A Study on Histogram Moments and their Application to Image Thresholding

Abstract

Histogram moments have been widely investigated for image thresholding. This paper proposes several novel schemes in this area. In some of the proposals, the idea is simply to match a moment from the original image (calculated from the histogram) to a corresponding moment of the thresholded image. In other proposals, the threshold is the one optimizing a specific moment. Comparative results with Otsu shows the effectiveness of the proposed schemes. 1.Introduction Image thresholding has been widely investigated due to its vital role in many applications and one of the effective methods for image segmentation. Various schemes have been proposed in the literature, a good review can be found in [1]. The histogram plays a crucial role in many of these schemes. In general, the histogram is used as an approximation to the probability density function [2 – 3]. In these cases and their extensions, the threshold is selected as a solution to an optimization problem for some objective function dependent on features extracted from the histogram. The aforementioned schemes can be generalized to multi-level thresholding as in [4]. However, the computational price is too high. An interesting scheme to preserve the moments was proposed by [5]. For binary thresholding, the first three moments of the thresholded image have to be equal to those of the original image. A higher dimensional histogram can be constructed using the local variance [6]. This research proposes few formulations that exploit the use of different moments deducted from the 1D histogram. In general, the optimum threshold(s) are the ones producing a moment match (to that of the original) or the moment attains its optimum value at these threshold(s).