Cups Products in Z2-Cohomology of 3D Polyhedral Complexes
نویسندگان
چکیده
Let I = (Z, 26, 6, B) be a 3D digital image, let Q(I) be the associated cubical complex and let ∂Q(I) be the subcomplex of Q(I) whose maximal cells are the quadrangles of Q(I) shared by a voxel of B in the foreground – the object under study – and by a voxel of Z rB in the background – the ambient space. We show how to simplify the combinatorial structure of ∂Q(I) and obtain a 3D polyhedral complex P (I) homeomorphic to ∂Q(I) but with fewer cells. We introduce an algorithm that computes cup products on H(P (I);Z2) directly from the combinatorics. The computational method introduced here can be effectively applied to any polyhedral complex embedded in R.
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Cup Products on Polyhedral Approximations of 3D Digital Images
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