittings in nonlinear diffusion: from spatial splitting to multiple timesteps. J. Math. Imaging Vision, 19(1):33\u201348.","journal-title":"J. Math. Imaging Vision"},{"issue":"1","key":"9140_CR4","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.apnum.2004.07.002","volume":"52","author":"D. Barash","year":"2005","unstructured":"Barash, D. 2005. Nonlinear diffusion filtering on extended neighborhood. Appl. Numer. Math., 52(1):1\u201311.","journal-title":"Appl. Numer. Math."},{"key":"9140_CR5","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1016\/j.jcp.2003.08.003","volume":"193","author":"T.F. Chan","year":"2003","unstructured":"Chan, T.F. and Tai, X.-C. 2003. Level set and total variation regularization for elliptic inverse problems with discontinuous coefficients. J. Comput. Physics, 193:40\u201366.","journal-title":"J. Comput. Physics"},{"issue":"2","key":"9140_CR6","doi-asserted-by":"crossref","first-page":"266","DOI":"10.1109\/83.902291","volume":"10","author":"T. Chan","year":"2001","unstructured":"Chan, T. and Vese, L.A. 2001. Active contours without edges. IEEE Image Proc., 10(2):266\u2013277.","journal-title":"IEEE Image Proc."},{"key":"9140_CR7","doi-asserted-by":"crossref","first-page":"1929","DOI":"10.1016\/S0031-3203(03)00056-6","volume":"36","author":"D. Cremers","year":"2003","unstructured":"Cremers, D., Kohlberger, T., and Schn\u00f6rr, C. 2003. Shape statistics in kernel space for variational image segmentation. Pattern Recognition, 36:1929\u20131943.","journal-title":"Pattern Recognition"},{"key":"9140_CR8","doi-asserted-by":"crossref","unstructured":"Cremers, D., Sochen, N., and Schn\u00f6rr, C. 2004. Multiphase dynamic labeling for variational recognition-driven image segmentation. In ECCV 2004, LNCS 3024, pages 74\u201386.","DOI":"10.1007\/978-3-540-24673-2_7"},{"issue":"2","key":"9140_CR9","doi-asserted-by":"crossref","first-page":"450","DOI":"10.1016\/j.jcp.2004.01.029","volume":"198","author":"Q. Du","year":"2004","unstructured":"Du, Q., Liu, C., and Wang, X. 2004. A phase field approach in the numerical study of the elastic bending energy for vesicle membranes. J. Comput. Phys., 198(2):450\u2013468.","journal-title":"J. Comput. Phys."},{"key":"9140_CR10","unstructured":"Esedoglu, S. and Tsai, Y.-H.R. 2004. Threshold dynamics for the piecewise constant mumford-shah functional. Tech. Rep. CAM04-63, UCLA Dep. Math."},{"issue":"9","key":"9140_CR11","doi-asserted-by":"crossref","first-page":"1097","DOI":"10.1002\/cpa.3160450903","volume":"45","author":"L.C. Evans","year":"1992","unstructured":"Evans, L.C., Soner, H.M., and Souganidis, P.E. 1992. Phase transitions and generalized motion by mean curvature. Comm. Pure Appl. Math., 45(9):1097\u20131123.","journal-title":"Comm. Pure Appl. Math."},{"key":"9140_CR12","unstructured":"Gibou, F. and Fedkiw, R. 2002. A fast hybrid k-means level set algorithm for segmentation. Stanford Technical Report, November 2002, (in review).."},{"key":"9140_CR13","doi-asserted-by":"crossref","first-page":"242","DOI":"10.1016\/S0010-4655(02)00823-8","volume":"152","author":"R. Glowinski","year":"2003","unstructured":"Glowinski, R., Lin, P., and Pan, X. 2003. An operator-splitting method for a liquid crystal model. Comput. Physics Comm., 152:242\u2013252.","journal-title":"Comput. Physics Comm."},{"key":"9140_CR14","unstructured":"Lie, J., Lysaker, M., and Tai, X.-C. 2003. A variant of the levelset method and applications to image segmentation. UCLA CAM03-50."},{"key":"9140_CR15","unstructured":"Lie, J., Lysaker, M., and Tai, X.-C. 2004. A binary level set model and some applications to image processing. UCLA CAM 04- 31."},{"key":"9140_CR16","doi-asserted-by":"crossref","unstructured":"Lie, J., Lysaker, M., and Tai, X.