Minimum error thresholding

Thresholding is a popular tool for segmenting grey level images. The approach is based on the assumption that object and background pixels in the image can be distinguished by their grey level values. By judiciously choosing a grey level threshold between the dominant values of object and background intensities the original grey level image can be transformed into a binary form so that the image points associated with the objects and the background will assume values one and zero, respectively. Although the method appears to be simplistic, it is very important and fundamental, with wide applicability, as it is relevant not only for segmenting the original sensor data but also for segmenting its linear and non-linear image-to-image transforms. Apart from the recently proposed direct threshold selection method, (1'2~ determination of a suitable threshold involves the computation of the histogram or other function of the grey level intensity and its subsequent analysis. For a more detailed review of various approaches to threshoiding the reader is referred to Kittler et al. [3~ An effective approach is to consider thresholding as a classification problem. If the grey level distributions of object and background pixeis are known or can be estimated, then the optimal, minimum error threshold can be obtained using the results of statistical decision theoryY ~ It is often realistic to assume that the respective populations are distributed normally with distinct means and standard deviations. Under this assumption the population parameters can be inferred from the grey level histogram by fitting, as advocated by Nagawa and Rosenfeld (s~ and then the corresponding optimal threshold can be determined. However, their approach is computationally involved. In this paper we propose an alternative solution which is more efficient. The principal idea behind the method is to optimise a criterion function related to the average pixel classification error rate. The approach is devel-