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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; The basis for these features is the gray-level co-occurrence matrix ( G in Equation 2.6). This matrix is square with dimension Ng, where Ng 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.

p(1,1) & p(1,2) & \cdot...
...N_g,1) & p(N_g,2) & \cdots & p(N_g,N_g) \\
\end{displaymath} (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 (Znl 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. |Znl|) [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:

\begin{longtable}{l\vert p{3.5in}}
Angular Second Moment & $\...
...,k)p(j,k)}{p_x(i)p_y(k)}$\space \tabularnewline

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.

next up previous contents
Next: Feature Selection Up: Materials and Methods Previous: Zernike Features
Copyright ©1999 Michael V. Boland