Maximum likelihood thresholding based on population mixture models

摘要

Maximum likelihood thresholding methods are presented on the basis of population mixture models. It turns out that the standard thresholding proposed by Otsu, which is based on a discriminant criterion and also minimizes the mean square errors between the original image and the resultant binary image, is equivalent to the maximization of the likelihood of the conditional distribution in the population mixture model under the assumption of normal distributions with a common variance. It is also shown that Kittler and Illingworth's thresholding, which minimizes a criterion related to the average classification error rate assuming normal distribution with different variances, is equivalent to the maximization of the likelihood of the joint distribution in the population mixture model. A multi-thresholding algorithm based on Dynamic Programming is also presented.