GLCM Mean
GLCM Mean Equations
The left hand equation calculates the mean based on the reference pixels, µi. It is also possible to calculate the mean using the neighbour pixels, µj, as in the right hand equation. For the symmetrical GLCM, where each pixel in the window is counted once as a reference and once as a neighbour, the two values are identical.
Calculation and notation details:
- The summation is from 0 to (N-1), not from 1 to N. Since the first cell in the upper left of the GLCM is numbered (0,0), then the i value (0) of this cell is the same as the value of the reference pixel (0). Similarly, the second cell down from the top has an i value of 1, and a reference pixel value of 1. If this is not clear, go back and look at the framework GLCM.
- The Pij value is the probability value from the GLCM, i.e. how many times that reference value occurs in a specific combination with a neighbour pixel. It is not a measure of how many times the reference pixel occurs, period, which would be the "regular" mean for the original window.
- Multiplying i by Pij effectively divides the entry i by the sum of entries in the GLCM, which is the number of combinations in the original window. This is the same as is done when calculating a mean in the "usual" way. If this is not clear, review how Pij is calculated in the first place.
- The GLCM Mean for the horizontal GLCM is different from that for the vertical GLCM because the combinations of pixels are different in the two cases.
Exercise: Calculate the GLCM Mean for the horizontal test image then for the vertical test image.