{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,17]],"date-time":"2026-04-17T16:59:01Z","timestamp":1776445141438,"version":"3.51.2"},"reference-count":81,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2013,3,8]],"date-time":"2013-03-08T00:00:00Z","timestamp":1362700800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/2.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Int J Comput Vis"],"published-print":{"date-parts":[[2013,8]]},"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:p>We introduce a new class of data-fitting energies that couple image segmentation with image restoration. These functionals model the image intensity using the statistical framework of generalized linear models. By duality, we establish an information-theoretic interpretation using Bregman divergences. We demonstrate how this formulation couples in a principled way image restoration tasks such as denoising, deblurring (deconvolution), and inpainting with segmentation. We present an alternating minimization algorithm to solve the resulting composite photometric\/geometric inverse problem. We use Fisher scoring to solve the photometric problem and to provide asymptotic uncertainty estimates. We derive the shape gradient of our data-fitting energy and investigate convex relaxation for the geometric problem. We introduce a new alternating split-Bregman strategy to solve the resulting convex problem and present experiments and comparisons on both synthetic and real-world images.<\/jats:p>","DOI":"10.1007\/s11263-013-0615-2","type":"journal-article","created":{"date-parts":[[2013,3,7]],"date-time":"2013-03-07T12:57:25Z","timestamp":1362661045000},"page":"69-93","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":74,"title":["Coupling Image Restoration and Segmentation: A Generalized Linear Model\/Bregman Perspective"],"prefix":"10.1007","volume":"104","author":[{"given":"Gr\u00e9gory","family":"Paul","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Janick","family":"Cardinale","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ivo F.","family":"Sbalzarini","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2013,3,8]]},"reference":[{"issue":"4","key":"615_CR1","doi-asserted-by":"publisher","first-page":"913","DOI":"10.1109\/78.564179","volume":"45","author":"S Alliney","year":"1997","unstructured":"Alliney, S. (1997). A property of the minimum vectors of a regularizing functional defined by means of the absolute norm. Signal Processing IEEE Transactions on, 45(4), 913\u2013917.","journal-title":"Signal Processing IEEE Transactions on"},{"key":"615_CR2","doi-asserted-by":"publisher","first-page":"251","DOI":"10.1007\/978-0-387-45524-2_12","volume-title":"Handbook of biological confocal microscopy","author":"J Art","year":"2006","unstructured":"Art, J. (2006). Photon detectors for confocal microscopy. In J. B. Pawley (Ed.), Handbook of biological confocal microscopy (pp. 251\u2013264). Berlin: Springer."},{"issue":"4","key":"615_CR3","doi-asserted-by":"publisher","first-page":"925","DOI":"10.1137\/060671814","volume":"68","author":"G Aubert","year":"2008","unstructured":"Aubert, G., & Aujol, J. F. (2008). A variational approach to removing multiplicative noise. SIAM Journal on Applied Mathematics, 68(4), 925\u2013946.","journal-title":"SIAM Journal on Applied Mathematics"},{"key":"615_CR4","doi-asserted-by":"crossref","unstructured":"Aubert, G., & Kornprobst, P. (2006). Mathematical problems in image processing: Partial differential equations and the calculus of variations, applied mathematical sciences, vol 147, 2nd edn. Berlin: Springer.","DOI":"10.1007\/978-0-387-44588-5"},{"issue":"6","key":"615_CR5","doi-asserted-by":"publisher","first-page":"2128","DOI":"10.1137\/S0036139902408928","volume":"63","author":"G Aubert","year":"2003","unstructured":"Aubert, G., Barlaud, M., Faugeras, O., & Jehan-Besson, S. (2003). Image segmentation using active contours: Calculus of variations or shape gradients? SIAM Journal of Applied Mathematics, 63(6), 2128\u20132154.","journal-title":"SIAM Journal of Applied