Gray level image thresholding based on fisher linear projection of two-dimensional histogram

Abstract

Thresholding is an important form of image segmentation and is a first step in the processing of images for many applications. The selection of suitable thresholds is ideally an automatic process, requiring the use of some criterion on which the selection is based. Most such criteria are only based on the one-dimensional (ID) gray-level histogram of image. In an effort to use more information available in the image, the present approaches use the criteria based on the two-dimensional (2D) histogram of the image. However, these methods which simply extend the 1D-histogram-based algorithms to the 2D histogram give rise to the exhaustive search for the threshold values. In this paper, an optimal projection of the 2D histogram is derived by applying Fisher Linear Discriminant. The optimal projection turns out to be the local average histogram. Analysis and experimental results show that, thresholding an image based on the local average histogram, one can obtain segmentation better than that of those simply using criteria based on 2D histogram, while the spent computation time is as much as that costed by the ones using criteria based on 1D histogram.