Statistical Texture Measures Computed from Gray Level Coocurrence Matrices

The purpose of the present text is to present the theory and techniques behind the Gray Level Coocurrence Matrix (GLCM) method, and the stateof-the-art of the field, as applied to two dimensional images. It does not present a survey of practical results. 1 Gray Level Coocurrence Matrices In statistical texture analysis, texture features are computed from the statistical distribution of observed combinations of intensities at specified positions relative to each other in the image. According to the number of intensity points (pixels) in each combination, statistics are classified into first-order, second-order and higher-order statistics. The Gray Level Coocurrence Matrix (GLCM) method is a way of extracting second order statistical texture features. The approach has been used in a number of applications, e.g. [5],[6],[14],[5],[7],[12],[2],[8],[10],[1]. A GLCM is a matrix where the number of rows and colums is equal to the number of gray levels, G, in the image. The matrix element P (i, j | ∆x, ∆y) is the relative frequency with which two pixels, separated by a pixel distance (∆x, ∆y), occur within a given neighborhood, one with intensity i and the other with intensity j. One may also say that the matrix element P (i, j | d, θ) contains the second order 1 Albregtsen : Texture Measures Computed from GLCM-Matrices 2 statistical probability values for changes between gray levels i and j at a particular displacement distance d and at a particular angle (θ). Given an M ×N neighborhood of an input image containing G gray levels from 0 to G − 1, let f(m, n) be the intensity at sample m, line n of the neighborhood. Then P (i, j | ∆x, ∆y) = WQ(i, j | ∆x, ∆y) (1) where W = 1 (M − ∆x)(N − ∆y) Q(i, j | ∆x, ∆y) = N−∆y ∑