-C. 2005. Piecewise constant level set methods and image segmentation. In Scale Space and PDE Methods in Computer Vision, Lectures notes in Computer Sciences 3459, pages 573\u2013584. Springer.","DOI":"10.1007\/11408031_49"},{"issue":"6","key":"9140_CR17","doi-asserted-by":"crossref","first-page":"964","DOI":"10.1137\/0716071","volume":"16","author":"P.-L. Lions","year":"1979","unstructured":"Lions, P.-L. and Mercier, B. 1979. Splitting algorithms for the sum of two nonlinear operators. SIAM J. Numer. Anal., 16(6):964\u2013979.","journal-title":"SIAM J. Numer. Anal."},{"key":"9140_CR18","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1016\/0893-9659(91)90161-N","volume":"4","author":"T. Lu","year":"1991","unstructured":"Lu, T., Neittaanmaki, P., and Tai, X-C. 1991. A parallel splitting up method and its application to navier-stoke equations. Applied Mathematics Letters, 4:25\u201329.","journal-title":"Applied Mathematics Letters"},{"key":"9140_CR19","doi-asserted-by":"crossref","first-page":"673","DOI":"10.1051\/m2an\/1992260606731","volume":"26","author":"T. Lu","year":"1992","unstructured":"Lu, T., Neittaanmaki, P., and Tai, X-C. 1992. A parallel splitting up method for partial differential equations and its application to navier-stokes equations. RAIRO Math. Model. and Numer. Anal., 26:673\u2013708.","journal-title":"RAIRO Math. Model. and Numer. Anal."},{"key":"9140_CR20","doi-asserted-by":"crossref","unstructured":"Marchuk, G.I. 1990. Splitting and alternating direction methods. In Handbook of numerical analysis, Vol. I, Handb. Numer. Anal., I, pages 197\u2013462. North-Holland, Amsterdam.","DOI":"10.1016\/S1570-8659(05)80035-3"},{"key":"9140_CR21","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1016\/0262-8856(92)90081-D","volume":"10","author":"R. March","year":"1992","unstructured":"March, R. 1992. Visual reconstruction with discontininuities using variational methods. Image and Vision Computing, 10:30\u201338.","journal-title":"Image and Vision Computing"},{"issue":"2","key":"9140_CR22","doi-asserted-by":"crossref","first-page":"334","DOI":"10.1006\/jcph.1994.1105","volume":"112","author":"B. Merriman","year":"1994","unstructured":"Merriman, B., Bence, J.K., and Osher, S.J. 1994. Motion of multiple functions: a level set approach. J. Comput. Phys., 112(2):334\u2013363.","journal-title":"J. Comput. Phys."},{"key":"9140_CR23","unstructured":"Modica, L. and Mortola, S. 1977. Un esempio di \u0393\u2212convergenza. Boll. Un. Mat. Ital. B (5), 14(1):285\u2013299."},{"issue":"5","key":"9140_CR24","doi-asserted-by":"crossref","first-page":"577","DOI":"10.1002\/cpa.3160420503","volume":"42","author":"D. Mumford","year":"1989","unstructured":"Mumford, D. and Shah, J. 1989. Optimal approximations by piecewise smooth functions and associated variational problems. Comm. Pure Appl. Math., 42(5):577\u2013685.","journal-title":"Comm. Pure Appl. Math."},{"issue":"1","key":"9140_CR25","doi-asserted-by":"crossref","first-page":"116","DOI":"10.1137\/0149007","volume":"49","author":"J. Rubinstein","year":"1989","unstructured":"Rubinstein, J., Sternberg, P., and Keller, J.B. 1989. Fast reaction, slow diffusion, and curve shortening. SIAM J. Appl. Math., 49(1):116\u2013133.","journal-title":"SIAM J. Appl. Math."},{"issue":"6","key":"9140_CR26","doi-asserted-by":"crossref","first-page":"1669","DOI":"10.1137\/0153077","volume":"53","author":"J. Rubinstein","year":"1993","unstructured":"Rubinstein, J., Sternberg, P., and Keller, J.B. 1993. Front interaction and nonhomogeneous equilibria for tristable reaction-diffusion equations. SIAM J. Appl. Math., 53(6):1669\u20131685.","journal-title":"SIAM J. Appl. Math."},{"issue":"2","key":"9140_CR27","doi-asserted-by":"crossref","first-page":"603","DOI":"10.1006\/jcph.1998.6025","volume":"144","author":"S.J. Ruuth","year":"1998","unstructured":"Ruuth, S.J. 1998. Efficient algorithms for diffusion-generated motion by mean curvature. J. Comput. Phys., 144(2):603\u2013625.","journal-title":"J. Comput. Phys."