Transposing: making the matrix symmetrical around the diagonal
The texture calculations require a symmetrical matrix. The next step is therefore to get the GLCM into this form.
A symmetrical matrix means that the same values occur in cells on opposite sides of the diagonal. For example, the value in cell 3,2 would be the same as the value in cell 2,3. The east matrix calculated above is not symmetrical.
The east matrix counted each
reference pixel with the neighbour to its right (east). If counting is done this
way, using one direction only, then the number of times the combination 2,3
occurs is not the same as the number of times the combination 3,2 occurs (for
example 3 may be to the right of 2 three times, but to the left of 2 only once).
However, symmetry will be achieved if each pixel pair is counted twice: once
"forwards" and once "backwards" (interchanging reference and neighbour pixels
for the second count).
Example: A reference pixel of 3 and its eastern neighbour of 2 would contribute one count to the matrix element 3,2 and one count to the matrix element 2,3.