{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T14:13:55Z","timestamp":1780323235172,"version":"3.54.1"},"reference-count":224,"publisher":"Emerald","issue":"1-2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2012,10,5]]},"abstract":"<jats:p>This monograph gives an introduction to the fundamentals of Markovian modeling in image segmentation as well as a brief overview of recent advances in the field. Segmentation is considered in a common framework, called image labeling, where the problem is reduced to assigning labels to pixels. In a probabilistic approach, label dependencies are modeled by Markov random fields (MRF) and an optimal labeling is determined by Bayesian estimation, in particular maximum a posteriori (MAP) estimation. The main advantage of MRF models is that prior information can be imposed locally through clique potentials. The primary goal is to demonstrate the basic steps to construct an easily applicable MRF segmentation model and further develop its multiscale and hierarchical implementations as well as their combination in a multilayer model. MRF models usually yield a non-convex energy function. The minimization of this function is crucial in order to find the most likely segmentation according to the MRF model. Besides classical optimization algorithms, like simulated annealing or deterministic relaxation, we also present recently introduced graph cut-based algorithms. We briefly discuss the possible parallelization techniques of simulated annealing, which allows efficient implementation on, e.g., GPU hardware without compromising convergence properties of the algorithms. While the main focus of this monograph is on generic model construction and related energy minimization methods, many sample applications are also presented to demonstrate the applicability of these models in real life problems such as remote sensing, biomedical imaging, change detection, and color- and motion-based segmentation. In real-life applications, parameter estimation is an important issue when implementing completely data-driven algorithms. Therefore some basic procedures, such as expectation-maximization, are also presented in the context of color image segmentation.<\/jats:p>\n                  <jats:p>Note: A sample implementation of the most important segmentation algorithms is available in grey scale at http:\/\/dx.doi.org\/10.1561\/2000000035 demogray and in color at http:\/\/dx.doi.org\/10.1561\/2000000035 democolor.<\/jats:p>","DOI":"10.1561\/2000000035","type":"journal-article","created":{"date-parts":[[2012,10,5]],"date-time":"2012-10-05T13:12:20Z","timestamp":1349442740000},"page":"1-155","source":"Crossref","is-referenced-by-count":73,"title":["Markov Random Fields in Image Segmentation"],"prefix":"10.1108","volume":"5","author":[{"given":"Zoltan","family":"Kato","sequence":"first","affiliation":[{"name":"Image Processing and Computer Graphics Dept., University of Szeged , Arpad ter 2, Szeged, 6720,","place":["Hungary"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Josiane","family":"Zerubia","sequence":"additional","affiliation":[{"name":"INRIA Sophia Antipolis-Mediterranee , 2004 Route des Lucioles, Sophia Antipolis, 06902 Cedex,","place":["France"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"140","published-online":{"date-parts":[[2012,10,5]]},"reference":[{"key":"2026040313415969100_ref001","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1006\/jcph.1995.1098","article-title":"\u201cA fast level set method for propagating interfaces,\u201d","volume":"118","author":"Adalsteinsson","year":"1995","journal-title":"Journal of Computational Physics,"},{"key":"2026040313415969100_ref002","volume-title":"Proceedings of Association Franaise pour la Cybernetique Economique et Technique,","author":"Azencott","year":"1987"},{"key":"2026040313415969100_ref003","first-page":"37","volume-title":"Simulated Annealing: Parallelization Techniques,","author":"Azencott","year":"1992"},{"key":"2026040313415969100_ref004","volume-title":"Parallel Simulated Annealing. Parallelization Techniques.","author":"Azencott","year":"1992"},{"key":"2026040313415969100_ref005","first-page":"81","volume-title":"Simulated Annealing: Parallelization Techniques,","author":"Azencott","year":"1992"},{"key":"2026040313415969100_ref006","article-title":"\u201cOptimization of positive generalized polynomials under l&gt;p constraints,\u201d","author":"BaratchartBerthod","year":"1995"},{"issue":"8","key":"2026040313415969100_ref007","doi-asserted-by":"crossref","first-page":"1239","DOI":"10.1109\/TPAMI.2005.161","article-title":"\u201cGeneralizing Swendsen-Wang to sampling arbitrary posterior probabilities,\u201d","volume":"27","author":"Barbu","year":"2005","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence,"},{"key":"2026040313415969100_ref008","volume-title":"Nonlinear Parameter Estimation.","author":"Bard","year":"1974"},{"key":"2026040313415969100_ref009","doi-asserted-by":"crossref","first-page":"587","DOI":"10.1016\/S0031-3203(99)00074-6","article-title":"\u201cUnsupervised image segmentation using Markov random field models,\u201d","volume":"33","author":"Barker","year":"2000","journal-title":"Pattern Recognition,"},{"key":"2026040313415969100_ref010","volume-title":"Exactly Solved Models in Statistical Mechanics.","author":"Baxter","year":"1990"},{"key":"2026040313415969100_ref011","doi-asserted-by":"crossref","first-page":"3416","DOI":"10.1109\/TGRS.2009.2022633","article-title":"\u201cChange detection in optical aerial images by a multi-layer conditional mixed markov model,\u201d","volume":"47","author":"Benedek","year":"2009","journal-title":"IEEE Transactions on Geoscience and Remote Sensing,"},{"key":"2026040313415969100_ref012","first-page":"141","volume-title":"Proceedings of International Conference on Image Processing,","author":"Benedek","year":"2007"},{"key":"2026040313415969100_ref013","author":"Benedek","year":"2007"},{"key":"2026040313415969100_ref014","doi-asserted-by":"crossref","first-page":"2303","DOI":"10.1109\/TIP.2009.2025808","volume":"18","author":"Benedek","year":"2009","journal-title":"IEEE Transactions on Image Processing,"},{"key":"2026040313415969100_ref015","doi-asserted-by":"crossref","first-page":"1312","DOI":"10.1109\/83.413175","article-title":"\u201cDPA: A deterministic approach to the MAP,\u201d","volume":"4","author":"Berthod","year":"1995","journal-title":"IEEE Transactions on Image Processing,"},{"issue":"2","key":"2026040313415969100_ref016","doi-asserted-by":"crossref","first-page":"192","DOI":"10.1111\/j.2517-6161.1974.tb00999.x","article-title":"\u201cSpatial interaction and the statistical analysis of lattice systems (with discussion),\u201d","volume":"36","author":"Besag","year":"1974","journal-title":"Journal of the Royal Statistical Society, Series B,"},{"issue":"3","key":"2026040313415969100_ref017","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1111\/j.2517-6161.1986.tb01412.x","article-title":"\u201cOn the statistical analysis of dirty pictures,\u201d","volume":"48","author":"Besag","year":"1986","journal-title":"Journal of the Royal Statistical Society, Series B"},{"key":"2026040313415969100_ref018","first-page":"428","article-title":"\u201cInteractive