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Computationally efficient method to compare the shape of planar Gaussian mixtures from point samples

[+] Author Affiliations
Hector J. Santos-Villalobos

Oak Ridge National Laboratory, One Bethel Valley Road, MS 6075, Oak Ridge, Tennessee 37831-6075

Mireille Boutin

Purdue University, School of Electrical and Computer Engineering, 465 Northwestern Avenue, West Lafayette, Indiana 47907

J. Electron. Imaging. 21(2), 023023 (Jun 22, 2012). doi:10.1117/1.JEI.21.2.023023
History: Received October 20, 2011; Revised April 3, 2012; Accepted May 15, 2012
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Abstract.  We discuss the problem of recognizing the shape of planar objects consisting of “blobs” that can be modeled as Gaussian mixture densities. We describe an empirical comparison method, assuming a large number of independent samples are given for each distribution. Instead of comparing the Gaussian mixtures directly, we compare the underlying distribution of distances of each mixture. Since distances are invariant under rotations and translations, this provides a workaround to the problem of aligning the objects before comparing them—thus speeding the comparison process. We prove that the distribution of distances is a lossless representation of the shape of generic Gaussian mixtures. Our numerical experiments indicate that, when all the components of the Gaussian mixtures are equally weighted and have the same standard deviation matrix, the proposed method is no less accurate than methods that compare the planar mixtures directly. The extension of our method to the problem of recognizing halftone patterns is briefly discussed.

© 2012 SPIE and IS&T

Citation

Hector J. Santos-Villalobos and Mireille Boutin
"Computationally efficient method to compare the shape of planar Gaussian mixtures from point samples", J. Electron. Imaging. 21(2), 023023 (Jun 22, 2012). ; http://dx.doi.org/10.1117/1.JEI.21.2.023023


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