Discriminative Image Thresholding

In this paper, we present discriminative approaches to histogram-based image thresholding, in which the optimal threshold is derived from the maximum likelihood based on the conditional distribution p(y|x) of y, the class indicator of a grey level x, given x. The discriminative approaches can be regarded as discriminative extensions of the traditional generative approaches to thresholding, such as Otsu’s method and Kittler and Illingworth’s minimum error thresholding (MET). The generative approaches assume a model for the data-generating process for each class whereas the discriminative approaches do not. As illustrations, we develop discriminative versions of Otsu’s method and MET by using discriminant functions corresponding to the original methods to represent p(y|x). These two discriminative thresholding approaches are compared with their original counterparts on selecting thresholds for a variety of histograms of mixture distributions. Results show that the discriminative Otsu method consistently provides relatively good performance. Although being of higher computational complexity than the original methods in parameter estimation, robustness and model simplicity can justify the discriminative Otsu method for scenarios in which the risk of model mis-specification is high and the computation is not demanding.