{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T16:35:46Z","timestamp":1772296546194,"version":"3.50.1"},"reference-count":42,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2011,10,20]],"date-time":"2011-10-20T00:00:00Z","timestamp":1319068800000},"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 Vis"],"published-print":{"date-parts":[[2012,5]]},"DOI":"10.1007\/s11263-011-0499-y","type":"journal-article","created":{"date-parts":[[2011,10,19]],"date-time":"2011-10-19T19:08:17Z","timestamp":1319051297000},"page":"103-121","source":"Crossref","is-referenced-by-count":131,"title":["Completely Convex Formulation of the Chan-Vese Image Segmentation Model"],"prefix":"10.1007","volume":"98","author":[{"given":"Ethan S.","family":"Brown","sequence":"first","affiliation":[]},{"given":"Tony F.","family":"Chan","sequence":"additional","affiliation":[]},{"given":"Xavier","family":"Bresson","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2011,10,20]]},"reference":[{"issue":"3","key":"499_CR1","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1016\/S0764-4442(00)88602-4","volume":"329","author":"G. Alberti","year":"1999","unstructured":"Alberti, G., Bouchitt\u00e9, G., & Dal Maso, G. (1999). The calibration method for the Mumford-Shah functional. Comptes Rendus de L\u2019Acad\u00e9mie Des Sciences. Series 1, Mathematics, 329(3), 249\u2013254.","journal-title":"Comptes Rendus de L\u2019Acad\u00e9mie Des Sciences. Series 1, Mathematics"},{"key":"499_CR2","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198502456.001.0001","volume-title":"Functions of bounded variation and free discontinuity problems","author":"L. Ambrosio","year":"2000","unstructured":"Ambrosio, L., Fusco, N., & Pallara, D. (2000). Functions of bounded variation and free discontinuity problems. Oxford: Clarendon Press."},{"key":"499_CR3","series-title":"Stanford mathematical studies in the social sciences","volume-title":"Studies in linear and non-linear programming. With contributions by H.\u00a0B.\u00a0Chenery, S.\u00a0M.\u00a0Johnson, S. Karlin, T. Marschak, R. M. Solow","author":"K. Arrow","year":"1958","unstructured":"Arrow, K., Hurwicz, L., & Uzawa, H. (1958). Stanford mathematical studies in the social sciences: Vol.\u00a0II. Studies in linear and non-linear programming. With contributions by H.\u00a0B.\u00a0Chenery, S.\u00a0M.\u00a0Johnson, S. Karlin, T. Marschak, R. M. Solow. Stanford: Stanford University Press."},{"key":"499_CR4","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/978-3-642-02256-2_1","volume-title":"International conference on scale space and variational methods in computer vision","author":"E. Bae","year":"2009","unstructured":"Bae, E., & Tai, X.-C. (2009). Graph cut optimization for the piecewise constant level set method applied to multiphase image segmentation. In International conference on scale space and variational methods in computer vision (pp. 1\u201313)."},{"issue":"1","key":"499_CR5","doi-asserted-by":"crossref","first-page":"112","DOI":"10.1007\/s11263-010-0406-y","volume":"92","author":"E. Bae","year":"2009","unstructured":"Bae, E., Yuan, J., & Tai, X.-C. (2009). Global minimization for continuous multiphase partitioning problems using a dual approach. International Journal of Computer Vision, 92(1), 112\u2013129.","journal-title":"International Journal of Computer Vision"},{"key":"499_CR6","unstructured":"Bae, E., Yuan, J., Tai, X.-C., & Boykov, Y. (2010). A study on continuous max-flow and min-cut approaches. Part II: multiple linearly ordered labels (UCLA CAM Report 10-62)."},{"key":"499_CR7","unstructured":"Berkeley Dataset. http:\/\/www.eecs.berkeley.edu\/CS\/vision ."},{"key":"499_CR8","volume-title":"Constrained optimization and Lagrange multiplier methods","author":"D. P. Bertsekas","year":"1982","unstructured":"Bertsekas, D. P. (1982). Constrained optimization and Lagrange multiplier methods. New York: Academic Press."