Image Thresholding by Histogram Segmentation Using Discriminant Analysis

Image segmentation is often used to distinguish the foreground from the background. This paper proposes a novel method of image thresholding using the optimal histogram segmentation by the cluster organization based on the similarity between adjacent clusters. Since this method is not based on the minimization of a function, the problem of selecting the threshold at the local minima is avoided. This approach overcomes the local minima that affect most of the conventional methods by maximizing the between-class and minimizing within-class objects. Agglomerative clustering is used in this method so as to merge two adjacent clusters in the histogram. The distance measurement using discriminant analysis is adapted from the criterion function defined by Otsu. It directly approaches the feasibility of evaluating the goodness of every pair and automatically grouping the closest pair. The most similar pair is selected, which is the most homogeneous one. In addition, this pair should be the closest pair in the sense of means distance. All steps are repeated iteratively until achieving two clusters. It is straightforward to extend the method to multi-level thresholding problem by stopping the grouping as the expected segment number is achieved. Results obtained from automatic thresholding of the experimental images are showing the validity of the method.