Mathematics"},{"key":"615_CR6","doi-asserted-by":"publisher","first-page":"111","DOI":"10.1007\/s11263-006-4331-z","volume":"67","author":"JF Aujol","year":"2006","unstructured":"Aujol, J. F., Gilboa, G., Chan, T., & Osher, S. (2006). Structure-texture image decomposition modeling, algorithms, and parameter selection. International Journal of Computer Vision, 67, 111\u2013136.","journal-title":"International Journal of Computer Vision"},{"issue":"5","key":"615_CR7","doi-asserted-by":"publisher","first-page":"412","DOI":"10.1093\/bioinformatics\/16.5.412","volume":"16","author":"P Baldi","year":"2000","unstructured":"Baldi, P., Brunak, S., Chauvin, Y., Andersen, C. A. F., & Nielsen, H. (2000). Assessing the accuracy of prediction algorithms for classification: An overview. Bioinformatics, 16(5), 412\u2013424.","journal-title":"Bioinformatics"},{"key":"615_CR8","first-page":"1705","volume":"6","author":"A Banerjee","year":"2005","unstructured":"Banerjee, A., Merugu, S., Dhillon, I., & Ghosh, J. (2005). Clustering with Bregman divergences. The Journal of Machine Learning Research, 6, 1705\u20131749.","journal-title":"The Journal of Machine Learning Research"},{"key":"615_CR9","volume-title":"Information and exponential families in statistical theory (Wiley series in probability and mathematical statistics)","author":"OE Barndorff-Nielsen","year":"1978","unstructured":"Barndorff-Nielsen, O. E. (1978). Information and exponential families in statistical theory (Wiley series in probability and mathematical statistics). Chichester: Wiley."},{"key":"615_CR10","doi-asserted-by":"publisher","DOI":"10.1887\/0750304359","volume-title":"Introduction to inverse problems in imaging","author":"M Bertero","year":"1998","unstructured":"Bertero, M., & Boccacci, P. (1998). Introduction to inverse problems in imaging. London: Taylor and Francis."},{"issue":"8","key":"615_CR11","doi-asserted-by":"publisher","first-page":"869","DOI":"10.1109\/5.5962","volume":"76","author":"M Bertero","year":"1988","unstructured":"Bertero, M., Poggio, T., & Torre, V. (1988). Ill-posed problems in early vision. Proceedings of the IEEE, 76(8), 869\u2013889.","journal-title":"Proceedings of the IEEE"},{"key":"615_CR12","volume-title":"Handbook of image and video processing (communications, networking and multimedia)","author":"AC Bovik","year":"2005","unstructured":"Bovik, A. C. (2005). Handbook of image and video processing (communications, networking and multimedia) (2nd ed.). Orlando: Academic Press, Inc.","edition":"2"},{"issue":"11","key":"615_CR13","doi-asserted-by":"publisher","first-page":"1222","DOI":"10.1109\/34.969114","volume":"23","author":"Y Boykov","year":"2001","unstructured":"Boykov, Y., Veksler, O., & Zabih, R. (2001). Fast approximate energy minimization via graph cuts. Pattern Analysis and Machine Intelligence, IEEE Transactions, 23(11), 1222\u20131239.","journal-title":"Pattern Analysis and Machine Intelligence, IEEE Transactions"},{"key":"615_CR14","doi-asserted-by":"crossref","unstructured":"Bresson, X., Esedo$${\\bar{\\text{ g}}}$$lu, S., Vandergheynst, P., Thiran, J. P., & Osher, S. (2007). Fast global minimization of the active contour\/snake model. Journal of Mathematical Imaging and Vision, 28, 151\u2013167.","DOI":"10.1007\/s10851-007-0002-0"},{"issue":"1","key":"615_CR15","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1007\/s11263-011-0499-y","volume":"98","author":"E. Brown","year":"2012","unstructured":"Brown, E., Chan, T., Bresson, X. (2012). Completely convex formulation of the Chan-Vese image segmentation model. International Journal of Computer Vision, 98(1), 103\u2013121.","journal-title":"International Journal of Computer Vision"},{"issue":"3","key":"615_CR16","doi-asserted-by":"publisher","first-page":"376","DOI":"10.1016\/j.imavis.2009.06.009","volume":"28","author":"T Brox","year":"2010","unstructured":"Brox, T., Rousson, M., Deriche, R., & Weickert, J. (2010). Colour, texture, and motion in level-set based segmentation and tracking. Image and Vision Computing, 28(3), 376\u2013390.","journal-title":"Image and Vision