},{"issue":"2","key":"499_CR9","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. (2007). Fast global minimization of the active contour\/snake models. Journal of Mathematical Imaging and Vision, 28(2), 151\u2013167.","journal-title":"Journal of Mathematical Imaging and Vision"},{"key":"499_CR10","unstructured":"Brown, E. S., Chan, T. F., & Bresson, X. (2009). Convex formulations for piecewise constant Mumford-Shah image segmentation (UCLA CAM Report 09-66)."},{"key":"499_CR11","unstructured":"Brown, E. S., Chan, T. F., & Bresson, X. (2010). A convex relaxation method for a class of vector-valued minimization problems with applications to Mumford-Shah segmentation (UCLA CAM Report 10-43)."},{"key":"499_CR12","unstructured":"Chambolle, A., Cremers, D., & Pock, T. (2008). A convex approach for computing minimal partitions (Technical report TR-2008-05). Bonn: Dept. of Computer Science, University of Bonn."},{"key":"499_CR13","unstructured":"Chambolle, A., & Pock, T. (2010). A first-order primal-dual algorithm for convex problems with applications to imaging (R.I. 685). CMAP, Ecole Polytechnique."},{"issue":"5","key":"499_CR14","doi-asserted-by":"crossref","first-page":"1632","DOI":"10.1137\/040615286","volume":"66","author":"T. F. Chan","year":"2006","unstructured":"Chan, T. F., Esedo\u1e21lu, S., & Nikolova, M. (2006). Algorithms for finding global minimizers of image segmentation and denoising models. SIAM Journal on Applied Mathematics, 66(5), 1632\u20131648.","journal-title":"SIAM Journal on Applied Mathematics"},{"issue":"2","key":"499_CR15","doi-asserted-by":"crossref","first-page":"266","DOI":"10.1109\/83.902291","volume":"10","author":"T. F. Chan","year":"2001","unstructured":"Chan, T. F., & Vese, L. A. (2001). Active contours without edges. IEEE Transactions on Image Processing, 10(2), 266\u2013277.","journal-title":"IEEE Transactions on Image Processing"},{"key":"499_CR16","first-page":"182","volume-title":"IASTED international conference on visualization, imaging and image processing","author":"N. El-Zehiry","year":"2007","unstructured":"El-Zehiry, N., Xu, S., Sahoo, P., & Elmaghraby, A. (2007). Graph cut optimization for the Mumford-Shah model. In IASTED international conference on visualization, imaging and image processing (pp. 182\u2013187)."},{"issue":"4","key":"499_CR17","doi-asserted-by":"crossref","first-page":"1015","DOI":"10.1137\/09076934X","volume":"3","author":"E. Esser","year":"2010","unstructured":"Esser, E., Zhang, X., & Chan, T. F. (2010). A general framework for a class of first order primal-dual algorithms for convex optimization in imaging science. SIAM Journal on Imaging Sciences, 3(4), 1015\u20131046.","journal-title":"SIAM Journal on Imaging Sciences"},{"key":"499_CR18","volume-title":"Measure theory and fine properties of functions","author":"L. C. Evans","year":"2000","unstructured":"Evans, L. C., & Gariepy, R. F. (2000). Measure theory and fine properties of functions. Boca Raton: CRC Press."},{"issue":"3","key":"499_CR19","doi-asserted-by":"crossref","first-page":"418","DOI":"10.1090\/S0002-9947-1959-0110078-1","volume":"93","author":"H. Federer","year":"1959","unstructured":"Federer, H. (1959). Curvature measures. Transactions of the American Mathematical Society, 93(3), 418\u2013491.","journal-title":"Transactions of the American Mathematical Society"},{"issue":"1","key":"499_CR20","doi-asserted-by":"crossref","first-page":"218","DOI":"10.1007\/BF01236935","volume":"11","author":"W. Fleming","year":"1960","unstructured":"Fleming, W., & Rishel, R. (1960). An integral formula for total gradient variation. Archiv der Mathematik, 11(1), 218\u2013222.","journal-title":"Archiv der Mathematik"},{"key":"499_CR21","first-page":"225","volume-title":"European conference on computer vision","author":"S. Goldluecke","year":"2010","unstructured":"Goldluecke, S., & Cremers, D. (2010). Convex relaxation for multilabel problems with product label spaces. In European conference on computer vision (pp. 225\u2013238)."