Abstract
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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