{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,27]],"date-time":"2026-01-27T13:51:07Z","timestamp":1769521867506,"version":"3.49.0"},"reference-count":52,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2014,7,24]],"date-time":"2014-07-24T00:00:00Z","timestamp":1406160000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Automatic image classification is of major importance for a wide range of applications and is supported by a complex process that usually requires the identification of individual regions and spatial patterns (contextual information) among neighboring regions within images. Hierarchical conditional random fields (CRF) consider both multi-scale and contextual information in a unified discriminative probabilistic framework, yet they suffer from two main drawbacks. On the one hand, their current classification performance still leaves space for improvement, mostly due to the use of very simple or inappropriate pairwise energy expressions to model complex spatial patterns; on the other hand, their training remains complex, particularly for multi-class problems. In this work, we investigated alternative pairwise energy expressions to better account for class transitions and developed an efficient parameters learning strategy for the resultant expression. We propose: (i) a multi-scale CRF model with novel energies that involves information related to the multi-scale image structure; and (ii) an efficient maximum margin parameters learning procedure where the complex learning problem is decomposed into simpler individual multi-class sub-problems. During experiments conducted on several well-known satellite image data sets, the suggested multi-scale CRF exhibited between a 1% and 15% accuracy improvement compared to other works. We also found that, on different multi-scale decompositions, the total number of regions and their average size have a direct impact on the classification results.<\/jats:p>","DOI":"10.3390\/rs6086727","type":"journal-article","created":{"date-parts":[[2014,7,24]],"date-time":"2014-07-24T11:00:50Z","timestamp":1406199650000},"page":"6727-6764","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Efficient Learning of Spatial Patterns with Multi-Scale Conditional Random Fields for Region-Based Classification"],"prefix":"10.3390","volume":"6","author":[{"given":"Mitchel","family":"Alioscha-Perez","sequence":"first","affiliation":[{"name":"Electronics and Informatics Department (ETRO), Vrije Universiteit Brussel (VUB), Pleinlaan 2,1050 Brussels, Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hichem","family":"Sahli","sequence":"additional","affiliation":[{"name":"Electronics and Informatics Department (ETRO), Vrije Universiteit Brussel (VUB), Pleinlaan 2,1050 Brussels, Belgium"},{"name":"Interuniveristy Microelectronics Center (IMEC), Kapeldreef 75, BE-3001 Leuven, Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2014,7,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Reynolds, J., and Murphy, K.P. (2007, January 28\u201330). Figure-ground segmentation using a hierarchical conditional random field. Montreal, QC, Canada.","DOI":"10.1109\/CRV.2007.32"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1915","DOI":"10.1109\/TPAMI.2012.231","article-title":"Learning hierarchical features for scene labeling","volume":"35","author":"Farabet","year":"2013","journal-title":"IEEE Trans. Patt. Anal. Mach. Intell"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"548","DOI":"10.1109\/TGRS.2004.842405","article-title":"A hierarchical Markovian model for multiscale region-based classification of vector-valued images","volume":"43","author":"Katartzis","year":"2005","journal-title":"IEEE Trans. Geosci. Remote Sens"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1111\/j.2517-6161.1986.tb01412.x","article-title":"On the statistical analysis of dirty pictures","volume":"48","author":"Besag","year":"1986","journal-title":"J. R. Stat. Soc. Ser. B"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1080\/02664769300000058","article-title":"Stochastic relaxation, Gibbs distributions and the bayesian restoration of images","volume":"20","author":"Geman","year":"1993","journal-title":"J. Appl. Stat"},{"key":"ref_6","unstructured":"Lafferty, J., McCallum, A., and Pereira, F. (2001). Proceedings of the Eighteenth International Conference on Machine Learning, Morgan Kaufmann Publishers Inc."},{"key":"ref_7","unstructured":"Kumar, S., and Hebert, M. (2003, January 13\u201316). Discriminative random fields: A discriminative framework for contextual interaction in classification. Nice, France."},{"key":"ref_8","unstructured":"He, X., Zemel, R.S., and Carreira Perpinan, M.A. (July, January 27). Multiscale conditional random fields for image labeling. In Proceedings of the 2004. IEEE Computer Society Conference on Computer Vision and Pattern Recognition, Washington, DC, USA."