Boundary: single form or plural form?
Solution 1:
"Boundary" designates the entire curve which encloses A; "boundaries" designates the several portions of that curve which respectively constitute the boundary between A and B, between A and C, between A and D, and so forth. So it seems to me the question is Which is more appropriate to your method?
Solution 2:
It depends on the nature of 'A region', but in some cases either boundary or boundaries can be used.