image segmentation using an adaptive GMMRF model,\u201d","author":"Blake","year":"2004","journal-title":"Proceedings of European Conference on Computer Vision,"},{"key":"2026040313415969100_ref019","doi-asserted-by":"crossref","DOI":"10.7551\/mitpress\/7132.001.0001","volume-title":"Visual Reconstruction.","author":"Blake","year":"1987"},{"key":"2026040313415969100_ref020","first-page":"1073","volume-title":"Proceedings of International Conference on Image Processing,","author":"Blaskovics","year":"2009"},{"key":"2026040313415969100_ref021","author":"Boros","year":"1991"},{"key":"2026040313415969100_ref022","author":"Bouman","year":"1991"},{"key":"2026040313415969100_ref023","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1109\/34.67641","article-title":"\u201cMultiple resolution segmentation of texture images,\u201d","volume":"13","author":"Bouman","year":"1991","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence"},{"key":"2026040313415969100_ref024","first-page":"565","article-title":"\u201cMultispectral image segmentation using a multiscale model,\u201d","author":"Bouman","year":"1992","journal-title":"Proceedings of International Conference on Acoustics, Speech and Signal Processing"},{"key":"2026040313415969100_ref025","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1007\/s11263-006-7934-5","article-title":"\u201cGraph cuts and efficient n-D image segmentation,\u201d","volume":"70","author":"Boykov","year":"2006","journal-title":"International Journal of Computer Vision,"},{"key":"2026040313415969100_ref026","first-page":"105","article-title":"\u201cInteractive graph cuts for optimal boundary & region segmentation of objects in n-D images,\u201d","author":"Boykov","year":"2001","journal-title":"Proceedings of International Conference on Computer Vision,"},{"key":"2026040313415969100_ref027","doi-asserted-by":"crossref","first-page":"1124","DOI":"10.1109\/TPAMI.2004.60","article-title":"\u201cAn experimental comparison of min-cut\/ max-flow algorithms for energy minimization in vision,\u201d","volume":"26","author":"Boykov","year":"2004","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence,"},{"key":"2026040313415969100_ref028","doi-asserted-by":"crossref","first-page":"1222","DOI":"10.1109\/34.969114","article-title":"\u201cFast approximate energy minimiza-tion via graph cuts,\u201d","volume":"23","author":"Boykov","year":"2001","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence,"},{"key":"2026040313415969100_ref029","doi-asserted-by":"crossref","first-page":"1222","DOI":"10.1109\/34.969114","article-title":"\u201cFast approximate energy minimization via graph cuts,\u201d","volume":"23","author":"Boykov","year":"2001","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence"},{"issue":"1","key":"2026040313415969100_ref030","first-page":"39","article-title":"\u201cGlobal and Local Methods of Unsupervised Bayesian Segmentation of Images,\u201d","volume":"2","author":"Braathen","year":"1993","journal-title":"Machine Graphics and Vision,"},{"issue":"1","key":"2026040313415969100_ref031","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1023\/A:1007979827043","article-title":"\u201cGeodesic active contours,\u201d","volume":"22","author":"Caselles","year":"1997","journal-title":"International Journal of Computer Vision,"},{"key":"2026040313415969100_ref032","first-page":"129","volume-title":"Simulated Annealing: Parallelization Techniques,","author":"Catoni","year":"1992"},{"key":"2026040313415969100_ref033","first-page":"73","article-title":"\u201cThe SEM algorithm: A probabilisitic teacher algorithm derived from the EM algorithm for the mixture problem,\u201d","volume":"2","author":"Celeux","year":"1985","journal-title":"Computational Statistics Quaterly,"},{"key":"2026040313415969100_ref034","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1007\/BF00940812","article-title":"\u201cThermodynamical approach to the traveling salesman problem: An efficient simulation algorithm,\u201d","volume":"45","author":"Cerny","year":"1985","journal-title":"Journal of Optimization Theory and Applications,"},{"key":"2026040313415969100_ref035","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1016\/0165-1684(88)90065-5","article-title":"\u201cImage restoration using an estimated Markov model,\u201d","volume":"15","author":"Chalmond","year":"1988","journal-title":"Signal Processing,"},{"issue":"6","key":"2026040313415969100_ref036","doi-asserted-by":"crossref","first-page":"747","DOI":"10.1016\/0031-3203(89)90011-3","article-title":"\u201cAn iterative Gibbsian technique for reconstruction of M-ary images,\u201d","volume":"22","author":"Chalmond","year":"1989","journal-title":"Pattern Recognition,"},{"key":"2026040313415969100_ref037","volume-title":"Modeling and Inverse Problems in Image Analysis.","author":"Chalmond","year":"2003"},{"key":"2026040313415969100_ref038","first-page":"141","article-title":"\u201cAn active contour model without edges,\u201d","author":"Chan","year":"1999","journal-title":"Proceedings of International Conference on Scale-Space Theories in Computer Vision,"},{"key":"2026040313415969100_ref039","volume-title":"Markov Random Fields: Theory and Applications","author":"Chellappa","year":"1993"},{"key":"2026040313415969100_ref040","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1111\/j.1365-2818.2008.01974.x","article-title":"\u201cConstraint factor graph cut-based active contour method for automated cellular image segmentation in RNAi screening,\u201d","volume":"230","author":"Chen","year":"2008","journal-title":"Journal of Microscopy"},{"issue":"3","key":"2026040313415969100_ref041","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1023\/A:1020878408985","article-title":"\u201cUsing prior shapes in geometric active contours in a variational framework,\u201d","volume":"50","author":"Chen","year":"2002","journal-title":"International Journal of Computer Vision,"},{"issue":"3","key":"2026040313415969100_ref042","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1007\/BF00054995","article-title":"\u201cThe theory and practice of Bayesian image labeling,\u201d","volume":"4","author":"Chou","year":"1990","journal-title":"International Journal of Computer Vision,"},{"key":"2026040313415969100_ref043","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1109\/TPAMI.1987.4767895","article-title":"\u201cSimple parallel hierarchical and relaxation algorithms for segmenting noncausal Markov random fields,\u201d","volume":"9","author":"Cohen","year":"1987","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence,"},{"key":"2026040313415969100_ref044","first-page":"211","article-title":"\u201cOn active contour models and balloons,\u201d","volume":"53","author":"Cohen","year":"1991","journal-title":"Computer Vision, Graphics and Image Processing: Image Understanding,"},{"key":"2026040313415969100_ref045","first-page":"1116","volume-title":"Proceedings of International Conference on Image Processing,","author":"Condat","year":"2005"},{"issue":"3","key":"2026040313415969100_ref046","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1023\/A:1020826424915","article-title":"\u201cDiffusion snakes: Introducing statistical shape knowledge into the Mumford-Shah