Image Segmentation Using Active Contours: Calculus of Variations or Shape Gradients?, SIAM Journal on Applied Mathematics, vol.63, issue.6, pp.2128-2154, 2003. ,
DOI : 10.1137/S0036139902408928
URL : https://hal.archives-ouvertes.fr/inria-00072105
Learning with submodular functions: a convex optimization perspective, Foundations and Trends, Machine Learning, pp.145-373, 2013. ,
DOI : 10.1561/2200000039
URL : http://arxiv.org/abs/1111.6453
Optimization with sparsity-inducing penalties, Foundations and Trends in Machine Learning, pp.1-106, 2012. ,
DOI : 10.1561/2200000015
URL : http://arxiv.org/abs/1108.0775
Shaping level sets with submodular functions, Advances in Neural Information Processing Systems, pp.10-18, 2011. ,
URL : https://hal.archives-ouvertes.fr/hal-00542949
Mumford and Shah model and its applications to image segmentation and image restoration, Handbook of Mathematical Methods in Imaging, pp.1095-1157, 2011. ,
DOI : 10.1007/978-0-387-92920-0_25
A note on cluster analysis and dynamic programming, Mathematical Biosciences, vol.18, issue.3-4, pp.311-312, 1973. ,
DOI : 10.1016/0025-5564(73)90007-2
The group fused Lasso for multiple change-point detection, arXiv preprint, 2011. ,
Convex analysis and nonlinear optimization: theory and examples, 2010. ,
An experimental comparison of min-cut/max- flow algorithms for energy minimization in vision, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.26, issue.9, pp.1124-1137, 2004. ,
DOI : 10.1109/TPAMI.2004.60
Fast approximate energy minimization via graph cuts, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.23, issue.11, pp.1222-1239, 2001. ,
DOI : 10.1109/34.969114
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.112.6806
Fast Global Minimization of the Active Contour/Snake Model, Journal of Mathematical Imaging and Vision, vol.7, issue.3, pp.151-167, 2007. ,
DOI : 10.1007/b98879
An introduction to total variation for image analysis, in Theoretical foundations and numerical methods for sparse recovery, pp.263-340, 2010. ,
On Total Variation Minimization and Surface Evolution Using Parametric Maximum Flows, International Journal of Computer Vision, vol.40, issue.9, pp.288-307, 2009. ,
DOI : 10.1006/jctb.2000.1989
A First-Order Primal-Dual Algorithm for Convex Problems with??Applications to Imaging, Journal of Mathematical Imaging and Vision, vol.60, issue.5, pp.120-145, 2011. ,
DOI : 10.1007/978-3-540-74936-3_22
URL : https://hal.archives-ouvertes.fr/hal-00490826
Total Variation Image Restoration: Overview and Recent Developments, Mathematical Models of Computer Vision, pp.17-31, 2005. ,
DOI : 10.1007/0-387-28831-7_2
Active contours without edges, IEEE Transactions on Image Processing, vol.10, issue.2, pp.266-277, 2001. ,
DOI : 10.1109/83.902291
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.2.1828
The Convex Geometry of Linear Inverse Problems, Foundations of Computational Mathematics, vol.1, issue.10, pp.805-849, 2012. ,
DOI : 10.1007/978-1-4613-8431-1
Orthogonal least squares learning algorithm for radial basis function networks, IEEE Transactions on Neural Networks, vol.2, issue.2, pp.302-309, 1991. ,
DOI : 10.1109/72.80341
URL : https://eprints.soton.ac.uk/251135/1/00080341.pdf
A Direct Algorithm for 1-D Total Variation Denoising, IEEE Signal Processing Letters, vol.20, issue.11, pp.1054-1057, 2013. ,
DOI : 10.1109/LSP.2013.2278339
URL : https://hal.archives-ouvertes.fr/hal-00675043
On Nonlinear Fractional Programming, Management Science, vol.13, issue.7, pp.492-498, 1967. ,
DOI : 10.1287/mnsc.13.7.492
Least angle regression, The Annals of statistics, pp.407-499, 2004. ,
Multiple regression analysis, Mathematical methods for digital computers, pp.191-203, 1960. ,
Discrete optimization of the multiphase piecewise constant Mumford-Shah functional, in Energy Minimization Methods in Computer Vision and Pattern Recognition, pp.233-246, 2011. ,
Combinatorial Optimization of the piecewise constant Mumford-Shah functional with application to scalar/vector valued and volumetric image segmentation, Image and Vision Computing, vol.29, issue.6, pp.29-365, 2011. ,
DOI : 10.1016/j.imavis.2010.09.002
