{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,24]],"date-time":"2026-02-24T18:56:50Z","timestamp":1771959410895,"version":"3.50.1"},"reference-count":45,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2019,3,14]],"date-time":"2019-03-14T00:00:00Z","timestamp":1552521600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002749","name":"Federaal Wetenschapsbeleid","doi-asserted-by":"publisher","award":["SR\/06\/357"],"award-info":[{"award-number":["SR\/06\/357"]}],"id":[{"id":"10.13039\/501100002749","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003130","name":"Fonds Wetenschappelijk Onderzoek","doi-asserted-by":"publisher","award":["G.0371.15N"],"award-info":[{"award-number":["G.0371.15N"]}],"id":[{"id":"10.13039\/501100003130","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Classification of hyperspectral images is a challenging task owing to the high dimensionality of the data, limited ground truth data, collinearity of the spectra and the presence of mixed pixels. Conventional classification techniques do not cope well with these problems. Thus, in addition to the spectral information, features were developed for a more complete description of the pixels, e.g., containing contextual information at the superpixel level or mixed pixel information at the subpixel level. This has encouraged an evolution of fusion techniques which use these myriad of multiple feature sets and decisions from individual classifiers to be employed in a joint manner. In this work, we present a flexible decision fusion framework addressing these issues. In a first step, we propose to use sparse fractional abundances as decision source, complementary to class probabilities obtained from a supervised classifier. This specific selection of complementary decision sources enables the description of a pixel in a more complete way, and is expected to mitigate the effects of small training samples sizes. Secondly, we propose to apply a fusion scheme, based on the probabilistic graphical Markov Random Field (MRF) and Conditional Random Field (CRF) models, which inherently employ spatial information into the fusion process. To strengthen the decision fusion process, consistency links across the different decision sources are incorporated to encourage agreement between their decisions. The proposed framework offers flexibility such that it can be extended with additional decision sources in a straightforward way. Experimental results conducted on two real hyperspectral images show superiority over several other approaches in terms of classification performance when very limited training data is available.<\/jats:p>","DOI":"10.3390\/rs11060624","type":"journal-article","created":{"date-parts":[[2019,3,15]],"date-time":"2019-03-15T04:12:09Z","timestamp":1552623129000},"page":"624","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Decision Fusion Framework for Hyperspectral Image Classification Based on Markov and Conditional Random Fields"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2291-5186","authenticated-orcid":false,"given":"Vera","family":"Andrejchenko","sequence":"first","affiliation":[{"name":"IMEC-VisionLab, University of Antwerp, 2000 Antwerp, Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2183-0324","authenticated-orcid":false,"given":"Wenzhi","family":"Liao","sequence":"additional","affiliation":[{"name":"IMEC-IPI, Ghent University, 9000 Gent, Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wilfried","family":"Philips","sequence":"additional","affiliation":[{"name":"IMEC-IPI, Ghent University, 9000 Gent, Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Paul","family":"Scheunders","sequence":"additional","affiliation":[{"name":"IMEC-VisionLab, University of Antwerp, 2000 Antwerp, Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,3,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1109\/TIT.1968.1054102","article-title":"On the Mean Accuracy of Statistical Pattern Recognizers","volume":"14","author":"Hughes","year":"2006","journal-title":"IEEE Trans. Inf. Theor."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"466","DOI":"10.1109\/TGRS.2004.841417","article-title":"Dimensionality reduction and classification of hyperspectral image data using sequences of extended morphological transformations","volume":"43","author":"Plaza","year":"2005","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"5975","DOI":"10.1080\/01431161.2010.512425","article-title":"Extended profiles with morphological attribute filters for the analysis of hyperspectral data","volume":"31","author":"Benediktsson","year":"2010","journal-title":"Int. J. Remote Sens."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1177","DOI":"10.1109\/JSTARS.2012.2190045","article-title":"Classification of Hyperspectral Data Over Urban Areas Using Directional Morphological Profiles and Semi-Supervised Feature Extraction","volume":"5","author":"Liao","year":"2012","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"480","DOI":"10.1109\/TGRS.2004.842478","article-title":"Classification of hyperspectral data from urban areas based on extended morphological profiles","volume":"43","author":"Benediktsson","year":"2005","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"8","DOI":"10.1109\/MGRS.2017.2663666","article-title":"Taking optimal advantage of fine spatial information: promoting partial image reconstruction for the morphological analysis of very-high-resolution images","volume":"5","author":"Liao","year":"2017","journal-title":"IEEE Geosci. Remote Sens. Mag."