functional,\u201d","volume":"50","author":"Cremers","year":"2002","journal-title":"International Journal of Computer Vision,"},{"key":"2026040313415969100_ref047","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1109\/TPAMI.1983.4767341","article-title":"\u201cMarkov random field texture models,\u201d","volume":"5","author":"Cross","year":"1983","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence"},{"issue":"1","key":"2026040313415969100_ref048","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1111\/j.2517-6161.1977.tb01600.x","article-title":"\u201cMaximum likelihood from incomplete data via the EM algorithm,\u201d","volume":"39","author":"Dempster","year":"1977","journal-title":"Journal of the Royal Statistical Society, Series B,"},{"key":"2026040313415969100_ref049","doi-asserted-by":"crossref","first-page":"800","DOI":"10.1109\/34.946985","article-title":"\u201cUnsupervised segmentation of color-texture regions in images and video,\u201d","volume":"23","author":"Deng","year":"2001","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence,"},{"key":"2026040313415969100_ref050","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1109\/TPAMI.1987.4767871","article-title":"\u201cModeling and segmentation of noisy and textured images using Gibbs random fields,\u201d","volume":"9","author":"Derin","year":"1987","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence"},{"key":"2026040313415969100_ref051","doi-asserted-by":"crossref","first-page":"707","DOI":"10.1109\/TPAMI.1984.4767595","article-title":"\u201cBayes smoothing algorithms for segmentation of binary images modeled by Markov random fields,\u201d","volume":"6","author":"Derin","year":"1984","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence,"},{"key":"2026040313415969100_ref052","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1016\/0734-189X(87)90056-9","article-title":"\u201cA parallel segmentation algorithm using relaxation with varying neighborhoods and its mapping to array procesors,\u201d","volume":"40","author":"Derin","year":"1987","journal-title":"Computer Vision, Graphics and Image Processing"},{"key":"2026040313415969100_ref053","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1007\/3-540-62909-2_77","article-title":"\u201cMaximum likelihood estimation of Markov random field paremeters using Markov chain Monte Carlo algorithms,\u201d","author":"Descombes","year":"1997","journal-title":"Energy Minimization Methods in Computer Vision and Pattern Recognition"},{"issue":"2","key":"2026040313415969100_ref054","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1137\/1113026","article-title":"\u201cThe description of a random field by means of conditional probabilities and constructions of its regularity,\u201d","volume":"XIII","author":"Dobruschin","year":"1968","journal-title":"Theory of Probability and its Applications,"},{"key":"2026040313415969100_ref055","doi-asserted-by":"crossref","first-page":"412","DOI":"10.1109\/TPAMI.1981.4767127","article-title":"\u201cImproving consistency and reducing ambiguity in stochastic labeling: An optimization approach,\u201d","volume":"4","author":"Faugeras","year":"1981","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence,"},{"key":"2026040313415969100_ref056","volume-title":"Mathematical Statistics. A Decision Theoretic Approach. Probability and Mathematical Statistics.","author":"Ferguson","year":"1967"},{"key":"2026040313415969100_ref057","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4419-7294-1","volume-title":"Statistical Image Processing and Multidimensional Modeling.","author":"Fieguth","year":"2011"},{"key":"2026040313415969100_ref058","article-title":"\u201cTotal internal reflection fluorescence (TIRF) microscopy,\u201d","volume":"12","author":"Fish","year":"2009.","journal-title":"Current Protocols in Cytometry,"},{"key":"2026040313415969100_ref059","first-page":"163","article-title":"\u201cMassive parallelization of simulated annealing: An experimental and theoretical approach for spin-glass models,\u201d","author":"Gaudron","year":"1992","journal-title":"Simulated Annealing: Parallelization Techniques,"},{"key":"2026040313415969100_ref060","first-page":"89","article-title":"\u201cParallel and deterministic algorithms for MRFs: Surface reconstruction and integration,\u201d","author":"Geiger","year":"1990","journal-title":"Proceedings of European Conference on Computer Vision,"},{"key":"2026040313415969100_ref061","first-page":"89","article-title":"\u201cA common framework for image segmentation,\u201d","author":"Geiger","year":"1989"},{"key":"2026040313415969100_ref062","first-page":"499","volume-title":"Markov Random Fields,","author":"Gelfand","year":"1993"},{"key":"2026040313415969100_ref063","first-page":"269","volume-title":"Proceedings of International Geoscience and Remote Sensing Symposium","author":"Geman","year":"1985"},{"key":"2026040313415969100_ref064","doi-asserted-by":"crossref","first-page":"721","DOI":"10.1109\/TPAMI.1984.4767596","article-title":"\u201cStochastic relaxation, Gibbs distributions and the Bayesian restoration of images,\u201d","volume":"6","author":"Geman","year":"1984","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence,"},{"key":"2026040313415969100_ref065","doi-asserted-by":"crossref","first-page":"609","DOI":"10.1109\/34.56204","article-title":"\u201cBoundary detection by constrained optimization,\u201d","volume":"12","author":"Geman","year":"1990","journal-title":"IEEE transactions on pattern analysis and machine intelligence,"},{"key":"2026040313415969100_ref066","author":"Geman","year":"1986"},{"key":"2026040313415969100_ref067","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1109\/34.16712","article-title":"\u201cA renormalization group approach to image processing problems,\u201d","volume":"11","author":"Gidas","year":"1989","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence"},{"key":"2026040313415969100_ref068","doi-asserted-by":"crossref","first-page":"465","DOI":"10.1109\/34.589206","article-title":"\u201cEstimation of generalized multisensor hidden Markov chains and unsupervised image segmentation,\u201d","volume":"19","author":"Giordana","year":"1997","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence,"},{"key":"2026040313415969100_ref069","first-page":"1441","volume-title":"Proceedings of International Conference on Image Processing,","author":"Giovannelli","year":"2010"},{"key":"2026040313415969100_ref070","volume-title":"Digital Image Processing","author":"Gonzalez","year":"2008"},{"key":"2026040313415969100_ref071","author":"Graffigne","year":"1984"},{"key":"2026040313415969100_ref072","first-page":"47","article-title":"\u201cParallel annealing by periodically interacting multiple searches: An experimental study,\u201d","author":"Graffigne","year":"1992","journal-title":"Simulated Annealing: Parallelization Techniques,"},{"key":"2026040313415969100_ref073","volume-title":"Proceedings of Conference on Neural, Morphological, and Stochastic Methods in Image and Signal Processing,","author":"Graffigne","year":"1995"},{"key":"2026040313415969100_ref074","author":"Graffigne","year":"1995"},{"key":"2026040313415969100_ref075","author":"Grenander","year":"1993","journal-title":"General Pattern Theory."