Duality of orthogonally connected digital surfaces

Alasdair McAndrew; Charles F. Osborne

doi:10.1117/12.216404

11 August 1995 Duality of orthogonally connected digital surfaces

Alasdair McAndrew, Charles F. Osborne

Proceedings Volume 2573, Vision Geometry IV; (1995) https://doi.org/10.1117/12.216404
Event: SPIE's 1995 International Symposium on Optical Science, Engineering, and Instrumentation, 1995, San Diego, CA, United States

Abstract

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.

Citation Download Citation

Alasdair McAndrew and Charles F. Osborne "Duality of orthogonally connected digital surfaces", Proc. SPIE 2573, Vision Geometry IV, (11 August 1995); https://doi.org/10.1117/12.216404

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