Properties of the GLCM
1. It is square:
The reference pixels have the same range of values as the neighbour pixels, so the values along the top are identical to the values along the side.
2. Has the same number of rows
and columns as the quantization level of the image:
The test image has four grey level values (0,1,2 and 3). Eight bit data has 256 possible values, so would yield a 256 x 256 square matrix, with 65,536 cells. 16 bit data would give a matrix of size 65536 x 65536 = 429,496,720 cells!
2a. Isn't that too much to handle, even for a computer?
Yes - even for 8-bit data. Some operational programs rescale the values into 4 bit (16 x 16 matrix with 256 cells). The rescaling algorithms vary from one software to another, and are usually proprietary, meaning they do not say precisely how they do it.
There is another reason for compressing the data. If all 256 x 256 (or more) cells were used, there would be many cells filled with zeros (because that combination of grey levels simply does not occur). The GLCM approximates the joint probability distribution of two pixels. Having many zeros in cells makes this a very bad approximation. If the number of grey levels is reduced, the number of zeros is reduced, and the statistical validity is greatly improved.
Because users often have no choice (unless writing their own algorithms), the question of the effects of quantization level is often overlooked.In practice, some statistics calculated from the GLCM don't help classification very much when a large number of grey levels are used. Other statistics don't degrade as much. See Clausi 2002 for a discussion.
3. It is symmetrical around the diagonal:
Some things to notice about the normalized symmetrical GLCM (called the GLCM from here on)
The diagonal elements all represent pixel pairs with no grey level difference (0-0, 1-1, 2-2, 3-3 etc.). If there are high probabilities in these elements, then the image does not show much contrast: most pixels are identical to their neighbours.
When values in the diagonal are summed, the result is the probability of any pixel's being the same grey level as its neighbour.
Look at lines parallel to the diagonal. Cells one cell away from the diagonal represent pixel pairs with a difference of only one grey level (0-1, 1-2, 2-3 etc.). Similarly, values in cells two away from the diagonal show how many pixels have 2 grey level differences, and so forth. The farther away from the diagonal, the greater the difference between pixel grey levels.
Sum up these parallel diagonals and the result is the probability of any pixel's being 1 or 2 or 3 etc. different from its neighbour.
Some software uses the GLDV (grey-Level Distance Vector) instead of the GLCM.
If you need information about it for your software, click
here.