Computing"},{"issue":"1","key":"615_CR17","doi-asserted-by":"publisher","first-page":"11","DOI":"10.1002\/pamm.200510004","volume":"5","author":"M Burger","year":"2005","unstructured":"Burger, M., & Hinterm\u00fcller, M. (2005). Projected gradient flows for BV\/level-set relaxation. PAMM, 5(1), 11\u201314.","journal-title":"PAMM"},{"issue":"02","key":"615_CR18","doi-asserted-by":"publisher","first-page":"263","DOI":"10.1017\/S0956792505006182","volume":"16","author":"M Burger","year":"2005","unstructured":"Burger, M., & Osher, S. (2005). A survey on level set methods for inverse problems and optimal design. European Journal of Applied Mathematics, 16(02), 263\u2013301.","journal-title":"European Journal of Applied Mathematics"},{"issue":"8","key":"615_CR19","doi-asserted-by":"publisher","first-page":"3531","DOI":"10.1109\/TIP.2012.2192129","volume":"21","author":"J Cardinale","year":"2012","unstructured":"Cardinale, J., Paul, G., & Sbalzarini, I. (2012). Discrete region competition for unknown numbers of connected regions. Image Processing IEEE Transactions, 21(8), 3531\u20133545.","journal-title":"Image Processing IEEE Transactions"},{"key":"615_CR20","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/BF01385685","volume":"66","author":"V Caselles","year":"1993","unstructured":"Caselles, V., Catt\u00e9, F., Coll, T., & Dibos, F. (1993). A geometric model for active contours in image processing. Numerische Mathematik, 66, 1\u201331.","journal-title":"Numerische Mathematik"},{"key":"615_CR21","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. (1997). Geodesic active contours. International Journal of Computer Vision, 22, 61\u201379.","journal-title":"International Journal of Computer Vision"},{"key":"615_CR22","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1023\/B:JMIV.0000011320.81911.38","volume":"20","author":"A Chambolle","year":"2004","unstructured":"Chambolle, A. (2004). An algorithm for total variation minimization and applications. Journal of Mathematical Imaging and Vision, 20, 89\u201397.","journal-title":"Journal of Mathematical Imaging and Vision"},{"key":"615_CR23","doi-asserted-by":"publisher","first-page":"120","DOI":"10.1007\/s10851-010-0251-1","volume":"40","author":"A Chambolle","year":"2011","unstructured":"Chambolle, A., & Pock, T. (2011). A first-order primal-dual algorithm for convex problems with applications to imaging. Journal of Mathematical Imaging and Vision, 40, 120\u2013145.","journal-title":"Journal of Mathematical Imaging and Vision"},{"issue":"4","key":"615_CR24","doi-asserted-by":"publisher","first-page":"1113","DOI":"10.1137\/110856733","volume":"5","author":"A Chambolle","year":"2012","unstructured":"Chambolle, A., Cremers, D., & Pock, T. (2012). A convex approach to minimal partitions. SIAM Journal on Imaging Sciences, 5(4), 1113\u20131158.","journal-title":"SIAM Journal on Imaging Sciences"},{"key":"615_CR25","doi-asserted-by":"crossref","unstructured":"Chan, T. F., & Esedo$${\\bar{\\text{ g}}}$$lu, S. (2005). Aspects of total variation regularized $$L^1$$ function approximation. SIAM Journal on Applied Mathematics, 65(5), 1817\u20131837.","DOI":"10.1137\/040604297"},{"key":"615_CR26","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898717877","volume-title":"Image processing and analysis: Variational, PDE, wavelet, and stochastic methods","author":"TF Chan","year":"2005","unstructured":"Chan, T. F., & Shen, J. J. (2005). Image processing and analysis: Variational, PDE, wavelet, and stochastic methods. Philadephia: Society for Industrial and Applied Mathematics."