Haralick texture features

Haralick's texture features [28] were calculated using the kharalick() function of the cytometry tool box [29] for Khoros (version 2.1 Pro, Khoral Research, Inc., Albuquerque, NM USA; http://www.khoral.com). The basis for these features is the gray-level co-occurrence matrix ( G in Equation 2.6). This matrix is square with dimension N_g, where N_g is the number of gray levels in the image. Element [i,j] of the matrix is generated by counting the number of times a pixel with value i is adjacent to a pixel with value j and then dividing the entire matrix by the total number of such comparisons made. Each entry is therefore considered to be the probability that a pixel with value i will be found adjacent to a pixel of value j.

$$\mathbf{G}=\left[ \begin{array}{cccc} p(1,1) & p(1,2) & \cdot... ...N_g,1) & p(N_g,2) & \cdots & p(N_g,N_g) \\ \end{array}\right]$$ (2.6)

Since adjacency can be defined to occur in each of four directions in a 2D, square pixel image (horizontal, vertical, left and right diagonals - see Figure 2.2), four such matrices can be calculated.

  

Figure 2.2: Four directions of adjacency as defined for calculation of the Haralick texture features. The Haralick statistics are calculated for co-occurrence matrices generated using each of these directions of adjacency.

Zernike moments through degree 12 were calculated (Z_nl such that $n\leq 12$ in Equation 2.4) using the code in Section 5.2.1 (p. ). Since the moments themselves are complex numbers and are sensitive to rotation of the image, the magnitudes of the moments were used as features (i.e. |Z_nl|) [21]. This provided 49 descriptive features for each image.

Haralick then described 14 statistics that can be calculated from the co-occurrence matrix with the intent of describing the texture of the image:

Since rotation invariance is a primary criterion for any features used with these images, a kind of invariance was achieved for each of these statistics by averaging them over the four directional co-occurrence matrices. The maximal correlation coefficient was not calculated due to computational instability so there were 13 texture features for each image.