},{"issue":"3","key":"9140_CR28","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1023\/A:1008183109594","volume":"40","author":"C. Samson","year":"2000","unstructured":"Samson, C., Blanc-Feraud, L., Aubert, G., and Zerubia, J. 2000. A level set model for image classification. IJCV, 40(3):187\u2013198.","journal-title":"IJCV"},{"issue":"5","key":"9140_CR29","doi-asserted-by":"crossref","first-page":"460","DOI":"10.1109\/34.857003","volume":"22","author":"C. Samson","year":"2000","unstructured":"Samson, C., Blanc-F\u00e9raud, L., Aubert, G., and Zerubia, J. 2000. A variational model for image classification and restoration. TPAMI, 22(5):460\u2013472, may.","journal-title":"TPAMI"},{"key":"9140_CR30","doi-asserted-by":"crossref","unstructured":"Shen, J. 2005. Gamma-convergence approximation to piecewise constant Mumford-Shah segmentation. Tech. Rep. CAM05-16, UCLA Dep. Math.","DOI":"10.1007\/11558484_63"},{"key":"9140_CR31","unstructured":"Shi, Y. and Karl, W.C. 2005. A fast level set method without solving pdes. In ICASSP\u201905."},{"key":"9140_CR32","unstructured":"Song, B. and Chan, T.F. 2002. Fast algorithm for level set segmentation. UCLA CAM report 02-68."},{"issue":"2","key":"9140_CR33","doi-asserted-by":"crossref","first-page":"686","DOI":"10.1137\/S0036142903422429","volume":"42","author":"G. Steidl","year":"2004","unstructured":"Steidl, G., Weickert, J., Brox, T., Mr\u00e1zek, P., and Welk, M. 2004. On the equivalence of soft wavelet shrinkage, total variation diffusion, total variation regularization, and sides. SIAM J. Numer. Anal., 42(2):686\u2013713 (electronic).","journal-title":"SIAM J. Numer. Anal."},{"key":"9140_CR34","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1023\/A:1020874308076","volume":"50","author":"L.A. Vese","year":"2002","unstructured":"Vese, L.A. and Chan, T.F. 2002. A new multiphase level set framework for image segmentation via the Mumford and Shah model. International Journal of Computer Vision, 50:271\u2013293.","journal-title":"International Journal of Computer Vision"},{"key":"9140_CR35","doi-asserted-by":"crossref","unstructured":"Weickert, J. and K\u00fchne, G. 2003. Fast methods for implicit active contour models. In Geometric level set methods in imaging, vision, and graphics, pages 43\u201357. Springer, New York.","DOI":"10.1007\/0-387-21810-6_3"},{"key":"9140_CR36","doi-asserted-by":"crossref","first-page":"398","DOI":"10.1109\/83.661190","volume":"7","author":"J. Weickert","year":"1998","unstructured":"Weickert, J., Romeny, B.H., and Viergever, M.A. 1998. Efficient and reliable schemes for nonlinear diffusion filtering. IEEE TRans. Image Process., 7:398\u2013409.","journal-title":"IEEE TRans. Image Process."},{"issue":"1","key":"9140_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., and Osher, S. 1996. A variational level set approach to multiphase motion. J. Comput. Phys., 127(1):179\u2013195.","journal-title":"J. Comput. Phys."},{"key":"9140_CR38","doi-asserted-by":"crossref","unstructured":"Ziemer, W.P. 1989. Weakly differentiable functions. Springer- Verlag.","DOI":"10.1007\/978-1-4612-1015-3"}],"container-title":["International Journal of Computer Vision"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11263-006-9140-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11263-006-9140-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11263-006-9140-x","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,4,16]],"date-time":"2020-04-16T11:57:35Z","timestamp":1587038255000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11263-006-9140-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,7,1]]},"references-count":38,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2007,6]]}},"alternative-id":["9140"],"URL":"https:\/\/doi.org\/10.1007\/s11263-006-9140-x","relation":{},"ISSN":["0920-5691","1573-1405"],"issn-type":[{"value":"0920-5691","type":"print"},{"value":"1573-1405","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,7,1]]}}}