},{"issue":"2","key":"615_CR27","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. (2001). Active contours without edges. Image Processing IEEE Transactions, 10(2), 266\u2013277.","journal-title":"Image Processing IEEE Transactions"},{"key":"615_CR28","doi-asserted-by":"crossref","unstructured":"Chan, T. F., Esedo$${\\bar{\\text{ g}}}$$lu, S., & Nikolova, M. (2006). Algorithms for finding global minimizers of image segmentation and denoising models. SIAM Journal on Applied Mathematics, 66(5), 1632\u20131648.","DOI":"10.1137\/040615286"},{"issue":"11","key":"615_CR29","doi-asserted-by":"publisher","first-page":"1145","DOI":"10.1109\/34.809108","volume":"21","author":"C Chesnaud","year":"1999","unstructured":"Chesnaud, C., R\u00e9fr\u00e9gier, P., & Boulet, V. (1999). Statistical region snake-based segmentation adapted to different physical noise models. Pattern Analysis and Machine Intelligence IEEE Transactions, 21(11), 1145\u20131157.","journal-title":"Pattern Analysis and Machine Intelligence IEEE Transactions"},{"issue":"3","key":"615_CR30","doi-asserted-by":"publisher","first-page":"591","DOI":"10.3934\/ipi.2011.5.591","volume":"5","author":"R Choksi","year":"2011","unstructured":"Choksi, R., van Gennip, Y., & Oberman, A. (2011). Anisotropic total variation regularized $$L^1$$ approximation and denoising\/deblurring of 2D bar codes. Inverse Problems and Imaging, 5(3), 591\u2013617.","journal-title":"Inverse Problems and Imaging"},{"key":"615_CR31","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1007\/s11263-006-8711-1","volume":"72","author":"D Cremers","year":"2007","unstructured":"Cremers, D., Rousson, M., & Deriche, R. (2007). A review of statistical approaches to level set segmentation: Integrating color, texture, motion and shape. International Journal of Computer Vision, 72, 195\u2013215.","journal-title":"International Journal of Computer Vision"},{"key":"615_CR32","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898719826","volume-title":"Shapes and geometries: Metrics, analysis, differential calculus, and optimization, (Vol. 22)","author":"M Delfour","year":"2011","unstructured":"Delfour, M., & Zol\u00e9sio, J. (2011). Shapes and geometries: Metrics, analysis, differential calculus, and optimization, (Vol. 22). Philadelphia: Society for Industrial Mathematics."},{"key":"615_CR33","unstructured":"Dey, N., Blanc-F\u00e9raud, L., Zimmer, C., Kam, Z., Olivo-Marin, J.C., Zerubia, J. (2004). A deconvolution method for confocal microscopy with total variation regularization. In: Biomedical imaging: Nano to macro, 2004. IEEE International Symposium on, (Vol. 2) (pp 1223\u20131226) . Arlington."},{"key":"615_CR34","unstructured":"Esser, E. (2009). Applications of Lagrangian-based alternating direction methods and connections to split Bregman. Technical report UCLA Computational and Applied Mathematics."},{"key":"615_CR35","doi-asserted-by":"publisher","first-page":"227","DOI":"10.1007\/BF00115697","volume":"6","author":"D Geiger","year":"1991","unstructured":"Geiger, D., & Yuille, A. (1991). A common framework for image segmentation. International Journal of Computational Vision, 6, 227\u2013243.","journal-title":"International Journal of Computational Vision"},{"issue":"6","key":"615_CR36","doi-asserted-by":"publisher","first-page":"721","DOI":"10.1109\/TPAMI.1984.4767596","volume":"6","author":"S Geman","year":"1984","unstructured":"Geman, S., & Geman, D. (1984). Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. Pattern Analysis and Machine Intelligence IEEE Transactions, 6(6), 721\u2013741.","journal-title":"Pattern Analysis and Machine Intelligence IEEE Transactions"},{"issue":"2","key":"615_CR37","doi-asserted-by":"publisher","first-page":"323","DOI":"10.1137\/080725891","volume":"2","author":"T Goldstein","year":"2009","unstructured":"Goldstein, T., & Osher, S. (2009). The split Bregman method for $$l^1$$-regularized problems. SIAM Journal on Imaging Sciences, 2(2), 323\u2013343.","journal-title":"SIAM Journal on Imaging Sciences"},{"key":"615_CR38","doi-asserted-by":"crossref","first-page":"272","DOI":"10.1007\/s10915-009-9331-z","volume":"45","author":"T. Goldstein","year":"2010","unstructured":"Goldstein, T., Bresson, X., & Osher, S. (2010). Geometric applications of the split Bregman method: Segmentation and surface reconstruction. Journal of Scientific Computing, 45, 272\u2013293.","journal-title":"Journal of Scientific Computing"},{"key":"615_CR39","unstructured":"Goudail, F., R\u00e9fr\u00e9gier, P., Ruch, O. (2003). Definition of a signal- to-noise ratio for object segmentation using polygonal MDL-based statistical snakes. In: Energy minimization methods in computer vision and pattern recognition, Vol. 2683 (pp. 373\u2013388). Berlin: Springer."