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"447","DOI":"10.1109\/LGRS.2011.2172185","article-title":"Linear versus nonlinear PCA for the classification of hyperspectral data based on the extended morphological profiles","volume":"9","author":"Licciardi","year":"2012","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"5122","DOI":"10.1109\/TGRS.2013.2286953","article-title":"Remotely sensed image classification using sparse representations of morphological attribute profiles","volume":"52","author":"Song","year":"2014","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"3804","DOI":"10.1109\/TGRS.2008.922034","article-title":"Spectral and spatial classification of hyperspectral data using SVMs and morphological profiles","volume":"46","author":"Fauvel","year":"2008","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Tuia, D., Matasci, G., Camps-Valls, G., and Kanevski, M. (2009, January 12\u201317). Learning the relevant image features with multiple kernels. Proceedings of the 2009 IEEE International Geoscience and Remote Sensing Symposium, Cape Town, South Africa.","DOI":"10.1109\/IGARSS.2009.5418002"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1592","DOI":"10.1109\/TGRS.2014.2345739","article-title":"Multiple feature learning for hyperspectral image classification","volume":"53","author":"Li","year":"2015","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"3857","DOI":"10.1109\/TGRS.2009.2029340","article-title":"Decision fusion for the classification of hyperspectral data: outcome of the 2008 GRSS data fusion contest","volume":"47","author":"Licciardi","year":"2009","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Song, B., Li, J., Li, P., and Plaza, A. (2013, January 26\u201328). Decision fusion based on extended multi-attribute profiles for hyperspectral image classification. Proceedings of the 5th Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing (WHISPERS), Gainesville, FL, USA.","DOI":"10.1109\/WHISPERS.2013.8080592"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Li, W., Prasad, S., Tramel, E.W., Fowler, J.E., and Du, Q. (2014, January 9\u201313). Decision fusion for hyperspectral image classification based on minimum-distance classifiers in the wavelet domain. Proceedings of the 2014 IEEE China Summit & International Conference on Signal and Information Processing (ChinaSIP), Xi\u2019an, China.","DOI":"10.1109\/ChinaSIP.2014.6889223"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1367","DOI":"10.1109\/36.763301","article-title":"Classification of multisource and hyperspectral data based on decision fusion","volume":"37","author":"Benediktsson","year":"1999","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_16","first-page":"4047","article-title":"Decision-level fusion of spectral reflectance and derivative information for robust hyperspectral land cover classification","volume":"48","author":"Kalluri","year":"2010","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"875","DOI":"10.1109\/LGRS.2010.2054063","article-title":"Decision fusion on supervised and unsupervised classifiers for hyperspectral imagery","volume":"7","author":"Yang","year":"2010","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"7416","DOI":"10.1109\/TGRS.2016.2603190","article-title":"Probabilistic fusion of pixel-level and superpixel-level hyperspectral image classification","volume":"54","author":"Li","year":"2016","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"6298","DOI":"10.1109\/TGRS.2013.2296031","article-title":"Spectral-spatial classification of hyperspectral data using local and global probabilities for mixed pixel characterization","volume":"52","author":"Khodadadzadeh","year":"2014","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Khodadadzadeh, M., Li, J., Plaza, A., Ghassemian, H., and Bioucas-Dias, J.M. (2013, January 21\u201326). Spectral-spatial classification for hyperspectral data using SVM and subspace MLR. Proceedings of the 2013 IEEE International Geoscience and Remote Sensing Symposium\u2014IGARSS, Melbourne, Australia.","DOI":"10.1109\/IGARSS.2013.6723247"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"2532","DOI":"10.1109\/TGRS.2014.2361618","article-title":"Spectral\u2013spatial classification for hyperspectral data using rotation forests with local feature extraction and markov random fields","volume":"53","author":"Xia","year":"2015","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"515","DOI":"10.1109\/LGRS.2016.2521418","article-title":"A novel MRF-based multifeature fusion for classification of remote sensing images","volume":"13","author":"Lu","year":"2016","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"4398","DOI":"10.1109\/TGRS.2017.2691906","article-title":"From subpixel to superpixel: a novel fusion framework for hyperspectral image classification","volume":"55","author":"Lu","year":"2017","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1560","DOI":"10.1109\/JPROC.2015.2449668","article-title":"Multimodal classification of remote sensing images: a review and future directions","volume":"103","author":"Tuia","year":"2015","journal-title":"Proc. IEEE"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"100","DOI":"10.1109\/36.481897","article-title":"A markov random field model for classification of multisource satellite imagery","volume":"34","author":"Solberg","year":"1996","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1109\/JSTARS.2010.2053521","article-title":"Building detection from one orthophoto and high-resolution InSAR data using conditional random fields","volume":"4","author":"Wegner","year":"2011","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1016\/j.isprsjprs.2017.04.006","article-title":"A higher order conditional random field model for simultaneous classification of land cover and land use","volume":"130","author":"Albert","year":"2017","journal-title":"Int. J. Photogramm. Remote Sens."