Algorithm of the Patch Cohesion Index

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Hello, I am recently going to implement Patch Cohesion Index in Python and Cython, but I am confused about the algorithm of the Patch Cohesion Index, if I take pij* which is the perimeter of the patch, and aij* which is the area of the patch, and Z which is the number of all the image elements in the sliding window, the computed results are not the same as that of the Fragstatas computed results.
I don't understand 'in terms of number of cell surfaces' and 'in terms of number of cells' in the official documentation.
I would appreciate it if you could answer my confusion.

pij is given as the number of cell surfaces along the patch perimeter as apposed to distance in meters, which would be the same as perimeter length (m) divided by cell size (m).
Same for aij. Path area (ha) divided by cell size (ha) would give number of cells in patch.
Hope this makes sense. Note, differences may be due to how you treat background and landscape boundary.