Image Thresholding by Histogram Segmentation Using Discriminant Analysis Agus Zainal Arifin 1 and Akira Asano 2 1 Graduate School of Engineering, Hiroshima University Email : agusza@hiroshima-u.ac.jp 2 Division of Mathematical and Information Sciences, Faculty of Integrated Arts and Sciences, Hiroshima University Email : asano@mis.hiroshima-u.ac.jp Abstract 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. 1. Introduction Image segmentation is very essential to image processing and pattern recognition. It leads to the high quality of the final result of analysis. Image segmentation is a process of dividing an image into different regions. One of the special kinds of segmentation is thresholding, which attempts to classify image pixels into one of the two categories (e.g. foreground and background). At the end of such thresholding, each object of the image, represented by a set of pixels, is isolated from the rest of the scene. In this case, the aim is to find a critical value or threshold. The most straightforward approach is to pick up a fixed grayscale value as the threshold and classify each grayscale by checking whether it lies above or below this value. In general, the threshold