},{"key":"2026040313415969100_ref076","doi-asserted-by":"crossref","first-page":"549","DOI":"10.1111\/j.2517-6161.1994.tb02000.x","article-title":"\u201cRepresentations of knowledge in complex systems,\u201d","volume":"56","author":"Grenander","year":"1994","journal-title":"Journal of the Royal Statistical Society, Series B,"},{"issue":"3","key":"2026040313415969100_ref077","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1016\/S0031-3203(97)00045-9","article-title":"\u201cA Gaussian-mixture-based image segmentation algorithm,\u201d","volume":"31","author":"Gupta","year":"1998","journal-title":"Pattern Recognition,"},{"issue":"3","key":"2026040313415969100_ref078","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1561\/2000000034","article-title":"\u201cTheory and use of the em algorithm,\u201d","volume":"4","author":"Gupta","year":"2010","journal-title":"Foundations and Trends in Signal Processing,"},{"key":"2026040313415969100_ref079","volume-title":"Champs al\u00e9atoires sur r\u00e9seaux: mod\u00e9lisations, statistique et applications","author":"Guyon","year":"1992"},{"key":"2026040313415969100_ref080","first-page":"755","article-title":"\u201cA tutorial survey of theory and applications of simulated anneal-ing,\u201d","author":"Hajek","year":"1985.","journal-title":"Proceedings of International Conference on Decision and Control"},{"key":"2026040313415969100_ref081","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1287\/moor.13.2.311","article-title":"\u201cCooling schedules for optimal annealing,\u201d","volume":"13","author":"Hajek","year":"1988","journal-title":"Mathematics of Operations Research,"},{"key":"2026040313415969100_ref082","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1007\/BF02612354","article-title":"\u201cRoof duality, complementation and persistency in quadratic 0-1 optimization,\u201d","volume":"28","author":"Hammer","year":"1984","journal-title":"Mathematical Programming,"},{"key":"2026040313415969100_ref083","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1016\/0146-664X(82)90040-5","article-title":"\u201cImage segmentation using simple Markov field models,\u201d","volume":"20","author":"Hansen","year":"1982","journal-title":"Computer Vision, Graphics and Image Processing,"},{"issue":"6","key":"2026040313415969100_ref084","doi-asserted-by":"crossref","first-page":"610","DOI":"10.1109\/TSMC.1973.4309314","article-title":"\u201cTextural features for image classification,\u201d","volume":"3","author":"Haralick","year":"1973","journal-title":"IEEE Transactions on Systems on Man, and Cybernetics,"},{"key":"2026040313415969100_ref085","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1093\/biomet\/57.1.97","article-title":"\u201cMonte Carlo sampling methods using Markov chains and their application,\u201d","volume":"57","author":"Hastings","year":"1970","journal-title":"Biometrika,"},{"key":"2026040313415969100_ref086","first-page":"695","volume-title":"Proceedings of International Conference on Computer Vision and Pattern Recognition,","author":"He","year":"2004"},{"key":"2026040313415969100_ref087","doi-asserted-by":"crossref","first-page":"1217","DOI":"10.1109\/34.250841","article-title":"\u201cMultimodal estimation of discontinuous optical flow using Markov random fields,\u201d","volume":"15","author":"Heitz","year":"1993","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence,"},{"key":"2026040313415969100_ref088","volume-title":"Proceedings of International Colloquiumon Parallel Image Processing","author":"Heitz","year":"1991"},{"issue":"1","key":"2026040313415969100_ref089","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1006\/cviu.1994.1008","article-title":"\u201cMultiscale minimization of global energy functions in some visual recovery problems,\u201d","volume":"59","author":"Heitz","year":"1994","journal-title":"Computer Vision, Graphics and Image Processing: Image Understanding,"},{"key":"2026040313415969100_ref090","volume-title":"Proceedings of Workshop on Motion,","author":"Heitz","year":"1991"},{"key":"2026040313415969100_ref091","doi-asserted-by":"crossref","first-page":"1901","DOI":"10.1364\/JOSAA.6.001901","article-title":"\u201cRestoration of piecewise-constant images by mean-field annealing,\u201d","volume":"6","author":"Hiriyannaiah","year":"1989","journal-title":"Journal of the Optical Society of America A,"},{"key":"2026040313415969100_ref092","first-page":"739","article-title":"\u201cA graphical model framework for coupling MRFs and deformable models,\u201d","author":"Huang","year":"2004","journal-title":"Proceedings of International Conference on Computer Vision and Pattern Recognition,"},{"key":"2026040313415969100_ref093","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1109\/TPAMI.1983.4767390","article-title":"\u201cOn the foundations of relaxation labeling processes,\u201d","volume":"5","author":"Hummel","year":"1983","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence"},{"key":"2026040313415969100_ref094","doi-asserted-by":"crossref","first-page":"1333","DOI":"10.1109\/TPAMI.2003.1233908","article-title":"\u201cExact optimization for markov random fields with convex priors,\u201d","volume":"25","author":"Ishikawa","year":"2003","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence"},{"key":"2026040313415969100_ref095","doi-asserted-by":"crossref","first-page":"1234","DOI":"10.1109\/TPAMI.2010.91","article-title":"\u201cTransformation of general binary mrf minimization to the first order case,\u201d","volume":"33","author":"Ishikawa","year":"2011","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence"},{"issue":"12","key":"2026040313415969100_ref096","doi-asserted-by":"crossref","first-page":"1167","DOI":"10.1016\/0031-3203(91)90143-S","article-title":"\u201cUnsupervised texture segmentation using Gabor filters,\u201d","volume":"24","author":"Jain","year":"1991","journal-title":"Pattern Recognition"},{"key":"2026040313415969100_ref097","doi-asserted-by":"crossref","first-page":"683","DOI":"10.1109\/78.80887","article-title":"\u201cCompound Gauss \u2014 Markov random fields for image estimation,\u201d","volume":"39","author":"Jeng","year":"1991","journal-title":"IEEE Transactions on Signal Processing,"},{"key":"2026040313415969100_ref098","doi-asserted-by":"crossref","first-page":"663","DOI":"10.1109\/36.158859","article-title":"\u201cClassification with spatio-temporal interpixel class dependency contexts,\u201d","volume":"30","author":"Jeon","year":"1992","journal-title":"IEEE Transaction on Geoscience and Remote Sensing"},{"key":"2026040313415969100_ref099","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4615-2792-3","volume-title":"A Pyramid Framework for Early Vision, Engineering and Computer Science.","author":"Jolion","year":"1994"},{"issue":"482","key":"2026040313415969100_ref100","article-title":"\u201cCellprofiler analyst: Data exploration and analysis software for complex image-based screens,\u201d","volume":"9","author":"Jones","year":"2008","journal-title":"BMC Bioinformatics,"},{"issue":"4","key":"2026040313415969100_ref101","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1007\/BF00133570","article-title":"\u201cSnakes: Active contour