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Yang, M.Y., F\u00f6rstner, W., and Drauschke, M. (2011, January 6\u201313). A Hierarchical conditional random field model for labeling and classifying images of man-made scenes. Barcelona, Spain.","DOI":"10.1109\/ICCVW.2011.6130243"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Munoz, D., Bagnell, J.A., Vandapel, N., and Hebert, M. (2009, January 20\u201325). Contextual classification with functional max-margin markov networks. Miami, FL, USA.","DOI":"10.1109\/CVPRW.2009.5206590"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"300","DOI":"10.1007\/s11263-008-0140-x","article-title":"Multi-class segmentation with relative location prior","volume":"80","author":"Gould","year":"2008","journal-title":"Int. J. Comput. Vis"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"497","DOI":"10.1109\/LGRS.2010.2089427","article-title":"A supervised classification method based on conditional random fields with multiscale region connection calculus model for SAR image","volume":"8","author":"Su","year":"2011","journal-title":"IEEE Geosci. Remote Sens. Lett"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2240","DOI":"10.3390\/rs2092240","article-title":"A hierarchical spatio-temporal Markov model for improved flood mapping using multi-temporal X-band SAR data","volume":"2","author":"Martinis","year":"2010","journal-title":"Remote Sens"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"5089","DOI":"10.3390\/rs5105089","article-title":"A joint land cover mapping and image registration algorithm based on a Markov random field model","volume":"5","author":"Kasetkasem","year":"2013","journal-title":"Remote Sens"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Vishwanathan, S.V.N., Schraudolph, N.N., Schmidt, M.W., and Murphy, K.P. (2006, January 25\u201329). Accelerated training of conditional random fields with stochastic gradient methods. Pittsburgh, PA, USA.","DOI":"10.1145\/1143844.1143966"},{"key":"ref_16","unstructured":"Ratliff, N.D., Bagnell, J.A., and Zinkevich, M.A. (2007, January 21\u201324). Subgradient methods for structured prediction. San Juan, Puerto Rico."},{"key":"ref_17","first-page":"1453","article-title":"Large margin methods for structured and interdependent output variables","volume":"6","author":"Tsochantaridis","year":"2005","journal-title":"J. Mach. Learn. Res"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Szummer, M., Kohli, P., and Hoiem, D. (2008, January 12\u201318). Learning CRFs using graph cuts. Marseille, France.","DOI":"10.1007\/978-3-540-88688-4_43"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Nowozin, S., Gehler, P., and Lampert, C. (2010, January 5\u201311). On parameter learning in CRF-based approaches to object class image segmentation. Heraklion, Crete, Greece.","DOI":"10.1007\/978-3-642-15567-3_8"},{"key":"ref_20","unstructured":"Sutton, C., and Mccallum, A. (2005, January 26\u201329). Piecewise training for undirected models. Edinburgh, Scotland."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Sutton, C., and Mccallum, A. (2007, January 20\u201324). Piecewise pseudolikelihood for efficient training of conditional random fields. Corvallis, OR, USA.","DOI":"10.1145\/1273496.1273605"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1890","DOI":"10.1109\/TIP.2010.2045034","article-title":"Learning conditional random fields for classification of hyperspectral images","volume":"19","author":"Zhong","year":"2010","journal-title":"IEEE Trans. Image Process"},{"key":"ref_23","unstructured":"Koltun, V. (2011). Efficient inference in fully connected CRFs with gaussian edge potentials.. Adv. Neural Inf. Process. Syst., arXiv:1210.5644."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Alahari, K., Russell, C., and Torr, P.H.S. (2010, January 13\u201318). Efficient piecewise learning for conditional random fields. San Francisco, CA, USA.","DOI":"10.1109\/CVPR.2010.5540123"},{"key":"ref_25","unstructured":"Kumar, M.P., Zisserman, A., and Torr, P.H.S. (October, January 29). Efficient discriminative learning of parts-based models.. Kyoto, Japan."},{"key":"ref_26","first-page":"265","article-title":"On the algorithmic implementation of multiclass kernel-based vector machines","volume":"2","author":"Crammer","year":"2001","journal-title":"J. Mach. Learn. Res"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"617","DOI":"10.1109\/TIP.2003.811490","article-title":"Multiscale gradient watersheds of color images","volume":"12","author":"Vanhamel","year":"2003","journal-title":"IEEE Trans. Image Process"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"182","DOI":"10.1137\/0729012","article-title":"Image selective smoothing and edge detection by nonlinear diffusion","volume":"29","author":"Lions","year":"1992","journal-title":"SIAM J. Numer. Anal"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"629","DOI":"10.1109\/34.56205","article-title":"Scale-space and edge detection using anisotropic diffusion","volume":"12","author":"Perona","year":"1990","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"421","DOI":"10.1109\/83.661192","article-title":"Robust anisotropic diffusion","volume":"7","author":"Black","year":"1998","journal-title":"IEEE Trans. Image Process"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1007\/BF00336961","article-title":"The structure of images","volume":"50","author":"Koenderink","year":"1984","journal-title":"Biol. Cybernet"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Vanhamel, I., Alrefaya, M., and