How would I attribute segmentation lines created using the watershed algorithm with the adjacent, segmented, basins?

I'm using MATLAB to analyse microCT scans of rock cores to determine the surface area and volume of discrete pores segmented at pore necks (using the watershed algorithm and minima suppression).

If the watershed analogy is used pores are watershed basins and pore necks are the watershed lines (or ridges).

To get an accurate representation of the surface area I need to subtract the pore necks from the discrete pores.

If S is the segmented and numbered image from the watershed transform and O is the original binary image, the individual pore necks can be found by subtracting (S>0) from O.

However, I am stuck on relating these individual pore necks to the adjacent pores.

In my head the algorithm for doing this involves; - Thickening of the pore necks (so they overlap surrounding pores) - Numbering the pore necks for identification

and then some algorithm that compares the thickened, numbered pore neck image, to the numbered segmented pore image which returns the values of the overlapped pores for each pore neck. Which is what I'm having trouble with.

Is there an in-built function for this, or are there any ideas for writing an algorithm to achieve this?