Median-based thresholding, minimum error thresholding, and their relationships with histogram-based image similarity

Abstract

A popular histogram-based thresholding method is minimum error thresholding (MET) proposed by Kittler and Illingworth [Minimum error thresholding, Pattern Recognition 19 (1) (1986) 41-47], whereas Xue and Titterington recently proposed a median-based thresholding (MBT) [Median-based image thresholding, Image and Vision Computing 29 (9) (2011) 631-637]. Both MET and MBT can be derived from the maximization of log-likelihood. In this paper, we present a different theoretical interpretation about MBT and MET, from the perspective of minimizing Kullback-Leibler (KL) divergence. Since the KL divergence is a measure of the difference between two probability distributions, it is reasonable to regard MET and MBT as the special applications of histogram-based image similarity (HBIS) in the image thresholding. Further, it is natural to suggest a more universal image thresholding framework based on image similarity concept, since HBIS is just one of many image similarity methodologies. This thresholding framework directly transforms the threshold determining problem into an image comparison issue. Its significance is that it provides a concise and clear theoretical framework for developing potential thresholding methods with the plentiful image similarity theories.