Connectivity in Digital Pictures
Journal of the ACM (JACM)
On the Topological Properties of Quantized Spaces, II. Connectivity and Order of Connectivity
Journal of the ACM (JACM)
RECOGNITION OF TOPOLOGICAL INVARIANTS BY ITERATIVE ARRAYS
RECOGNITION OF TOPOLOGICAL INVARIANTS BY ITERATIVE ARRAYS
Computational geometry: a retrospective
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Journal of Mathematical Imaging and Vision
Weak lighting functions and strong 26-surfaces
Theoretical Computer Science
Discrete Polyhedrization of a Lattice Point Set
Digital and Image Geometry, Advanced Lectures [based on a winter school held at Dagstuhl Castle, Germany in December 2000]
Discrete polyhedrization of a lattice point set
Digital and image geometry
The Discrete Equation of the Straight Line
IEEE Transactions on Computers
Curves, hypersurfaces, and good pairs of adjacency relations
IWCIA'04 Proceedings of the 10th international conference on Combinatorial Image Analysis
An invitation to 'Shape Theory'
Pattern Recognition Letters
Digital connectedness: An algebraic approach
Pattern Recognition Letters
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It is the object of this paper to study the topological properties of finite graphs that can be embedded in the n-dimensional integral lattice (denoted Nn). The basic notion of deletability of a node is first introduced. A node is deletable with respect to a graph if certain computable conditions are satisfied on its neighborhood. An equivalence relation on graphs called reducibility and denoted by “∼” is then defined in terms of deletability, and it is shown that (a) most important topological properties of the graph (homotogy, homology, and cohomology groups) are ∼-invariants; (b) for graphs embedded in N3, different knot types belong to different ∼-equivalence classes; (c) it is decidable whether two graphs are reducible to each other in N2 but this problem is undecidable in Nn for n ≥ 4. Finally, it is shown that two different methods of approximating an n-dimensional closed manifold with boundary by a graph of the type studied in this paper lead to graphs whose corresponding homology groups are isomorphic.