Duality of orthogonally connected digital surfaces
Alasdair McAndrew, Charles F. Osborne · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1995
We investigate the notion of duality as it applies to digital surfaces, and in particular to those surfaces which are orthogonally connected. We show how to define and prove a Poincare duality theorem, which relates the homology groups of a surface to its cohomology groups, and how this can be generalized to relative surfaces--a Lefschetz-Poincare duality. We show how a surface can be `refined' to include more points, in such a way that orthogonal connectivity can be used for both the surface and its complement. We then show how to define and prove an Alexander duality theorem, which relates the homology of a surface to the cohomology of its complement, and discuss some of the results of this theorem.