},{"issue":"7","key":"615_CR40","doi-asserted-by":"publisher","first-page":"1231","DOI":"10.1364\/JOSAA.21.001231","volume":"21","author":"F Goudail","year":"2004","unstructured":"Goudail, F., R\u00e9fr\u00e9gier, P., & Delyon, G. (2004). Bhattacharyya distance as a contrast parameter for statistical processing of noisy optical images. Journal of the Optical Society of America A, 21(7), 1231\u20131240.","journal-title":"Journal of the Optical Society of America A"},{"issue":"2","key":"615_CR41","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1111\/j.2517-6161.1989.tb01764.x","volume":"51","author":"DM Greig","year":"1989","unstructured":"Greig, D. M., Porteous, B. T., & Seheult, A. H. (1989). Exact maximum a posteriori estimation for binary images. Journal of the Royal Statistical Society Series B (Methodological), 51(2), 271\u2013279.","journal-title":"Journal of the Royal Statistical Society Series B (Methodological)"},{"key":"615_CR42","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898718874","volume-title":"Deblurring images: Matrices, spectra, and filtering (fundamentals of algorithms 3) (fundamentals of algorithms)","author":"PC Hansen","year":"2006","unstructured":"Hansen, P. C., Nagy, J. G., & O\u2019Leary, D. P. (2006). Deblurring images: Matrices, spectra, and filtering (fundamentals of algorithms 3) (fundamentals of algorithms). Philadelphia: Society for Industrial and Applied Mathematics."},{"issue":"2","key":"615_CR43","doi-asserted-by":"publisher","first-page":"194","DOI":"10.1109\/42.24868","volume":"8","author":"T Hebert","year":"1989","unstructured":"Hebert, T., & Leahy, R. (1989). A generalized EM algorithm for 3D Bayesian reconstruction from Poisson data using Gibbs priors. Medical Imaging IEEE Transactions, 8(2), 194\u2013202.","journal-title":"Medical Imaging IEEE Transactions"},{"key":"615_CR44","unstructured":"Helmuth, J., Sbalzarini, I. (2009). Deconvolving active contours for fluorescence microscopy images. In: Advances in visual xomputing, lecture notes in computer science (Vol. 5875, pp. 544\u2013553). Berlin: Springer."},{"issue":"1","key":"615_CR45","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.jsb.2009.03.017","volume":"167","author":"J Helmuth","year":"2009","unstructured":"Helmuth, J., Burckhardt, C., Greber, U., & Sbalzarini, I. (2009). Shape reconstruction of subcellular structures from live cell fluorescence microscopy images. Journal of Structural Biology, 167(1), 1\u201310.","journal-title":"Journal of Structural Biology"},{"key":"615_CR46","unstructured":"Jung, M., Chung, G., Sundaramoorthi, G., Vese, L., Yuille, A. (2009). Sobolev gradients and joint variational image segmentation, denoising and deblurring. In: SPIE Electronic Imaging Conference Proceedings, Computational Imaging VII, SPIE (Vol. 7246)."},{"key":"615_CR47","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. (1988). Snakes: Active contour models. International Journal of Computer Vision, 1, 321\u2013331.","journal-title":"International Journal of Computer Vision"},{"key":"615_CR48","doi-asserted-by":"publisher","first-page":"271","DOI":"10.1146\/annurev.psych.55.090902.142005","volume":"55","author":"D Kersten","year":"2004","unstructured":"Kersten, D., Mamassian, P., & Yuille, A. (2004). Object perception as bayesian inference. Annual Review of Psychology, 55, 271\u2013304.","journal-title":"Annual Review of Psychology"},{"key":"615_CR49","unstructured":"Lecellier, F., Jehan-Besson, S., Fadili, J., Aubert, G., Revenu, M. (2006). Statistical region-based active contours with exponential family observations. In: Proceedings of IEEE International Acoustics, Speech and Signal Processing Conference ICASSP 2006 (Vol. 2)."