{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:40:04Z","timestamp":1760244004494,"version":"build-2065373602"},"reference-count":31,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2009,9,24]],"date-time":"2009-09-24T00:00:00Z","timestamp":1253750400000},"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>By a \u201ccovering\u201d we mean a Gaussian mixture model fit to observed data. Approximations of the Bayes factor can be availed of to judge model fit to the data within a given Gaussian mixture model. Between families of Gaussian mixture models, we propose the R\u00e9nyi quadratic entropy as an excellent and tractable model comparison framework. We exemplify this using the segmentation of an MRI image volume, based (1) on a direct Gaussian mixture model applied to the marginal distribution function, and (2) Gaussian model fit through k-means applied to the 4D multivalued image volume furnished by the wavelet transform. Visual preference for one model over another is not immediate. The R\u00e9nyi quadratic entropy allows us to show clearly that one of these modelings is superior to the other.<\/jats:p>","DOI":"10.3390\/e11030513","type":"journal-article","created":{"date-parts":[[2009,9,24]],"date-time":"2009-09-24T10:41:20Z","timestamp":1253788880000},"page":"513-528","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Scale-Based Gaussian Coverings: Combining Intra and Inter Mixture Models in Image Segmentation"],"prefix":"10.3390","volume":"11","author":[{"given":"Fionn","family":"Murtagh","sequence":"first","affiliation":[{"name":"Science Foundation Ireland, Wilton Park House, Wilton Place, Dublin 2, Ireland"},{"name":"Department of Computer Science, Royal Holloway University of London, Egham TW20 0EX, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pedro","family":"Contreras","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Royal Holloway University of London, Egham TW20 0EX, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jean-Luc","family":"Starck","sequence":"additional","affiliation":[{"name":"CEA-Saclay, DAPNIA\/SEDI-SAP, Service d\u2019Astrophysique, 91191 Gif sur Yvette, France"},{"name":"Laboratoire AIM (UMR 7158), CEA\/DSM-CNRS, Universit\u00e9 Paris Diderot, Diderot, IRFU, SEDI-SAP, Service d'Astrophysique, Centre de Saclay, F-91191 Gif-Sur-Yvette cedex, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2009,9,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1225","DOI":"10.1214\/aos\/1035844977","article-title":"What is a statistical model?","volume":"30","author":"McCullagh","year":"2002","journal-title":"Ann. 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