},{"issue":"1\u20133","key":"499_CR22","first-page":"272","volume":"45","author":"T. Goldstein","year":"2009","unstructured":"Goldstein, T., Bresson, X., & Osher, S. (2009). Geometric applications of the split Bregman method: segmentation and surface reconstruction. Journal of Scientific Computing, 45(1\u20133), 272\u2013293.","journal-title":"Journal of Scientific Computing"},{"key":"499_CR23","unstructured":"Goldstein, T., Bresson, X., & Osher, S. (2009). Global minimization of Markov random fields with applications to optical flow (UCLA CAM Report 09-77)."},{"issue":"10","key":"499_CR24","doi-asserted-by":"crossref","first-page":"1333","DOI":"10.1109\/TPAMI.2003.1233908","volume":"25","author":"H. Ishikawa","year":"2003","unstructured":"Ishikawa, H. (2003). Exact optimization for Markov random fields with convex priors. IEEE Transactions on Pattern Analysis and Machine Intelligence, 25(10), 1333\u20131336.","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence"},{"key":"499_CR25","doi-asserted-by":"crossref","first-page":"646","DOI":"10.1109\/ICCV.2009.5459176","volume-title":"International conference on computer vision","author":"J. Lellmann","year":"2009","unstructured":"Lellmann, J., Becker, F., & Schn\u00f6rr, C. (2009). Convex optimization for multi-class image labeling with a novel family of total variation based regularizers. In International conference on computer vision (pp. 646\u2013653)."},{"key":"499_CR26","doi-asserted-by":"crossref","first-page":"150","DOI":"10.1007\/978-3-642-02256-2_13","volume-title":"International conference on scale space and variational methods in computer vision","author":"J. Lellmann","year":"2009","unstructured":"Lellmann, J., Kappes, J., Yuan, J., Becker, F., & Schn\u00f6rr, C. (2009). Convex multi-class image labeling by simplex-constrained total variation. In International conference on scale space and variational methods in computer vision (pp. 150\u2013162)."},{"key":"499_CR27","unstructured":"Lellmann, J., & Schn\u00f6rr, C. (2010). Continuous multiclass labeling approaches and algorithms (Tech. Rep.). Heidelberg: University of Heidelberg."},{"issue":"5","key":"499_CR28","doi-asserted-by":"crossref","first-page":"1171","DOI":"10.1109\/TIP.2005.863956","volume":"15","author":"J. Lie","year":"2006","unstructured":"Lie, J., Lysaker, M., & Tai, X.-C. (2006). A binary level set model and some applications to Mumford-Shah image segmentation. IEEE Transactions on Image Processing, 15(5), 1171\u20131181.","journal-title":"IEEE Transactions on Image Processing"},{"key":"499_CR29","doi-asserted-by":"crossref","DOI":"10.1090\/gsm\/014","volume-title":"Analysis","author":"E. H. Lieb","year":"2001","unstructured":"Lieb, E. H., & Loss, M. (2001). Analysis. Providence: Am. Math. Soc."},{"key":"499_CR30","first-page":"281","volume-title":"Proceedings of the fifth Berkeley symposium on mathematical statistics and probability","author":"J. MacQueen","year":"1967","unstructured":"MacQueen, J. (1967). Some methods for classification and analysis of multivariate observations. In Proceedings of the fifth Berkeley symposium on mathematical statistics and probability (pp.\u00a0281\u2013297)."},{"key":"499_CR31","doi-asserted-by":"crossref","first-page":"577","DOI":"10.1002\/cpa.3160420503","volume":"42","author":"D. Mumford","year":"1989","unstructured":"Mumford, D., & Shah, J. (1989). Optimal approximations of piecewise smooth functions and associated variational problems. Communications on Pure and Applied Mathematics, 42, 577\u2013685.","journal-title":"Communications on Pure and Applied Mathematics"},{"issue":"1","key":"499_CR32","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. (1988). Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations. Journal of Computational Physics, 79(1), 12\u201349.","journal-title":"Journal of Computational Physics"},{"key":"499_CR33","volume-title":"IEEE conference on computer vision (ICCV)","author":"T. Pock","year":"2009","unstructured":"Pock, T., Chambolle, A., Bischof, H., & Cremers, D. (2009). An algorithm for minimizing the Mumford-Shah functional. In IEEE conference on computer vision (ICCV)."},{"issue":"3","key":"499_CR34","doi-asserted-by":"crossref","first-page":"1122","DOI":"10.1137\/090757617","volume":"2","author":"T. Pock","year":"2010","unstructured":"Pock, T., Cremers, D., Bischof, H., & Chambolle, A. (2010). Global solutions of variational models with convex regularization. SIAM Journal on Imaging Sciences, 2(3), 1122\u20131145.","journal-title":"SIAM Journal on Imaging Sciences"},{"key":"499_CR35","first-page":"792","volume-title":"European conference on computer vision (ECCV)","author":"T. Pock","year":"2008","unstructured":"Pock, T., Schoenemann, T., Graber, G., Bischof, H., & Cremers, D. (2008). A convex formulation of continuous multi-label problems. In European conference on computer vision (ECCV) (pp. 792\u2013805)."},{"issue":"5","key":"499_CR36","first-page":"777","volume":"28","author":"L. D. Popov","year":"1980","unstructured":"Popov, L. D. (1980). A modification of the Arrow-Hurwitz method of search for saddle points. Matemati\u010deskie Zametki, 28(5), 777\u2013784, 803.","journal-title":"Matemati\u010deskie Zametki"},{"issue":"1","key":"499_CR37","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1016\/j.cviu.2008.06.006","volume":"112","author":"A. Shekhovtsov","year":"2008","unstructured":"Shekhovtsov, A., Kovtun, I., & Hlav\u00e1c, V. (2008). Efficient MRF deformation model for non-rigid image matching. Computer Vision and Image Understanding, 112(1), 91\u201399.","journal-title":"Computer Vision and Image Understanding"},{"key":"499_CR38","doi-asserted-by":"crossref","first-page":"2240","DOI":"10.1109\/ICCV.2009.5459464","volume-title":"International conference on computer vision","author":"P. Strandmark","year":"2009","unstructured":"Strandmark, P., Kahl, F., & Overgaard, N. C. (2009). Optimizing parametric total variation models. In International conference on computer vision (pp. 2240\u20132247)."},{"issue":"2","key":"499_CR39","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1007\/BF02592050","volume":"26","author":"G. Strang","year":"1983","unstructured":"Strang, G. (1983). Maximal flow through a domain. Mathematical Programming, 26(2), 123\u2013143.","journal-title":"Mathematical Programming"},{"key":"499_CR40","unstructured":"Weizmann Dataset. http:\/\/www.weizmann.ac.il\/~vision ."},{"key":"499_CR41","unstructured":"Yuan, J., Bae, E., Tai, X.-C., & Boykov, Y. (2010). A study on continuous max-flow and min-cut approaches. Part I: binary labeling (UCLA CAM Report 10-61)."},{"key":"499_CR42","first-page":"243","volume-title":"Vision, modeling, and visualization","author":"C. Zach","year":"2008","unstructured":"Zach, C., Gallup, D., Frahm, J. M., & Niethammer, M. (2008). Fast global labeling for real-time stereo using multiple plane sweeps. In Vision, modeling, and visualization (pp. 243\u2013252)."}],"container-title":["International Journal of Computer Vision"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11263-011-0499-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11263-011-0499-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11263-011-0499-y","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,4,13]],"date-time":"2024-04-13T22:36:13Z","timestamp":1713047773000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11263-011-0499-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,10,20]]},"references-count":42,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2012,5]]}},"alternative-id":["499"],"URL":"https:\/\/doi.org\/10.1007\/s11263-011-0499-y","relation":{},"ISSN":["0920-5691","1573-1405"],"issn-type":[{"value":"0920-5691","type":"print"},{"value":"1573-1405","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,10,20]]}}}