Open Access
December 2011 On image segmentation using information theoretic criteria
Alexander Aue, Thomas C. M. Lee
Ann. Statist. 39(6): 2912-2935 (December 2011). DOI: 10.1214/11-AOS925


Image segmentation is a long-studied and important problem in image processing. Different solutions have been proposed, many of which follow the information theoretic paradigm. While these information theoretic segmentation methods often produce excellent empirical results, their theoretical properties are still largely unknown. The main goal of this paper is to conduct a rigorous theoretical study into the statistical consistency properties of such methods. To be more specific, this paper investigates if these methods can accurately recover the true number of segments together with their true boundaries in the image as the number of pixels tends to infinity. Our theoretical results show that both the Bayesian information criterion (BIC) and the minimum description length (MDL) principle can be applied to derive statistically consistent segmentation methods, while the same is not true for the Akaike information criterion (AIC). Numerical experiments were conducted to illustrate and support our theoretical findings.


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Alexander Aue. Thomas C. M. Lee. "On image segmentation using information theoretic criteria." Ann. Statist. 39 (6) 2912 - 2935, December 2011.


Published: December 2011
First available in Project Euclid: 24 January 2012

zbMATH: 1246.94012
MathSciNet: MR3012396
Digital Object Identifier: 10.1214/11-AOS925

Primary: 62H35 , 62P30
Secondary: 62G05

Keywords: Akaike information criterion (AIC) , Bayesian information criterion (BIC) , image modeling , minimum description length (MDL) , piecewise constant function modeling , statistical consistency

Rights: Copyright © 2011 Institute of Mathematical Statistics

Vol.39 • No. 6 • December 2011
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