models,\u201d","volume":"1","author":"Kass","year":"1988","journal-title":"International Journal of Computer Vision"},{"key":"2026040313415969100_ref102","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1016\/j.imavis.2006.12.004","article-title":"\u201cSegmentation of color images via reversible jump MCMC sampling,\u201d","volume":"26","author":"Kato","year":"2008","journal-title":"Image and Vision Computing,"},{"key":"2026040313415969100_ref103","volume-title":"Proceedings of International Workshop on Image and Multidimensional Digital Signal Processing","author":"Kato","year":"1993"},{"key":"2026040313415969100_ref104","first-page":"253","volume-title":"Proceedings of International Conference on Computer Vision,","author":"Kato","year":"1993"},{"key":"2026040313415969100_ref105","first-page":"137","article-title":"\u201cParallel image classification using multiscale Markov random fields,\u201d","author":"Kato","year":"1993","journal-title":"Proceedings of International Conference on Acoustics, Speech and Signal Processing,"},{"key":"2026040313415969100_ref106","first-page":"18","article-title":"\u201cA hierarchical Markov random field model and multi&temperature annealing for parallel image classification,\u201d","volume":"58","author":"Kato","year":"1996","journal-title":"Computer Graphics and Image Processing: Graphical Models and Image Processing,"},{"key":"2026040313415969100_ref107","first-page":"137","article-title":"\u201cParallel image classification using multiscale Markov random fields,\u201d","author":"Kato","year":"1993","journal-title":"Proceedings of International Conference on Acoustics, Speech and Signal Processing"},{"key":"2026040313415969100_ref108","first-page":"2399","volume-title":"Proceedings of International Conference on Acoustics, Speech and Signal Processing","author":"Kato","year":"1995"},{"key":"2026040313415969100_ref109","first-page":"547","article-title":"\u201cA Markov random field image segmentation model using combined color and texture features,\u201d","author":"Kato","year":"2001","journal-title":"Proceedings of International Conference on Computer Analysis of Images and Patterns,"},{"key":"2026040313415969100_ref110","first-page":"111","volume-title":"Joint Hungarian-Austrian Conference on Image Processing and Pattern Recognition,","author":"Kato","year":"2005"},{"key":"2026040313415969100_ref111","doi-asserted-by":"crossref","first-page":"1103","DOI":"10.1016\/j.imavis.2006.03.005","article-title":"\u201cA Markov random field image segmentation model for color textured images,\u201d","volume":"24","author":"Kato","year":"2006","journal-title":"Image and Vision Computing,"},{"key":"2026040313415969100_ref112","first-page":"953","volume-title":"Proceedings of Asian Conference on Computer Vision","author":"Kato","year":"2006"},{"key":"2026040313415969100_ref113","first-page":"660","volume-title":"Proceedings of the International Conference on Pattern Recognition,","author":"Kato","year":"2002"},{"key":"2026040313415969100_ref114","first-page":"961","article-title":"\u201cUnsupervised segmentation of color textured images using a multi-layer MRF model,\u201d","author":"Kato","year":"2003","journal-title":"Proceedings of International Conference on Image Processing,"},{"key":"2026040313415969100_ref115","article-title":"\u201cImage classification using Markov random fields with two new relaxation methods: Deterministic pseudo annealing and modified Metropolis dynamics,\u201d","author":"Kato","year":"1992"},{"key":"2026040313415969100_ref116","first-page":"573","article-title":"\u201cSatellite image classification using a modified Metropolis dynamics,\u201d","author":"Kato","year":"1992","journal-title":"Proceedings of International Conference on Acoustics, Speech and Signal Processing"},{"key":"2026040313415969100_ref117","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1007\/978-94-017-2217-9_45","volume-title":"Maximum Entropy and Bayesian Methods","author":"Kato","year":"1993"},{"key":"2026040313415969100_ref118","author":"Kato","year":"1995"},{"key":"2026040313415969100_ref119","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1109\/ICCV.1995.466790","volume-title":"Proceedings of International Conference on Computer Vision,","author":"Kato","year":"1995"},{"key":"2026040313415969100_ref120","doi-asserted-by":"crossref","first-page":"591","DOI":"10.1016\/S0031-3203(98)00104-6","article-title":"\u201cUnsupervised parallel image classification using Markovian models,\u201d","volume":"32","author":"Kato","year":"1999","journal-title":"Pattern Recognition,"},{"key":"2026040313415969100_ref121","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1146\/annurev.psych.55.090902.142005","article-title":"\u201cObject perception as Bayesian inference,\u201d","volume":"55","author":"Kersten","year":"2004","journal-title":"Annual Review of Psychology"},{"key":"2026040313415969100_ref122","first-page":"284","volume-title":"Proceedings of Scandinavian Conferences on Image Analysis,","author":"Kervrann","year":"1993"},{"key":"2026040313415969100_ref123","doi-asserted-by":"crossref","first-page":"583","DOI":"10.1109\/83.753745","article-title":"\u201cStatistical deformable model-based segmentation of image motion,\u201d","volume":"8","author":"Kervrann","year":"1999","journal-title":"IEEE Transactions on Image Processing,"},{"key":"2026040313415969100_ref124","first-page":"746","volume-title":"Proceedings of International Conference on Computer Vision and Pattern Recognition,","author":"Khan","year":"2001"},{"key":"2026040313415969100_ref125","doi-asserted-by":"crossref","DOI":"10.1090\/conm\/001","volume-title":"Markov Random Fields and their Applications.","author":"Kindermann","year":"1980"},{"key":"2026040313415969100_ref126","doi-asserted-by":"crossref","first-page":"671","DOI":"10.1126\/science.220.4598.671","article-title":"\u201cOptimization by simulated annealing,\u201d","volume":"220","author":"Kirkpatrick","year":"1983","journal-title":"Science,"},{"key":"2026040313415969100_ref127","doi-asserted-by":"crossref","first-page":"1645","DOI":"10.1109\/TPAMI.2008.217","article-title":"\u201cP&gt;3 & beyond: Move making algorithms for solving higher order functions,\u201d","volume":"31","author":"Kohli","year":"2009","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence,"},{"key":"2026040313415969100_ref128","first-page":"1","article-title":"\u201cRobust higher order potentials for enforcing label consistency,\u201d","author":"Kohli","year":"2008","journal-title":"Proceedings of International Conference on Computer Vision and Pattern Recognition,"},{"key":"2026040313415969100_ref129","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4471-3485-5","volume-title":"Motion Picture Restoration.","author":"Kokaram","year":"1998"},{"key":"2026040313415969100_ref130","article-title":"\u201cQPBO algorithm,\u201d","author":"Kolmogorov","year":"2007","journal-title":"software,"},{"key":"2026040313415969100_ref131","doi-asserted-by":"crossref","first-page":"1274","DOI":"10.1109\/TPAMI.2007.1031","article-title":"\u201cMinimizing nonsubmodular functions with graph cuts-a