ImageGLCM

ImageGLCM [/Z /FREE /D=distance /E=structure /P=plane /HTFP /DEST=destGLCM /DETP=destParamWave] srcWave

The ImageGLCM operation calculates the gray-level co-occurrence matrix for an 8-bit grayscale image and optionally evaluates Haralick's texture parameters.

The ImageGLCM operation was added in Igor Pro 7.00.

Flags

/D=distance	Sets the offset in pixels for which the co-occurrence matrix is calculated. The default value is 1.
/DEST=destGLCM
	Specifies the wave to hold the co-occurrence matrix. If you omit /DEST the operation stores the matrix in the wave M_GLCM in the current data folder.
/DETP=destParamWave
	Specifies the wave to hold the computed texture parameters. If you omit /DETP the operation stores the texture parameters in the wave W_TextureParams in the current data folder.
	If the destination wave already exists it is overwritten. Note that you must specify the /HTFP flag to compute the texture parameters.
/E=structureBits
	structureBits is a bitwise setting that lets you control the combination of co-occurrences that you want to compute.
	Consider a wave displayed in a table and a pixel at position x
	$\displaystyle \begin{array}{lll} 0 & 3 & 5 \\ 1 & x & 6 \\ 2 & 4 & 7 \end{array}$
	The structureBits corresponding to co-occurrence between x and any direction is simply 2^direction. By default the operation computes all combinations. This is equivalent to structureBits=255.
	Note that the structureBits only define directions. The combination of the distance (/D) and the the structureBits define the full co-occurrence calculation.
	See Setting Bit Parameters for details about bit settings.
/FREE	Creates output waves as free waves.
	/FREE is permitted in user-defined functions only, not from the command line or in macros.
	If you use /FREE then destGLCM and destParamWave must be simple names, not paths.
	See Free Waves for details on free waves.
/HTFP	Computes Haralick's texture parameters. See the discussion in the Details section below for more information about the texture parameters.
/P=plane	If the image consists of more than one plane you can use this flag to determine which plane in srcWave is analysed. By default it is plane zero.
/Z	No error reporting.

Details

ImageGLCM computes the co-occurrence matrix for the image in srcWave and optionally evaluates Haralick's texture parameters. The operation supports 8-bit grayscale images and generates a 256x256 single-precision floating point co-occurrence matrix.

The elements of the matrix P[i][j] are defined as the normalized number of pixels that have a spatial relationship defined by the distance (/D) and the structure (/E) such that the first pixel has gray-level i and the second pixel has gray-level j. The matrix is normalized so that the sum of all its elements is 1.

If you specify the /HTFP flag the operation computes the 13 Haralick texture parameters and stores them sequentially in the destination wave (see /DETP). The wave is saved with dimension labels defining each element. The expressions for the texture parameters are:

$$\displaystyle f_{1}=\sum_{i} \sum_{j}(p[i][j])^{2},$$ $$\displaystyle f_{2}=\sum_{n=0}^{254} n^{2}\left\{\sum_{i=0}^{255} \sum_{\substack{j=0 \\\quad|i-j|=n}}^{255} p[i][j]\right\},$$ $$\displaystyle f_{3}=\sum_{i} \sum_{j} \frac{\left(i-\mu_{x}\right)\left(j-\mu_{y}\right) p[i][j]}{\sigma_{x} \sigma_{y}},$$ $$\displaystyle f_{4}=\sum_{i} \sum_{j}(i-\mu)^{2} p[i][j],$$ $$\displaystyle f_{5}=\sum_{i} \sum_{j} \frac{1}{1+(i-j)^{2}} p[i][j],$$ $$\displaystyle f_{6}=\sum_{i} i p_{x+y}(i),$$ $$\displaystyle f_{7}=\sum_{i}\left(i-f_{6}\right)^{2} p_{x+y}(i),$$ $$\displaystyle f_{8}=-\sum_{i} p_{x+y}(i) \log \left(p_{x+y}(i)\right),$$ $$\displaystyle f_{9}=-\sum_{i} \sum_{j} p[i][j] \log (p[i][j]),$$ $$\displaystyle f_{10}=\operatorname{Variance}\left(p_{x-y}\right),$$ $$\displaystyle f_{11}=\sum_{i} p_{x-y}(i) \log \left(p_{x-y}(i)\right),$$ $$\displaystyle f_{12}=\frac{f_{9}-H X Y 1}{\max (H X, H Y)},$$ $$\displaystyle f_{13}=\sqrt{1-\exp (-2(H X Y 2-f 9))} .$$

Here

$$\displaystyle p_{x}(i)=\sum_{j} p[i][j], \quad p_{y}(j)=\sum_{i} p[i][j],$$ $$\displaystyle \mu_{x}=\sum_{i} i p_{x}(i), \quad \mu_{y}=\sum_{i} i p_{y}(i), \quad \mu=\left(\mu_{x}+\mu_{y}\right) / 2 .$$ $$\displaystyle \sigma_{x}=\sqrt{\sum_{i}\left(1-\mu_{x}\right)^{2} p_{x}(i)}, \quad \sigma_{y}=\sqrt{\sum_{i}\left(1-\mu_{y}\right)^{2} p_{y}(i)},$$ $$\displaystyle p_{x+y}(k)=\sum_{i} \sum_{\substack{j \\ \quad i+j=k}} p[i][j],$$ $$\displaystyle p_{x-y}(k)=\sum_{i} \sum_{\substack{j \\\quad \quad |i-j|=k}} p[i][j],$$ $$\displaystyle H X Y 1=-\sum_{i} \sum_{j} p[i][j] \log \left(p_{x}(i) p_{y}(j)\right),$$ $$\displaystyle H X Y 2=-\sum_{i} \sum_{j} p_{x}(i) p_{y}(j) \log \left(p_{x}(i) p_{y}(j)\right),$$ $$\displaystyle H X=-\sum_{i} p_{x}(i) \log \left(p_{x}(i)\right), \quad H Y=-\sum_{i} p_{y}(i) \log \left(p_{y}(i)\right) .$$

There are at least two versions of f₇ used in the literature and in software. We know of at least three versions of f₁₄ so ImageGLCM does not compute it.

References

R.M. Haralick, K. Shanmugam and Itshak Dinstein, "Textural Features for Image Classification", IEEE Transactions on Systems, Man, and Cybernetics, 1973.