Brain MRI tissue classification using graph cut optimization of the Mumford?Shah functional, Proceedings of the International Vision Conference of New Zealand, pp.321-326, 2007. ,
Regularization Paths for Generalized Linear Models via Coordinate Descent, Journal of Statistical Software, vol.33, issue.1, pp.1-22, 2010. ,
DOI : 10.18637/jss.v033.i01
URL : http://doi.org/10.18637/jss.v033.i01
Class segmentation and object localization with superpixel neighborhoods, 2009 IEEE 12th International Conference on Computer Vision, pp.670-677, 2009. ,
DOI : 10.1109/ICCV.2009.5459175
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.150.4613
An Overview of the Mumford-Shah Problem, Milan Journal of Mathematics, vol.71, issue.1, pp.95-119, 2003. ,
DOI : 10.1007/s00032-003-0016-z
Constrained restoration and the recovery of discontinuities, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.14, issue.3, pp.367-383, 1992. ,
DOI : 10.1109/34.120331
Parametric Maximum Flow Algorithms for Fast Total Variation Minimization, SIAM Journal on Scientific Computing, vol.31, issue.5, pp.31-3712, 2009. ,
DOI : 10.1137/070706318
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.413.5958
Conditional gradient algorithms for normregularized smooth convex optimization, Mathematical Programming, pp.75-112, 2015. ,
DOI : 10.1007/s10107-014-0778-9
URL : https://hal.archives-ouvertes.fr/hal-00978368
Exact optimization for markov random fields with convex priors, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.25, issue.10, pp.1333-1336, 2003. ,
DOI : 10.1109/TPAMI.2003.1233908
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.106.8689
Revisiting Frank-Wolfe: projection-free sparse convex optimization, Proceedings of the 30th International Conference on Machine Learning, pp.427-435, 2013. ,
Reflection methods for user-friendly submodular optimization, Advances in Neural Information Processing Systems, pp.1313-1321, 2013. ,
URL : https://hal.archives-ouvertes.fr/hal-00905258
-Segmentation, Journal of Computational and Graphical Statistics, vol.9, issue.2, pp.246-260, 2013. ,
DOI : 10.1093/biostatistics/kxm013
URL : https://hal.archives-ouvertes.fr/halshs-00250206
Snakes: Active contour models, International Journal of Computer Vision, vol.5, issue.6035, pp.321-331, 1988. ,
DOI : 10.1007/BF00133570
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.124.5318
Efficiently solving dynamic Markov random fields using graph cuts, Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1, pp.922-929, 2005. ,
DOI : 10.1109/ICCV.2005.81
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.399.3048
Total Variation on a Tree, SIAM Journal on Imaging Sciences, vol.9, issue.2, pp.605-636, 2016. ,
DOI : 10.1137/15M1010257
What energy functions can be minimized via graph cuts?, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.26, issue.2, pp.147-159, 2004. ,
DOI : 10.1109/TPAMI.2004.1262177
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.113.1823
Maximum likelihood detection and estimation of Bernoulli - Gaussian processes, IEEE Transactions on Information Theory, vol.28, issue.3, pp.482-488, 1982. ,
DOI : 10.1109/TIT.1982.1056496
Active-set methods for submodular optimization, arXiv preprint, 2015. ,
Constructing simple stable descriptions for image partitioning, International Journal of Computer Vision, vol.1, issue.2, pp.73-102, 1989. ,
DOI : 10.1109/TPAMI.1986.4767807
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.52.2727
On minimizing partitions with infinitely many components, Annali dell, pp.41-57, 1998. ,
An Inertial Forward-Backward Algorithm for Monotone Inclusions, Journal of Mathematical Imaging and Vision, vol.23, issue.3, pp.311-325, 2014. ,
DOI : 10.1137/110844805
URL : http://arxiv.org/abs/1403.3522
Adaptive time-frequency decomposition with matching pursuits, in Time- Frequency and Time-Scale Analysis, Proceedings of the IEEE-SP International Symposium, pp.7-10, 1992. ,
DOI : 10.1109/tftsa.1992.274245
Optimal approximations by piecewise smooth functions and associated variational problems, Communications on pure and applied mathematics, pp.577-685, 1989. ,
DOI : 10.1002/cpa.3160420503