review,\u201d","volume":"29","author":"Kolmogorov","year":"2007","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence,"},{"key":"2026040313415969100_ref132","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1109\/TPAMI.2004.1262177","article-title":"\u201cWhat energy functions can be minimized via graph cuts?,\u201d","volume":"26","author":"Kolmogorov","year":"2004","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence,"},{"issue":"1","key":"2026040313415969100_ref133","doi-asserted-by":"crossref","first-page":"148","DOI":"10.1109\/LGRS.2010.2053517","article-title":"\u201cEnhanced dictionary-based SAR amplitude distribution estimation and its validation with very high resolution data,\u201d","volume":"8","author":"Krylov","year":"2011","journal-title":"IEEE Transaction on Geoscience and Remote Sensing,"},{"issue":"3","key":"2026040313415969100_ref134","doi-asserted-by":"crossref","first-page":"554","DOI":"10.1109\/JSTSP.2010.2103925","article-title":"\u201cSupervised high resolution dual polarization SAR image classification by finite mixtures and copulas,\u201d","volume":"5","author":"Krylov","year":"2011","journal-title":"IEEE Journal of Selected Topics in Signal Processing"},{"key":"2026040313415969100_ref135","article-title":"\u201cDiscriminative fields for modeling spatial dependencies in natural images,\u201d","author":"Kumar","year":"2003","journal-title":"Proceedings of Neural Information Processing Systems"},{"key":"2026040313415969100_ref136","first-page":"1284","article-title":"\u201cA hierarchical field framework for unified context&based classification,\u201d","author":"Kumar","year":"2005","journal-title":"Proceedings of International Conference on Computer Vision,"},{"key":"2026040313415969100_ref137","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-015-7744-1","volume-title":"Simulated Annealing: Theory and Applications.","author":"Laarhoven","year":"1987"},{"key":"2026040313415969100_ref138","first-page":"239","volume-title":"Proceedings of European Conference on Computer Vision,","author":"Ladicky","year":"2010"},{"issue":"3","key":"2026040313415969100_ref139","doi-asserted-by":"crossref","first-page":"390","DOI":"10.1109\/83.826777","article-title":"\u201cDiscrete Markov modeling and inference on the quad-tree,\u201d","volume":"9","author":"Laferte","year":"2000","journal-title":"IEEE Transactions on Image Processing,"},{"key":"2026040313415969100_ref140","first-page":"282","article-title":"\u201cConditional random fields: Probabilistic models for segmenting and labeling sequence data,\u201d","author":"Lafferty","year":"2001","journal-title":"International Conference on Machine Learning"},{"key":"2026040313415969100_ref141","doi-asserted-by":"crossref","first-page":"799","DOI":"10.1109\/34.31443","article-title":"\u201cSimultaneous parameter estimation and segmentation of Gibbs random fields using simulated annealing,\u201d","volume":"11","author":"Lakshmanan","year":"1989","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence,"},{"key":"2026040313415969100_ref142","first-page":"131","volume-title":"Markov Random Fields,","author":"Lakshmanan","year":"1993"},{"key":"2026040313415969100_ref143","first-page":"1485","volume-title":"Proceedings of the International Conference on Pattern Recognition","author":"Lesk\u00f3","year":"2010"},{"key":"2026040313415969100_ref144","volume-title":"Markov Random Field Modeling in Image Analysis.","author":"Li","year":"2009","edition":"3rd Edition"},{"key":"2026040313415969100_ref145","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1109\/72.554203","article-title":"\u201cAdaptive color segmentation \u2014a comparison of neural and statistical methods,\u201d","volume":"8","author":"Littmann","year":"1997","journal-title":"IEEE Transactions on Neural Networks"},{"key":"2026040313415969100_ref146","article-title":"\u201cReconnaissance de formes par vision par ordinateur: application \u00e1 l\u2019identification de foraminiferes planctoniques,\u201d","author":"Liu-Yu","year":"1992"},{"key":"2026040313415969100_ref147","volume-title":"Proceedings of International Conference on Acoustics, Speech and Signal Processing,","author":"Marques","year":"1992"},{"key":"2026040313415969100_ref148","author":"Marroquin","year":"1985"},{"key":"2026040313415969100_ref149","doi-asserted-by":"crossref","first-page":"618","DOI":"10.1109\/36.225529","article-title":"\u201cSEM Algorithm and unsupervised statistical segmentation of satellite images,\u201d","volume":"31","author":"Masson","year":"1993.","journal-title":"IEEE Transactions on Geoscience and Remote Sensing,"},{"key":"2026040313415969100_ref150","author":"Memin","year":"1993"},{"key":"2026040313415969100_ref151","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1006\/jpdc.1995.1110","article-title":"\u201cEfficient parallel non-linear multigrid relaxation algorithms for low-level vision applications,\u201d","volume":"29","author":"Memin","year":"1995","journal-title":"Journal of Parallel Distributed Computing"},{"key":"2026040313415969100_ref152","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4615-6335-8","volume-title":"Physics-based Deformable Models: Applications to Computer Vision, Graphics and Medical Imaging.","author":"Metaxas","year":"1997"},{"issue":"6","key":"2026040313415969100_ref153","doi-asserted-by":"crossref","first-page":"1087","DOI":"10.1063\/1.1699114","article-title":"\u201cEquation of state calculations by fast computing machines,\u201d","volume":"21","author":"Metropolis","year":"1953","journal-title":"Journal of Chemical Physics,"},{"key":"2026040313415969100_ref154","volume-title":"Theoretical Aspects of Local Search.","author":"Michiels","year":"2007"},{"key":"2026040313415969100_ref155","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1023\/A:1011161132514","article-title":"\u201cGroup actions, homeomorphisms, and matching: A general framework,\u201d","volume":"41","author":"Miller","year":"2001","journal-title":"International Journal of Computer Vision,"},{"key":"2026040313415969100_ref156","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1109\/83.552104","article-title":"\u201cAutomatic target recognition organized via jump-diffusion algorithms,\u201d","volume":"6","author":"Miller","year":"1997","journal-title":"IEEE Transactions on Image Processing"},{"key":"2026040313415969100_ref157","volume-title":"Proceedings of International Conference on Image Processing,","author":"Morris","year":"1997"},{"key":"2026040313415969100_ref158","first-page":"1","volume-title":"Proceedings of SPIE IS&T\/SPIE Electronic Imaging,","author":"Moser","year":"2010"},{"issue":"1","key":"2026040313415969100_ref159","doi-asserted-by":"crossref","first-page":"188","DOI":"10.1109\/TGRS.2005.859349","article-title":"\u201cDictionary-based Stochastic Expectation Maximization for SAR amplitude probability density function estimation,\u201d","volume":"44","author":"Moser","year":"2006","journal-title":"IEEE Transactions on Geoscience and Remote Sensing,"},{"key":"2026040313415969100_ref160","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1007\/BF01011714","article-title":"\u201cGibbs and Markov random system with constrainsts,\u201d","volume":"10","author":"Moussouris","year":"1974","journal-title":"Journal of Statistical Physics,"},{"key":"2026040313415969100_ref161","first-page":"141","article-title":"\u201cThe