On image segmentation using information theoretic criteria

TL;DR

This paper provides a theoretical analysis of information theoretic image segmentation methods, demonstrating that BIC and MDL are statistically consistent for recovering true image segments, unlike AIC.

Contribution

It offers a rigorous theoretical study of the consistency properties of information theoretic segmentation methods, highlighting the effectiveness of BIC and MDL.

Findings

BIC and MDL yield statistically consistent segmentation results

AIC does not guarantee consistency in segmentation

Numerical experiments support theoretical conclusions

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.