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"3277","DOI":"10.1109\/TGRS.2018.2797316","article-title":"Decision fusion with multiple spatial supports by conditional random fields","volume":"56","author":"Tuia","year":"2018","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Bioucas-Dias, J., and Figueiredo, M. (2010, January 14\u201316). Alternating direction algorithms for constrained sparse regression: Application to hyperspectral unmixing. Proceedings of the 2nd Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing (WHISPERS), Reykjavik, Iceland.","DOI":"10.1109\/WHISPERS.2010.5594963"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"3619","DOI":"10.1109\/JSTARS.2014.2322143","article-title":"A new hybrid strategy combining semisupervised classification and unmixing of hyperspectral data","volume":"7","author":"Dopido","year":"2014","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"3973","DOI":"10.1109\/TGRS.2011.2129595","article-title":"Hyperspectral image classification using dictionary-based sparse representation","volume":"49","author":"Chen","year":"2011","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"2200","DOI":"10.1109\/JSTARS.2014.2306956","article-title":"Joint within-class collaborative representation for hyperspectral image classification","volume":"7","author":"Li","year":"2014","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1235","DOI":"10.1109\/LGRS.2013.2290531","article-title":"Structured priors for sparse-representation-based hyperspectral image classification","volume":"11","author":"Sun","year":"2014","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_34","unstructured":"Bishop, C.M. (2006). Pattern Recognition and Machine Learning, Springer."},{"key":"ref_35","unstructured":"Liang, S. (2017). Contributions of machine learning to remote sensing data analysis. Comprehensive Remote Sensing, Elsevier. Chapter 10."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Hastie, T., Tibshirani, R., and Friedman, J. (2009). The Elements of Statistical Learning, Springer.","DOI":"10.1007\/978-0-387-84858-7"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Namin, S.T., Najafi, M., Salzmann, M., and Petersson, L. (2015, January 5\u20139). A multi-modal graphical model for scene analysis. Proceedings of the 2015 IEEE Winter Conference on Applications of Computer Vision, Waikoloa, HI, USA.","DOI":"10.1109\/WACV.2015.139"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1124","DOI":"10.1109\/TPAMI.2004.60","article-title":"An experimental comparison of min-cut\/max-flow algorithms for energy minimization in vision","volume":"26","author":"Boykov","year":"2004","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1222","DOI":"10.1109\/34.969114","article-title":"Fast approximation energy minimization via graph cuts","volume":"23","author":"Boykov","year":"2001","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"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. Comp. Vis."},{"key":"ref_41","unstructured":"Kohli, P., Ladicky, L., and Torr, P. (2008). Graph Cuts for Minimizing Robust Higher Order Potentials, Technical Report; Oxford Brookes University."},{"key":"ref_42","unstructured":"Boykov, Y., and Jolly, M.P. (2001, January 7\u201314). Interactive graph cuts for optimal boundary and region segmentation of objects in n-D images. Proceedings of the Eighth IEEE International Conference on Computer Vision, Vancouver, BC, Canada."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"271","DOI":"10.5194\/isprsannals-II-3-W4-271-2015","article-title":"Contextual classification of point cloud data by exploiting individual 3D neighborhoods","volume":"II-3\/W4","author":"Weinmann","year":"2015","journal-title":"ISPRS Ann. Photogramm. Remote Sensi. Spat. Inf. Sci."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1109\/TGRS.2013.2240001","article-title":"Collaborative sparse regression for hyperspectral unmixing","volume":"52","author":"Iordache","year":"2013","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"4484","DOI":"10.1109\/TGRS.2012.2191590","article-title":"Total variation spatial regularization for sparse hyperspectral unmixing","volume":"50","author":"Iordache","year":"2012","journal-title":"IEEE Trans. Geosci. Remote Sens."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/11\/6\/624\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:38:46Z","timestamp":1760186326000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/11\/6\/624"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,3,14]]},"references-count":45,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2019,3]]}},"alternative-id":["rs11060624"],"URL":"https:\/\/doi.org\/10.3390\/rs11060624","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,3,14]]}}}