Bayesian rationale for energy functionals,\u201d","author":"Mumford","year":"1994","journal-title":"Geometry- Driven Diffusion in Computer Vision,"},{"key":"2026040313415969100_ref162","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1017\/CBO9780511984037.003","article-title":"\u201cPattern theory: A unifying perspective,\u201d","author":"Mumford","year":"1996","journal-title":"Perception as Bayesian Inference,"},{"issue":"5","key":"2026040313415969100_ref163","doi-asserted-by":"crossref","first-page":"577","DOI":"10.1002\/cpa.3160420503","article-title":"\u201cOptimal approximations by piecewise smooth functions and associated variational problems,\u201d","volume":"42","author":"Mumford","year":"1989","journal-title":"Communications on Pure and Applied Mathematics,"},{"key":"2026040313415969100_ref164","first-page":"7945","volume-title":"Proceedings of National Academy Science USA","author":"Nagy","year":"2007"},{"key":"2026040313415969100_ref165","volume-title":"An Introduction to Copulas.","author":"Nelsen","year":"2006","edition":"2nd Edition"},{"key":"2026040313415969100_ref166","first-page":"206","article-title":"\u201cHigh&speed potato grading and quality inspection based on a color vision system,\u201d","author":"Noordam","year":"2000","journal-title":"Proceedings of SPIE Machine Vision Applications in Industrial Inspection"},{"key":"2026040313415969100_ref167","first-page":"628","volume-title":"Proceedings of International Conference on Image Processing,","author":"Odobez","year":"1995"},{"key":"2026040313415969100_ref168","volume-title":"Understanding Synthetic Aperture Radar images.","author":"Oliver","year":"2004"},{"key":"2026040313415969100_ref169","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1023\/A:1014080923068","article-title":"\u201cGeodesic active regions and level set methods for supervised texture segmentation,\u201d","volume":"46","author":"Paragios","year":"2002","journal-title":"International Journal of Computer Vision,"},{"key":"2026040313415969100_ref170","volume-title":"Statistical Field Theory.","author":"Parisi","year":"1998"},{"key":"2026040313415969100_ref171","author":"Perez","year":"1993"},{"key":"2026040313415969100_ref172","first-page":"61","volume-title":"Proceedings of International Conference on Acoustics, Speech and Signal Processing,","author":"Perez","year":"1992"},{"key":"2026040313415969100_ref173","author":"Perez","year":"1994"},{"key":"2026040313415969100_ref174","doi-asserted-by":"crossref","first-page":"695","DOI":"10.1016\/j.patcog.2005.10.028","article-title":"\u201cA study of Gaussian mixture models of colour and texture features for image classification and segmentation,\u201d","volume":"39","author":"Permuter","year":"2006","journal-title":"Pattern Recognition,"},{"key":"2026040313415969100_ref175","first-page":"261","volume-title":"Proceedings of Machine Graphics and Vision,","author":"Pieczynski","year":"1992"},{"key":"2026040313415969100_ref176","author":"Rajasekaran","year":"1990"},{"key":"2026040313415969100_ref177","first-page":"427","article-title":"\u201cGeometric approach to segmentation and protein localization in cell cultured assays,\u201d","author":"Raman","year":"2005","journal-title":"Advances in Visual Computing"},{"key":"2026040313415969100_ref178","first-page":"564","volume-title":"Handbook of Brain Theory and Neural Networks,","author":"Rangarajan","year":"1995"},{"key":"2026040313415969100_ref179","volume-title":"Artificial Neural Networks and Statistical Pattern Recognition: Old and New Connections,","author":"Rangarajan","year":"1991"},{"issue":"8","key":"2026040313415969100_ref180","doi-asserted-by":"crossref","first-page":"1266","DOI":"10.1109\/83.506761","article-title":"\u201cAn FFT-based technique for translation, rotation and scale-invariant image registration,\u201d","volume":"5","author":"Reddy","year":"1996","journal-title":"IEEE Transactions on Image Processing,"},{"key":"2026040313415969100_ref181","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1137\/1026034","article-title":"\u201cMixture densities, maximum likelihood and the EM algorithm,\u201d","volume":"26","author":"Redner","year":"1984","journal-title":"SIAM Review,"},{"issue":"4","key":"2026040313415969100_ref182","doi-asserted-by":"crossref","first-page":"573","DOI":"10.1364\/JOSAA.10.000573","article-title":"\u201cMaximum a posteriori classification of multi7#x0026;frequency, multilook, synthetic aperture radar intensity data,\u201d","volume":"10","author":"Rignot","year":"1993","journal-title":"Journal of the Optical Society of America a-Optics Image Science and Vision,"},{"key":"2026040313415969100_ref183","volume-title":"Proceedings of Workshop on Variational, Geometric and Level Set Methods in Computer Vision","author":"Rochery","year":"2003"},{"key":"2026040313415969100_ref184","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4613-8190-7","volume-title":"Markov Random Fields.","author":"Rosanov","year":"1982"},{"key":"2026040313415969100_ref185","first-page":"1","volume-title":"Proceedings of International Conference on Computer Vision and Pattern Recognition","author":"Rother","year":"2007"},{"key":"2026040313415969100_ref186","first-page":"78","volume-title":"Proceedings of European Conference on Computer Vision","author":"Rousson","year":"2002"},{"key":"2026040313415969100_ref187","first-page":"1","volume-title":"International Conference on Computer Vision,","author":"Russell","year":"2007"},{"issue":"3","key":"2026040313415969100_ref188","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1023\/A:1008183109594","article-title":"\u201cA level set model for image classification,\u201d","volume":"40","author":"Samson","year":"2000","journal-title":"International Journal of Computer Vision"},{"key":"2026040313415969100_ref189","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4615-5779-1","author":"Sangwine","year":"1998","journal-title":"The Colour Image Processing Hand&book"},{"key":"2026040313415969100_ref190","doi-asserted-by":"crossref","first-page":"442","DOI":"10.1109\/83.826782","article-title":"\u201cMultiscale statistical methods for the segmentation of images,\u201d","volume":"9","author":"Schneider","year":"2000","journal-title":"IEEE Transactions on Image Processing"},{"key":"2026040313415969100_ref191","doi-asserted-by":"crossref","DOI":"10.7551\/mitpress\/4175.001.0001","volume-title":"Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond.","author":"Sch\u00f6lkopf","year":"2001"},{"key":"2026040313415969100_ref192","author":"Sethian","year":"1999","journal-title":"Level Set Methods and Fast Marching Methods Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science. Cambridge Monograph on Applied and Computational Mathematics"},{"key":"2026040313415969100_ref193","first-page":"141","volume-title":"Proceedings of International Conference on Image Processing,","author":"Shima","year":"2010"},{"key":"2026040313415969100_ref194","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1007\/s11263-007-0109-1","article-title":"\u201cTextonboost for image understanding: Multi&class object recognition and segmentation by jointly modeling texture, layout, and