},{"key":"615_CR50","doi-asserted-by":"publisher","first-page":"28","DOI":"10.1007\/s10851-009-0168-8","volume":"36","author":"F Lecellier","year":"2010","unstructured":"Lecellier, F., Fadili, J., Jehan-Besson, S., Aubert, G., Revenu, M., & Saloux, E. (2010). Region-based active contours with exponential family observations. Journal of Mathematical Imaging and Vision, 36, 28\u201345.","journal-title":"Journal of Mathematical Imaging and Vision"},{"issue":"4","key":"615_CR51","doi-asserted-by":"publisher","first-page":"1049","DOI":"10.1137\/100805844","volume":"4","author":"J Lellmann","year":"2011","unstructured":"Lellmann, J., & Schn\u00f6rr, C. (2011). Continuous multiclass labeling approaches and algorithms. SIAM Journal on Imaging Sciences, 4(4), 1049\u20131096.","journal-title":"SIAM Journal on Imaging Sciences"},{"key":"615_CR52","unstructured":"Leung, S., Osher, S. (2005). Global minimization of the active contour model with TV-inpainting and two-phase denoising. In: Variational, geometric, and level set methods in computer vision (Vol. 3752, pp. 149\u2013160). Springer: Berlin."},{"issue":"2","key":"615_CR53","doi-asserted-by":"publisher","first-page":"158","DOI":"10.1109\/34.368173","volume":"17","author":"R Malladi","year":"1995","unstructured":"Malladi, R., Sethian, J., & Vemuri, B. (1995). Shape modeling with front propagation: A level-set approach. Pattern Analysis and Machine Intelligence IEEE Transactions, 17(2), 158\u2013175.","journal-title":"Pattern Analysis and Machine Intelligence IEEE Transactions"},{"key":"615_CR54","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1007\/s10915-008-9214-8","volume":"37","author":"A. Marquina","year":"2008","unstructured":"Marquina, A., & Osher, S. (2008). Image super-resolution by TV-regularization and Bregman iteration. Journal of Scientific Computing, 37, 367\u2013382.","journal-title":"Journal of Scientific Computing"},{"issue":"6","key":"615_CR55","doi-asserted-by":"publisher","first-page":"799","DOI":"10.1109\/TPAMI.2004.11","volume":"26","author":"P Martin","year":"2004","unstructured":"Martin, P., R\u00e9fr\u00e9gier, P., Goudail, F., & Gu\u00e9rault, F. (2004). Influence of the noise model on level-set active contour segmentation. Pattern Analysis and Machine Intelligence IEEE Transactions, 26(6), 799\u2013803.","journal-title":"Pattern Analysis and Machine Intelligence IEEE Transactions"},{"issue":"2","key":"615_CR56","doi-asserted-by":"publisher","first-page":"442","DOI":"10.1016\/0005-2795(75)90109-9","volume":"405","author":"B Matthews","year":"1975","unstructured":"Matthews, B. (1975). Comparison of the predicted and observed secondary structure of t4 phage lysozyme. Biochimica et Biophysica Acta (BBA)\u2014Protein Structure, 405(2), 442\u2013451.","journal-title":"Biochimica et Biophysica Acta (BBA)\u2014Protein Structure"},{"key":"615_CR57","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4899-3242-6","volume-title":"Generalized linear models, 2nd edn","author":"P McCullagh","year":"1989","unstructured":"McCullagh, P., & Nelder, J. (1989). Generalized linear models, 2nd edn. London: Chapman and Hall\/CRC."},{"key":"615_CR58","unstructured":"Mumford, D. (1994). The Bayesian rationale for energy functionals. In: Geometry-driven diffusion in computer vision (pp. 141\u2013153). Dordrecht: Kluwer Academic Publishers."},{"issue":"5","key":"615_CR59","doi-asserted-by":"publisher","first-page":"577","DOI":"10.1002\/cpa.3160420503","volume":"42","author":"D Mumford","year":"1989","unstructured":"Mumford, D., & Shah, J. (1989). Optimal approximations by piecewise smooth functions and associated variational problems. Communications on Pure and Applied Mathematics, 42(5), 577\u2013685.","journal-title":"Communications on Pure and Applied Mathematics"},{"issue":"3","key":"615_CR60","doi-asserted-by":"publisher","first-page":"370","DOI":"10.2307\/2344614","volume":"135","author":"J Nelder","year":"1972","unstructured":"Nelder, J., & Wedderburn, R. (1972). Generalized linear models. Journal of the Royal Statistical Society Series A (General), 135(3), 370\u2013384.","journal-title":"Journal of the Royal Statistical Society Series A (General)"},{"key":"615_CR61","doi-asserted-by":"publisher","first-page":"99","DOI":"10.1023\/B:JMIV.0000011920.58935.9c","volume":"20","author":"M Nikolova","year":"2004","unstructured":"Nikolova, M. (2004). A variational approach to remove outliers and impulse noise. Journal of Mathematical Imaging and Vision, 20, 99\u2013120.","journal-title":"Journal of Mathematical Imaging and Vision"},{"key":"615_CR62","doi-asserted-by":"crossref","DOI":"10.1007\/b98879","volume-title":"Level set methods and dynamic implicit surfaces, applied mathematical sciences (Vol. 153)","author":"S Osher","year":"2003","unstructured":"Osher, S., & Fedkiw, R. (2003). Level set methods and dynamic implicit surfaces, applied mathematical sciences (Vol. 153). New York: Springer."