{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T22:05:51Z","timestamp":1772834751771,"version":"3.50.1"},"reference-count":33,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2013,11,4]],"date-time":"2013-11-04T00:00:00Z","timestamp":1383523200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The paper addresses image feature characterization and the structuring of large and heterogeneous image databases through the stochasticity or randomness appearance. Measuring stochasticity involves finding suitable representations that can significantly reduce statistical dependencies of any order. Wavelet packet representations provide such a framework for a large class of stochastic processes through an appropriate dictionary of parametric models. From this dictionary and the Kolmogorov stochasticity index, the paper proposes semantic stochasticity templates upon wavelet packet sub-bands in order to provide high level classification and content-based image retrieval. The approach is shown to be relevant for texture images.<\/jats:p>","DOI":"10.3390\/e15114782","type":"journal-article","created":{"date-parts":[[2013,11,4]],"date-time":"2013-11-04T10:44:54Z","timestamp":1383561894000},"page":"4782-4801","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Stochasticity: A Feature for the Structuring of Large and Heterogeneous Image Databases"],"prefix":"10.3390","volume":"15","author":[{"given":"Abdourrahmane","family":"Atto","sequence":"first","affiliation":[{"name":"LISTIC (Laboratory of Informatics, Systems, Information and Knowledge Processing), University of Savoie, B.P. 80439, 74944 Annecy le Vieux Cedex, France"}]},{"given":"Yannick","family":"Berthoumieu","sequence":"additional","affiliation":[{"name":"IMS (Laboratory of Material to System Integration), CNRS UMR 5218, University of Bordeaux, IPB, ENSEIRB-MATMECA, 351 cours de la lib\u00e9ration, 33400 Talence, France"}]},{"given":"R\u00e9mi","family":"M\u00e9gret","sequence":"additional","affiliation":[{"name":"IMS (Laboratory of Material to System Integration), CNRS UMR 5218, University of Bordeaux, IPB, ENSEIRB-MATMECA, 351 cours de la lib\u00e9ration, 33400 Talence, France"}]}],"member":"1968","published-online":{"date-parts":[[2013,11,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Korostelev, A.P., and Tsybakov, A.B. (1993). Minimax Theory of Image Reconstruction, Springer.","DOI":"10.1007\/978-1-4612-2712-0"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"460","DOI":"10.1109\/TSMC.1978.4309999","article-title":"Textural features corresponding to visual perception","volume":"8","author":"Tamura","year":"1978","journal-title":"IEEE Trans. Syst. Man Cybern."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1007\/BF01213413","article-title":"A multiscale regularity measure as a geometric criterion for image segmentation","volume":"7","author":"Vasselle","year":"1994","journal-title":"Mach. Vision Appl."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"703","DOI":"10.1109\/76.927424","article-title":"Color and texture descriptors","volume":"11","author":"Manjunath","year":"1998","journal-title":"IEEE Trans. Circuits Syst. Video Technol."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"975","DOI":"10.1016\/S0262-8856(00)00041-X","article-title":"Pattern regularity as a visual key","volume":"18","author":"Chetverikov","year":"2000","journal-title":"Image Vision Comput."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1007\/s00426-002-0113-6","article-title":"Textural properties corresponding to visual perception based on the correlation mechanism in the visual system","volume":"67","author":"Fujii","year":"2003","journal-title":"Psychol. Res."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"6140","DOI":"10.1364\/OE.15.006140","article-title":"Regularity based descriptor computed from local image oscillations","volume":"15","author":"Trujillo","year":"2007","journal-title":"Opt. Express"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1160","DOI":"10.1364\/JOSAA.2.001160","article-title":"Uncertainty relation for resolution in space, spatial frequency, and orientation optimized by two-dimensional visual cortical filters","volume":"2","author":"Daugmann","year":"1985","journal-title":"J. Opt. Soc. Am. A"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"722","DOI":"10.1109\/34.506794","article-title":"Periodicity, directionality, and randomness: Wold features for image modeling and retrieval","volume":"18","author":"Liu","year":"1996","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"947","DOI":"10.1109\/34.955109","article-title":"SIMPLIcity: Semantics-sensitive integrated matching for picture libraries","volume":"23","author":"Wang","year":"2001","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"3247","DOI":"10.1109\/TSP.2007.894415","article-title":"Three-dimensional textured image blocks model based on wold decomposition","volume":"55","author":"Stitou","year":"2007","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1549","DOI":"10.1109\/83.469936","article-title":"Texture classification and segmentation using wavelet frames","volume":"4","author":"Unser","year":"1995","journal-title":"IEEE Trans. Image Process."