context,\u201d","volume":"81","author":"Shotton","year":"2009","journal-title":"International Journal of Computer Vision,"},{"key":"2026040313415969100_ref195","volume-title":"Proceedings of European Association of Remote Sensing,","author":"Sigelle","year":"1992"},{"key":"2026040313415969100_ref196","first-page":"449","article-title":"\u201cMod\u00f9les de Potts et relaxation d\u2019images de labels par champs de markov,\u201d","volume":"9","author":"Sigelle","year":"1993","journal-title":"Traitement du Signal,"},{"key":"2026040313415969100_ref197","first-page":"109","volume-title":"Image Restoration","author":"Simchony","year":"1991"},{"key":"2026040313415969100_ref198","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1103\/PhysRevLett.58.86","article-title":"\u201cNonuniversal critical dynamics in Monte Carlo simulations,\u201d","volume":"58","author":"Swendsen","year":"1987","journal-title":"Physical Review Letters,"},{"key":"2026040313415969100_ref199","doi-asserted-by":"crossref","first-page":"1068","DOI":"10.1109\/TPAMI.2007.70844","article-title":"\u201cA comparative study of energy minimization methods for Markov random fields with smoothness-based priors,\u201d","volume":"30","author":"Szeliski","year":"2008","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence"},{"key":"2026040313415969100_ref200","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1109\/34.107010","article-title":"\u201cA cost minimization approach to edge detection using simulated annealing,\u201d","volume":"14","author":"Tan","year":"1991","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence,"},{"key":"2026040313415969100_ref201","first-page":"145","volume-title":"Simulated Annealing: Parallelization Techniques,","author":"Trouv\u00f9","year":"1992"},{"key":"2026040313415969100_ref202","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1007\/s11263-005-6642-x","article-title":"\u201cImage parsing: Unifying segmentation, detection, and recognition,\u201d","volume":"63","author":"Tu","year":"2005","journal-title":"International Journal of Computer Vision,"},{"key":"2026040313415969100_ref203","doi-asserted-by":"crossref","first-page":"657","DOI":"10.1109\/34.1000239","article-title":"\u201cImage segmentation by data-driven Markov chain Monte Carlo,\u201d","volume":"24","author":"Tu","year":"2002","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence,"},{"key":"2026040313415969100_ref204","doi-asserted-by":"crossref","first-page":"434","DOI":"10.1109\/36.662728","article-title":"\u201cDetection of linear features in SAR images: Application to road network extraction,\u201d","volume":"36","author":"Tupin","year":"1998","journal-title":"IEEE Transactions on Geoscience and Remote Sensing,"},{"key":"2026040313415969100_ref205","first-page":"621","volume-title":"Proceedings of the International Conference on Pattern Recognition,","author":"Vandenbroucke","year":"2000"},{"key":"2026040313415969100_ref206","first-page":"1553","article-title":"\u201cScene segmentation with CRFs learned from partially labeled images,\u201d","author":"Verbeek","year":"2008","journal-title":"Proceedings of Advances in Neural Information Processing Systems,"},{"key":"2026040313415969100_ref207","first-page":"1","volume-title":"Computer Vision and Pattern Recognition","author":"Vicente","year":"2008"},{"key":"2026040313415969100_ref208","first-page":"424","volume-title":"Proceedings of European Conference on Computer Vision,","author":"\u02c7Lubor Ladick\u00b4y","year":"2010"},{"key":"2026040313415969100_ref209","author":"Voisin","year":"2011"},{"key":"2026040313415969100_ref210","first-page":"22","volume-title":"IS&T\/SPIE Electronic Imaging 2012, Proceedings of SPIE, volume 8296, 82960K,","author":"Voisin","year":"2012"},{"key":"2026040313415969100_ref211","doi-asserted-by":"crossref","first-page":"78300O","DOI":"10.1117\/12.865023","article-title":"\u201cClassification of very high resolution SAR images of urban areas by dictionary-based mixture models, copulas and Markov random fields using textural features,\u201d","author":"Voisin","year":"2010","journal-title":"Proceedings of SPIE,"},{"key":"2026040313415969100_ref212","author":"Wallach","year":"2004"},{"key":"2026040313415969100_ref213","doi-asserted-by":"crossref","first-page":"1348","DOI":"10.1109\/TPAMI.2004.76","article-title":"\u201cAnalysis and synthesis of textured motion: Particles and waves,\u201d","volume":"26","author":"Wang","year":"2004","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence"},{"key":"2026040313415969100_ref214","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-55760-6","volume-title":"Image Analysis, Random Fields and Markov Chain Monte Carlo Methods","author":"Winkler","year":"2003"},{"key":"2026040313415969100_ref215","doi-asserted-by":"crossref","first-page":"232","DOI":"10.1109\/TIT.1972.1054786","article-title":"\u201cTwo-dimensional discrete Markovian fields,\u201d","volume":"18","author":"Woods","year":"1972","journal-title":"IEEE Transactions on Information Theory,"},{"key":"2026040313415969100_ref216","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1103\/RevModPhys.54.235","article-title":"\u201cThe Potts model,\u201d","volume":"54","author":"Wu","year":"1982","journal-title":"Reviews of Modern Physics,"},{"key":"2026040313415969100_ref217","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1109\/83.661186","article-title":"\u201cSnakes, shapes, gradient vector flow,\u201d","volume":"7","author":"Xu","year":"1998","journal-title":"IEEE Transactions on Image Processing"},{"issue":"1","key":"2026040313415969100_ref218","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1006\/cviu.1995.1003","article-title":"\u201cA game strategy approach for image labeling,\u201d","volume":"61","author":"Yu","year":"1995","journal-title":"Computer Vision and Image Understanding,"},{"key":"2026040313415969100_ref219","volume-title":"Proceedings of International Conference on Acoustics, Speech and Signal Processing,","author":"Zerubia","year":"1990"},{"key":"2026040313415969100_ref220","doi-asserted-by":"crossref","first-page":"703","DOI":"10.1109\/72.238324","article-title":"\u201cMean field annealing using Compound Gauss- Markov Random fields for edge detection and image estimation,\u201d","volume":"8","author":"Zerubia","year":"1993","journal-title":"IEEE Transactions on Neural Networks,"},{"key":"2026040313415969100_ref221","volume-title":"Analyse d\u2019images: filtrage et segmentation,","author":"Zerubia","year":"1995"},{"key":"2026040313415969100_ref222","doi-asserted-by":"crossref","first-page":"520","DOI":"10.1109\/ICPR.1994.576342","volume-title":"Proceedings of the International Conference on Pattern Recognition,","author":"Zerubia","year":"1994"},{"key":"2026040313415969100_ref223","author":"Zerubia","year":"1991"},{"issue":"9","key":"2026040313415969100_ref224","doi-asserted-by":"crossref","first-page":"884","DOI":"10.1109\/34.537343","article-title":"\u201cRegion competition: Unifying snakes, region growing, and Bayes\/MDL for multiband image segmentation,\u201d","volume":"18","author":"Zhu","year":"1996","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence,"}],"container-title":["Foundations and Trends\u00ae in Signal 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