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.Comment: Published in at http://dx.doi.org/10.1214/11-AOS925 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
