The Potts Model with Different Piecewise Constant Representations and Fast Algorithms: A Survey

[1]  Abderrahim Elmoataz,et al.  Nonlocal Discrete Regularization on Weighted Graphs: A Framework for Image and Manifold Processing , 2008, IEEE Transactions on Image Processing.

[2]  Camille Couprie,et al.  Combinatorial Continuous Maximal Flows , 2010, ArXiv.

[3]  Abderrahim Elmoataz,et al.  Geometric PDEs on Weighted Graphs for Semi-supervised Classification , 2014, 2014 13th International Conference on Machine Learning and Applications.

[4]  T. Chan,et al.  Fast numerical algorithms for total variation based image restoration , 2008 .

[5]  Vladimir Kolmogorov,et al.  An Experimental Comparison of Min-Cut/Max-Flow Algorithms for Energy Minimization in Vision , 2004, IEEE Trans. Pattern Anal. Mach. Intell..

[6]  A. Bertozzi,et al.  $\Gamma$-convergence of graph Ginzburg-Landau functionals , 2012, Advances in Differential Equations.

[7]  Daniel Cremers,et al.  A Convex Approach to Minimal Partitions , 2012, SIAM J. Imaging Sci..

[8]  Matthias Hein,et al.  Spectral clustering based on the graph p-Laplacian , 2009, ICML '09.

[9]  Abderrahim Elmoataz,et al.  Partial Difference Operators on Weighted Graphs for Image Processing on Surfaces and Point Clouds , 2014, IEEE Transactions on Image Processing.

[10]  Jérôme Darbon,et al.  Image Restoration with Discrete Constrained Total Variation Part I: Fast and Exact Optimization , 2006, Journal of Mathematical Imaging and Vision.

[11]  T. Chan,et al.  A Variational Level Set Approach to Multiphase Motion , 1996 .

[12]  Roger Fletcher,et al.  Projected Barzilai-Borwein methods for large-scale box-constrained quadratic programming , 2005, Numerische Mathematik.

[13]  Vladlen Koltun,et al.  Efficient Inference in Fully Connected CRFs with Gaussian Edge Potentials , 2011, NIPS.

[14]  I. Ekeland,et al.  Convex analysis and variational problems , 1976 .

[15]  Tony F. Chan,et al.  A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model , 2002, International Journal of Computer Vision.

[16]  Jianbo Shi,et al.  Spectral segmentation with multiscale graph decomposition , 2005, 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05).

[17]  Hiroshi Ishikawa,et al.  Exact Optimization for Markov Random Fields with Convex Priors , 2003, IEEE Trans. Pattern Anal. Mach. Intell..

[18]  D. Mumford,et al.  Optimal approximations by piecewise smooth functions and associated variational problems , 1989 .

[19]  Antonin Chambolle,et al.  A First-Order Primal-Dual Algorithm for Convex Problems with Applications to Imaging , 2011, Journal of Mathematical Imaging and Vision.

[20]  Tony F. Chan,et al.  A General Framework for a Class of First Order Primal-Dual Algorithms for Convex Optimization in Imaging Science , 2010, SIAM J. Imaging Sci..

[21]  Xue-Cheng Tai,et al.  An Effective Region Force for Some Variational Models for Learning and Clustering , 2017, Journal of Scientific Computing.

[22]  Ekaterina Merkurjev,et al.  Convex Variational Methods on Graphs for Multiclass Segmentation of High-Dimensional Data and Point Clouds , 2016, Journal of Mathematical Imaging and Vision.

[23]  Xue-Cheng Tai,et al.  A Continuous Max-Flow Approach to Potts Model , 2010, ECCV.

[24]  Xue-Cheng Tai,et al.  Efficient Global Minimization Methods for Image Segmentation Models with Four Regions , 2014, Journal of Mathematical Imaging and Vision.

[25]  Xue-Cheng Tai,et al.  A new continuous max-flow algorithm for multiphase image segmentation using super-level set functions , 2014, J. Vis. Commun. Image Represent..

[26]  Andrew McCallum,et al.  Conditional Random Fields: Probabilistic Models for Segmenting and Labeling Sequence Data , 2001, ICML.

[27]  Jérôme Darbon,et al.  Image Restoration with Discrete Constrained Total Variation Part II: Levelable Functions, Convex Priors and Non-Convex Cases , 2006, Journal of Mathematical Imaging and Vision.

[28]  Xue-Cheng Tai,et al.  Global Minimization for Continuous Multiphase Partitioning Problems Using a Dual Approach , 2011, International Journal of Computer Vision.

[29]  D. Bertsekas On the Goldstein-Levitin-Polyak gradient projection method , 1974, CDC 1974.

[30]  Donald Geman,et al.  Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[31]  Xue-Cheng Tai,et al.  Graph Cut Optimization for the Piecewise Constant Level Set Method Applied to Multiphase Image Segmentation , 2009, SSVM.

[32]  Alexander Schrijver,et al.  On the history of the transportation and maximum flow problems , 2002, Math. Program..

[33]  Guy Gilboa,et al.  Nonlocal Operators with Applications to Image Processing , 2008, Multiscale Model. Simul..

[34]  Xue-Cheng Tai,et al.  A variant of the level set method and applications to image segmentation , 2006, Math. Comput..

