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Entropy 2009, 11(3), 513-528; doi:10.3390/e11030513
Article

Scale-Based Gaussian Coverings: Combining Intra and Inter Mixture Models in Image Segmentation

1,2,* , 2
 and 3,4
Received: 1 September 2009; Accepted: 14 September 2009 / Published: 24 September 2009
(This article belongs to the Special Issue Entropy and Information)
Download PDF [387 KB, uploaded 24 September 2009]
Abstract: By a “covering” 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 Rényi 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 Rényi quadratic entropy allows us to show clearly that one of these modelings is superior to the other.
Keywords: image segmentation; clustering; model selection; minimum description length; Bayes factor; Rényi entropy; Shannon entropy image segmentation; clustering; model selection; minimum description length; Bayes factor; Rényi entropy; Shannon entropy
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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MDPI and ACS Style

Murtagh, F.; Contreras, P.; Starck, J.-L. Scale-Based Gaussian Coverings: Combining Intra and Inter Mixture Models in Image Segmentation. Entropy 2009, 11, 513-528.

AMA Style

Murtagh F, Contreras P, Starck J-L. Scale-Based Gaussian Coverings: Combining Intra and Inter Mixture Models in Image Segmentation. Entropy. 2009; 11(3):513-528.

Chicago/Turabian Style

Murtagh, Fionn; Contreras, Pedro; Starck, Jean-Luc. 2009. "Scale-Based Gaussian Coverings: Combining Intra and Inter Mixture Models in Image Segmentation." Entropy 11, no. 3: 513-528.


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