URL : https://dash.harvard.edu/bitstream/handle/1/3637121/Mumford_OptimalApproxPiece.pdf?sequence=1
CoSaMP, Communications of the ACM, vol.53, issue.12, pp.301-321, 2009. ,
DOI : 10.1145/1859204.1859229
A unified framework for highdimensional analysis of m-estimators with decomposable regularizers, Advances in Neural Information Processing Systems, pp.1348-1356, 2009. ,
Gradient methods for minimizing composite objective function, tech. report, Center for Operations Research and Econometrics (CORE), 2007. ,
DOI : 10.1007/s10107-012-0629-5
Optimal Interval Clustering: Application to Bregman Clustering and Statistical Mixture Learning, IEEE Signal Processing Letters, vol.21, issue.10, pp.1289-1292, 2014. ,
DOI : 10.1109/LSP.2014.2333001
URL : http://arxiv.org/pdf/1403.2485
Fast Nonconvex Nonsmooth Minimization Methods for Image Restoration and Reconstruction, IEEE Transactions on Image Processing, vol.19, issue.12, pp.3073-3088, 2010. ,
DOI : 10.1109/TIP.2010.2052275
Multi-task feature selection, 2006. ,
On Iteratively Reweighted Algorithms for Nonsmooth Nonconvex Optimization in Computer Vision, SIAM Journal on Imaging Sciences, vol.8, issue.1, pp.331-372, 2015. ,
DOI : 10.1137/140971518
Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations, Journal of Computational Physics, vol.79, issue.1, pp.12-49, 1988. ,
DOI : 10.1016/0021-9991(88)90002-2
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.413.5254
Minimum cuts and related problems, Networks, vol.17, issue.4, pp.357-370, 1975. ,
DOI : 10.1007/978-3-642-85823-9
Diagonal preconditioning for first order primal-dual algorithms in convex optimization, 2011 International Conference on Computer Vision, pp.1762-1769, 2011. ,
DOI : 10.1109/ICCV.2011.6126441
A Generalized Forward-Backward Splitting, SIAM Journal on Imaging Sciences, vol.6, issue.3, pp.1199-1226, 2013. ,
DOI : 10.1137/120872802
URL : https://hal.archives-ouvertes.fr/hal-00613637
Preconditioning of a Generalized Forward-Backward Splitting and Application to Optimization on Graphs, SIAM Journal on Imaging Sciences, vol.8, issue.4, pp.2706-2739, 2015. ,
DOI : 10.1137/15M1018253
URL : https://hal.archives-ouvertes.fr/hal-01144566
Forward–Backward Greedy Algorithms for Atomic Norm Regularization, IEEE Transactions on Signal Processing, vol.63, issue.21, pp.5798-5811, 2015. ,
DOI : 10.1109/TSP.2015.2461515
Convex analysis, 1970. ,
DOI : 10.1515/9781400873173
The Group-Lasso for generalized linear models, Proceedings of the 25th international conference on Machine learning, ICML '08, pp.848-855, 2008. ,
DOI : 10.1145/1390156.1390263
Nonlinear total variation based noise removal algorithms, Physica D: Nonlinear Phenomena, pp.259-268, 1992. ,
DOI : 10.1016/0167-2789(92)90242-f
The Fourier reconstruction of a head section, IEEE Transactions on Nuclear Science, vol.21, issue.3, pp.21-43, 1974. ,
DOI : 10.1109/TNS.1974.6499235
From Bernoulli–Gaussian Deconvolution to Sparse Signal Restoration, IEEE Transactions on Signal Processing, vol.59, issue.10, pp.59-4572, 2011. ,
DOI : 10.1109/TSP.2011.2160633
A Comparative Study of Energy Minimization Methods for Markov Random Fields, Proceeding of the European Conference in Computer Vision (ECCV), pp.16-29, 2006. ,
DOI : 10.1109/ICCV.2005.14
Optimal segmentation of unbounded functions, pp.153-174, 1996. ,
Total variation and level set methods in image science, Acta Numerica, vol.14, pp.509-573, 2005. ,
DOI : 10.1017/S0962492904000273
A multiphase level set framework for image segmentation using the Mumford and Shah model, International Journal of Computer Vision, pp.50-271, 2002. ,
Trend filtering on graphs, Journal of Machine Learning Research, vol.17, pp.1-41, 2016. ,
Adaptive forward-backward greedy algorithm for sparse learning with linear models, Advances in Neural Information Processing Systems, pp.1921-1928, 2009. ,
DOI : 10.1109/tit.2011.2146690
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.388.4812
The Adaptive Lasso and Its Oracle Properties, Journal of the American Statistical Association, vol.101, issue.476, pp.1418-1429, 2006. ,
DOI : 10.1198/016214506000000735
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.649.404