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"537","DOI":"10.1109\/TIP.2011.2164412","article-title":"Wavelet variance analysis for random fields on a regular lattice","volume":"21","author":"Mondal","year":"2012","journal-title":"IEEE Trans. Image Process."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1016\/j.cageo.2012.11.020","article-title":"Two-dimensional wavelet variance estimation with application to sea ice SAR images","volume":"54","author":"Geilhufe","year":"2013","journal-title":"Comput. Geosci."},{"key":"ref_15","first-page":"83","article-title":"Sulla determinazione empirica di una legge di distribuzione","volume":"4","author":"Kolmogorov","year":"1933","journal-title":"Giornale dell\u2019Istituto Italiano degli Attuari"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"T109","DOI":"10.1088\/0951-7715\/21\/7\/T02","article-title":"Orbits\u2019 statistics in chaotic dynamical systems","volume":"21","author":"Arnold","year":"2008","journal-title":"Nonlinearity"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"L33","DOI":"10.1051\/0004-6361:200811188","article-title":"Kolmogorov stochasticity parameter measuring the randomness in the cosmic microwave background","volume":"492","author":"Gurzadyan","year":"2008","journal-title":"Astron. Astrophys."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1109\/TIT.2011.2167496","article-title":"Wavelet packets of nonstationary random processes: Contributing factors for stationarity and decorrelation","volume":"58","author":"Atto","year":"2012","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"4741","DOI":"10.1109\/TIT.2010.2053865","article-title":"Wavelet packets of fractional brownian motion: Asymptotic analysis and spectrum estimation","volume":"56","author":"Atto","year":"2010","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"896","DOI":"10.1109\/TSP.2009.2031726","article-title":"Central limit theorems for wavelet packet decompositions of stationary random processes","volume":"58","author":"Atto","year":"2010","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1080\/01621459.1951.10500769","article-title":"The Kolmogorov-Smirnov test for goodness of fit","volume":"253","author":"Massey","year":"1951","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_22","unstructured":"Kenney, J.F., and Keeping, E.S. (1951). Mathematics of Statistics, Part II, Van Nostrand Company, Inc."},{"key":"ref_23","unstructured":"Lions, P.-L. (1991). Probl\u00e8mes Non-Lin\u00e9aires Appliqu\u00e9s, Ondelettes et Paquets D\u2019Ondes, INRIA."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Daubechies, I. (1992). Ten Lectures on Wavelets, SIAM.","DOI":"10.1137\/1.9781611970104"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"713","DOI":"10.1109\/18.119732","article-title":"Entropy-based algorithms for best basis selection","volume":"38","author":"Coifman","year":"1992","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"523","DOI":"10.1109\/5.488698","article-title":"Wavelets and time-frequency analysis","volume":"84","author":"Wickerhauser","year":"1996","journal-title":"Proc. IEEE"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1186","DOI":"10.1109\/34.244679","article-title":"Texture classification by wavelet packet signatures","volume":"15","author":"Laine","year":"1993","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"429","DOI":"10.1109\/83.242353","article-title":"Texture analysis and classification with tree-structured wavelet transform","volume":"2","author":"Chang","year":"1993","journal-title":"IEEE Trans. Image Process."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2613","DOI":"10.1109\/TSP.2010.2042490","article-title":"Best basis compressed sensing","volume":"58","year":"2010","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_30","unstructured":"Eakins, J., and Graham, M. (1999). Content-Based Image Retrieval, University of Northumbria. Technical Report."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Atto, A.M., and Berthoumieu, Y. (2011, January 22\u201327). How to Perform Texture Recognition from Stochastic Modeling in the Wavelet Domain. Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), Prague, Czech Republic.","DOI":"10.1109\/ICASSP.2011.5947309"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"262","DOI":"10.1016\/j.patcog.2006.04.045","article-title":"A survey of content-based image retrieval with high-level semantics","volume":"40","author":"Liu","year":"2007","journal-title":"Pattern Recognit."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1349","DOI":"10.1109\/34.895972","article-title":"Content-based image retrieval at the end of the early years","volume":"22","author":"Smeulders","year":"2000","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/15\/11\/4782\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:50:22Z","timestamp":1760219422000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/15\/11\/4782"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,11,4]]},"references-count":33,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2013,11]]}},"alternative-id":["e15114782"],"URL":"https:\/\/doi.org\/10.3390\/e15114782","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,11,4]]}}}