[35]  Jing Yuan,et al.  Convex Multi-class Image Labeling by Simplex-Constrained Total Variation , 2009, SSVM.

[36]  M. Nikolova An Algorithm for Total Variation Minimization and Applications , 2004 .

[37]  R. B. Potts Some generalized order-disorder transformations , 1952, Mathematical Proceedings of the Cambridge Philosophical Society.

[38]  Mason A. Porter,et al.  A Method Based on Total Variation for Network Modularity Optimization Using the MBO Scheme , 2013, SIAM J. Appl. Math..

[39]  Camille Couprie,et al.  Combinatorial Continuous Maximum Flow , 2010, SIAM J. Imaging Sci..

[40]  Richard Szeliski,et al.  A Comparative Study of Energy Minimization Methods for Markov Random Fields , 2006, ECCV.

[41]  Kenneth Steiglitz,et al.  Combinatorial Optimization: Algorithms and Complexity , 1981 .

[42]  Daniel Cremers,et al.  A Convex Formulation of Continuous Multi-label Problems , 2008, ECCV.

[43]  Xue-Cheng Tai,et al.  Convex Relaxations for a Generalized Chan-Vese Model , 2013, EMMCVPR.

[44]  Olga Veksler,et al.  Fast Approximate Energy Minimization via Graph Cuts , 2001, IEEE Trans. Pattern Anal. Mach. Intell..

[45]  Daniel Cremers,et al.  A convex relaxation approach for computing minimal partitions , 2009, CVPR.

[46]  Mila Nikolova,et al.  Algorithms for Finding Global Minimizers of Image Segmentation and Denoising Models , 2006, SIAM J. Appl. Math..

[47]  L. Rudin,et al.  Nonlinear total variation based noise removal algorithms , 1992 .

[48]  Xue-Cheng Tai,et al.  A spatially continuous max-flow and min-cut framework for binary labeling problems , 2014, Numerische Mathematik.

[49]  Tony F. Chan,et al.  Active contours without edges , 2001, IEEE Trans. Image Process..

[50]  Xue-Cheng Tai,et al.  Efficient Global Minimization for the Multiphase Chan-Vese Model of Image Segmentation , 2009, EMMCVPR.

[51]  Ronald Fedkiw,et al.  Level set methods and dynamic implicit surfaces , 2002, Applied mathematical sciences.

[52]  Xue-Cheng Tai,et al.  Augmented Lagrangian Method, Dual Methods, and Split Bregman Iteration for ROF, Vectorial TV, and High Order Models , 2010, SIAM J. Imaging Sci..

[53]  Andrea L. Bertozzi,et al.  An MBO Scheme on Graphs for Classification and Image Processing , 2013, SIAM J. Imaging Sci..

[54]  Xavier Bresson,et al.  Convergence and Energy Landscape for Cheeger Cut Clustering , 2012, NIPS.

[55]  C. Michelot A finite algorithm for finding the projection of a point onto the canonical simplex of ∝n , 1986 .

[56]  Xue-Cheng Tai,et al.  Piecewise Constant Level Set Methods and Image Segmentation , 2005, Scale-Space.

[57]  R. Dykstra,et al.  A Method for Finding Projections onto the Intersection of Convex Sets in Hilbert Spaces , 1986 .

[58]  Braxton Osting,et al.  Minimal Dirichlet Energy Partitions for Graphs , 2013, SIAM J. Sci. Comput..

[59]  Olga Veksler,et al.  Markov random fields with efficient approximations , 1998, Proceedings. 1998 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No.98CB36231).

[60]  Arjuna Flenner,et al.  Diffuse Interface Models on Graphs for Classification of High Dimensional Data , 2012, Multiscale Model. Simul..

[61]  C. Vogel,et al.  Analysis of bounded variation penalty methods for ill-posed problems , 1994 .

[62]  J. Borwein,et al.  Two-Point Step Size Gradient Methods , 1988 .

[63]  Hugues Talbot,et al.  Globally minimal surfaces by continuous maximal flows , 2003, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[64]  Xue-Cheng Tai,et al.  A Fast Continuous Max-Flow Approach to Non-convex Multi-labeling Problems , 2011, Efficient Algorithms for Global Optimization Methods in Computer Vision.

[65]  Pietro Perona,et al.  Self-Tuning Spectral Clustering , 2004, NIPS.

[66]  W. Fleming,et al.  An integral formula for total gradient variation , 1960 .

[67]  Xue-Cheng Tai,et al.  Global Binary Optimization on Graphs for Classification of High-Dimensional Data , 2015, Journal of Mathematical Imaging and Vision.

[68]  Gilbert Strang,et al.  Maximal flow through a domain , 1983, Math. Program..

[69]  A. Chambolle,et al.  An introduction to Total Variation for Image Analysis , 2009 .

[70]  Arjuna Flenner,et al.  Multiclass Data Segmentation Using Diffuse Interface Methods on Graphs , 2013, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[71]  Xue-Cheng Tai,et al.  A binary level set model and some applications to Mumford-Shah image segmentation , 2006, IEEE Transactions on Image Processing.

[72]  Bernhard Schölkopf,et al.  Kernel Methods in Computational Biology , 2005 .

[73]  S. Osher,et al.  A level set approach for computing solutions to incompressible two-phase flow , 1994 .