},{"key":"615_CR63","doi-asserted-by":"crossref","DOI":"10.1007\/b97541","volume-title":"Geometric level set methods in imaging, vision, and graphics","author":"S Osher","year":"2003","unstructured":"Osher, S., & Paragios, N. (2003). Geometric level set methods in imaging, vision, and graphics. New York: Springer."},{"issue":"1\u20132","key":"615_CR64","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1006\/jvci.2001.0475","volume":"13","author":"N. Paragios","year":"2002","unstructured":"Paragios, N., & Deriche, R. (2002). Geodesic active regions: A new framework to deal with frame partition problems in computer vision. Journal of Visual Communication and Image Representation, 13(1\u20132), 249\u2013268.","journal-title":"Journal of Visual Communication and Image Representation"},{"key":"615_CR65","unstructured":"Paul, G., Cardinale, J., Sbalzarini, I. (2011). An alternating split Bregman algorithm for multi-region segmentation. In: Signals, systems and computers (ASILOMAR), 2011 Conference Record of the Forty Fifth Asilomar Conference on, (pp. 426\u2013430)."},{"key":"615_CR66","unstructured":"Pock, T., Schoenemann, T., Graber, G., Bischof, H., Cremers, D. (2008). A convex formulation of continuous multi-label problems. In: Computer vision-ECCV 2008 (Vol. 5304, pp 792\u2013805). Berlin: Springer."},{"key":"615_CR67","unstructured":"Pock, T., Chambolle, A., Cremers, D., Bischof, H. (2009). A convex relaxation approach for computing minimal partitions. In: IEEE Conference on Computer vision and pattern recognition, 2009. CVPR 2009 (pp. 810\u2013817)."},{"issue":"1\u20134","key":"615_CR68","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. (1992). Nonlinear total variation based noise removal algorithms. Physica D: Nonlinear Phenomena, 60(1\u20134), 259\u2013268.","journal-title":"Physica D: Nonlinear Phenomena"},{"issue":"3","key":"615_CR69","doi-asserted-by":"publisher","first-page":"1482","DOI":"10.1529\/biophysj.104.057885","volume":"89","author":"IF Sbalzarini","year":"2005","unstructured":"Sbalzarini, I. F., Mezzacasa, A., Helenius, A., & Koumoutsakos, P. (2005). Effects of organelle shape on fluorescence recovery after photobleaching. Biophysical Journal, 89(3), 1482\u20131492.","journal-title":"Biophysical Journal"},{"issue":"3","key":"615_CR70","doi-asserted-by":"publisher","first-page":"878","DOI":"10.1529\/biophysj.105.073809","volume":"90","author":"IF Sbalzarini","year":"2006","unstructured":"Sbalzarini, I. F., Hayer, A., Helenius, A., & Koumoutsakos, P. (2006). Simulations of (an)isotropic diffusion on curved biological surfaces. Biophysical Journal, 90(3), 878\u2013885.","journal-title":"Biophysical Journal"},{"key":"615_CR71","unstructured":"Sethian, J. (1999). Level set methods and fast marching methods: Evolving interfaces in computational geometry, fluid mechanics, computer vision, and material science. Cambridge: Cambridge University Press."