Sahli, H. (2010, January 25\u201330). Multi scale representation for remotely sensed images using fast anisotropic diffusion filtering. Honolulu, HI, USA.","DOI":"10.1109\/IGARSS.2010.5651194"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"194","DOI":"10.1007\/s11263-008-0154-4","article-title":"Scale selection for compact scale-space representation of vector-valued images","volume":"84","author":"Vanhamel","year":"2008","journal-title":"Int. J. Comput. Vis"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1016\/j.isprsjprs.2009.06.004","article-title":"Object based image analysis for remote sensing","volume":"65","author":"Blaschke","year":"2010","journal-title":"J. Photogramm. Remote Sens"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Paletta, L., and Tsotsos, J.K. (2009). Attention in Cognitive Systems, Springer-Verlag.","DOI":"10.1007\/978-3-642-00582-4"},{"key":"ref_36","unstructured":"Marcotegui, B.B.S. (2005). 40 Years On Mathematical Morphology, Springer-Verlag."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1109\/TIP.2004.838695","article-title":"Combined morphological-spectral unsupervised image segmentation","volume":"14","author":"Bull","year":"2005","journal-title":"Image Process"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"116","DOI":"10.1016\/0734-189X(86)90223-9","article-title":"A note on the gradient of a multi-image","volume":"33","author":"DiZenzo","year":"1986","journal-title":"Comput. Vis. Graph. Image Process"},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Ladicky, L., Russell, C., Kohli, P., and Torr, P.H.S. (2009\u20132, January 29). Associative hierarchical CRFs for object class image segmentation. Kyoto, Japan.","DOI":"10.1109\/ICCV.2009.5459248"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"302","DOI":"10.1007\/s11263-008-0202-0","article-title":"Robust higher order potentials for enforcing label consistency","volume":"82","author":"Kohli","year":"2009","journal-title":"Int. J. Comput. Vis"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1090\/S0002-9947-1950-0051437-7","article-title":"Theory of reproducing kernels","volume":"68","author":"Aronszajn","year":"1950","journal-title":"Trans. Am. Math. Soc"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"4314","DOI":"10.1016\/j.ins.2008.07.015","article-title":"A novel extended local-binary-pattern operator for texture analysis","volume":"178","author":"Zhou","year":"2008","journal-title":"Inf. Sci"},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Komodakis, N. (2011, January 20\u201325). Efficient training for pairwise or higher order CRFs via dual decomposition. Providence, RI, USA.","DOI":"10.1109\/CVPR.2011.5995375"},{"key":"ref_44","unstructured":"Yedidia, J., and Freeman, W. (2003). Exploring Artificial Intelligence in the New Millennium, Morgan Kaufmann Publishers Inc."},{"key":"ref_45","first-page":"97","article-title":"Tree-reweighted belief propagation algorithms and approximate ML estimation by pseudo-moment matching","volume":"21","author":"Wainwright","year":"2003","journal-title":"Workshop Artif. Intell. Stat"},{"key":"ref_46","first-page":"1124","article-title":"An experimental comparison of min-cut\/max-flow algorithms for energy minimization in vision","volume":"26","author":"Boykov","year":"2004","journal-title":"Science"},{"key":"ref_47","unstructured":"Aksoy, S. (2006). Signal and Image Processing for Remote Sensing, CRC Press."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1016\/j.cageo.2011.08.019","article-title":"Support vector machines and object-based classification for obtaining land-use\/cover cartography from Hyperion hyperspectral imagery","volume":"41","author":"Petropoulos","year":"2012","journal-title":"Comput. Geosci"},{"key":"ref_49","unstructured":"Schmidt, M. UGM: Matlab Code for Undirected Graphical Models. Available online: http:\/\/www.cs.ubc.ca\/~schmidtm\/Software\/UGM.html\/."},{"key":"ref_50","first-page":"25","article-title":"Max-Margin Markov networks","volume":"16","author":"Taskar","year":"2004","journal-title":"Adv. Neural. Inf. Process. Syst"},{"key":"ref_51","doi-asserted-by":"crossref","unstructured":"Bach, F.R., Lanckriet, G.R.G., and Jordan, M.I. (2004, January 4\u20138). Multiple kernel learning, conic duality, and the SMO algorithm. Banff, AB, Canada.","DOI":"10.1145\/1015330.1015424"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"2781","DOI":"10.1016\/S0031-3203(03)00170-5","article-title":"Perceptual grouping of segmented regions in color images","volume":"36","author":"Luo","year":"2003","journal-title":"Patt. Recogn"}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/6\/8\/6727\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:14:02Z","timestamp":1760217242000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/6\/8\/6727"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,7,24]]},"references-count":52,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2014,8]]}},"alternative-id":["rs6086727"],"URL":"https:\/\/doi.org\/10.3390\/rs6086727","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,7,24]]}}}