Topological models for boundary representation: a comparison with n-dimensional generalized maps
Computer-Aided Design - Beyond solid modelling
Near optimal algorithms for computing Smith normal forms of integer matrices
ISSAC '96 Proceedings of the 1996 international symposium on Symbolic and algebraic computation
Directly computing the generators of image homology using graph pyramids
Image and Vision Computing
Border operator for generalized maps
DGCI'09 Proceedings of the 15th IAPR international conference on Discrete geometry for computer imagery
Invariant representative cocycles of cohomology generators using irregular graph pyramids
Computer Vision and Image Understanding
Multi-resolution cell complexes based on homology-preserving euler operators
DGCI'13 Proceedings of the 17th IAPR international conference on Discrete Geometry for Computer Imagery
Topological modifications and hierarchical representation of cell complexes in arbitrary dimensions
Computer Vision and Image Understanding
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In this paper, we present an efficient way for computing homology generators of nD generalized maps. The algorithm proceeds in two steps: (1) cell removals reduces the number of cells while preserving homology; (2) homology generator computation is performed on the reduced object by reducing incidence matrices into their Smith-Agoston normal form. In this paper, we provide a definition of cells that can be removed while preserving homology. Some results on 2D and 3D homology generators computation are presented.