},{"key":"615_CR72","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1007\/s11263-010-0357-3","volume":"92","author":"S. Setzer","year":"2011","unstructured":"Setzer, S. (2011). Operator splittings, Bregman methods and frame shrinkage in image processing. International Journal of Computer Vision, 92, 265\u2013280.","journal-title":"International Journal of Computer Vision"},{"issue":"3","key":"615_CR73","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1016\/j.jvcir.2009.10.006","volume":"21","author":"S Setzer","year":"2010","unstructured":"Setzer, S., Steidl, G., & Teuber, T. (2010). Deblurring Poissonian images by split Bregman techniques. Journal of Visual Communication and Image Representation, 21(3), 193\u2013199.","journal-title":"Journal of Visual Communication and Image Representation"},{"issue":"2","key":"615_CR74","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1109\/TMI.1982.4307558","volume":"1","author":"L. A. Shepp","year":"1982","unstructured":"Shepp, L. A., & Vardi, Y. (1982). Maximum likelihood reconstruction for emission tomography. Medical Imaging IEEE Transactions, 1(2), 113\u2013122.","journal-title":"Medical Imaging IEEE Transactions"},{"key":"615_CR75","unstructured":"Song, P.X.K. (2007). Vector generalized linear models. In: Correlated data analysis: Modeling, analytics, and applications, Springer series in statistics (pp. 121\u2013155). New York: Springer."},{"issue":"1","key":"615_CR76","doi-asserted-by":"publisher","first-page":"135","DOI":"10.1137\/S0036144598336745","volume":"41","author":"G Strang","year":"1999","unstructured":"Strang, G. (1999). The discrete cosine transform. SIAM Review, 41(1), 135\u2013147.","journal-title":"SIAM Review"},{"key":"615_CR77","unstructured":"Tai, X.C., Wu, C. (2009). Augmented lagrangian method, dual methods and split bregman iteration for rof model. In: Scale space and variational methods in computer vision (Vol. 5567, pp. 502\u2013513). Berlin: Springer."},{"key":"615_CR78","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898717570","volume-title":"Computational methods for inverse problems","author":"CR Vogel","year":"2002","unstructured":"Vogel, C. R. (2002). Computational methods for inverse problems. Philadelphia: Society for Industrial and Applied Mathematics."},{"issue":"4","key":"615_CR79","doi-asserted-by":"publisher","first-page":"539","DOI":"10.1109\/TIP.2008.917103","volume":"17","author":"C Vonesch","year":"2008","unstructured":"Vonesch, C., & Unser, M. (2008). A fast thresholded Landweber algorithm for wavelet-regularized multidimensional deconvolution. IEEE Transactions on Image Processing, 17(4), 539\u2013549.","journal-title":"IEEE Transactions on Image Processing"},{"issue":"3","key":"615_CR80","doi-asserted-by":"crossref","first-page":"667","DOI":"10.1242\/dev.088872","volume":"143","author":"J. Zartman","year":"2013","unstructured":"Zartman, J., Restrepo, S., Basler, K. (2013). A high-throughput template for optimizing Drosophila organ culture with response-surface methods. Development, 143(3), 667\u2013674.","journal-title":"Development"},{"issue":"9","key":"615_CR81","doi-asserted-by":"publisher","first-page":"884","DOI":"10.1109\/34.537343","volume":"18","author":"S Zhu","year":"1996","unstructured":"Zhu, S., & Yuille, A. (1996). Region competition: Unifying snakes, region growing, and Bayes\/MDL for multiband image segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 18(9), 884\u2013900.","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence"}],"container-title":["International Journal of Computer Vision"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11263-013-0615-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11263-013-0615-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11263-013-0615-2","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11263-013-0615-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,9,16]],"date-time":"2020-09-16T20:58:34Z","timestamp":1600289914000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11263-013-0615-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,3,8]]},"references-count":81,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2013,8]]}},"alternative-id":["615"],"URL":"https:\/\/doi.org\/10.1007\/s11263-013-0615-2","relation":{},"ISSN":["0920-5691","1573-1405"],"issn-type":[{"value":"0920-5691","type":"print"},{"value":"1573-1405","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,3,8]]},"assertion":[{"value":"15 February 2012","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 January 2013","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 March 2013","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}