Finite topology as applied to image analysis
Computer Vision, Graphics, and Image Processing
Digital topology: introduction and survey
Computer Vision, Graphics, and Image Processing
Digital topology: a comparison of the graph-based and topological approaches
Topology and category theory in computer science
Digital Picture Processing
Algorithms and Data Structures for Computer Topology
Digital and Image Geometry, Advanced Lectures [based on a winter school held at Dagstuhl Castle, Germany in December 2000]
Topologies for the digital spaces Z2 and Z3
Computer Vision and Image Understanding
Algorithms in digital geometry based on cellular topology
IWCIA'04 Proceedings of the 10th international conference on Combinatorial Image Analysis
Digital Topology on Adaptive Octree Grids
Journal of Mathematical Imaging and Vision
Thinning on cell complexes from polygonal tilings
Discrete Applied Mathematics
Thinning on quadratic, triangular, and hexagonal cell complexes
IWCIA'08 Proceedings of the 12th international conference on Combinatorial image analysis
Homological spanning forest framework for 2D image analysis
Annals of Mathematics and Artificial Intelligence
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
Hi-index | 0.00 |
The paper presents a new set of axioms of digital topology, which are easily understandable for application developers. They define a class of locally finite (LF) topological spaces. An important property of LF spaces satisfying the axioms is that the neighborhood relation is antisymmetric and transitive. Therefore any connected and non-trivial LF space is isomorphic to an abstract cell complex. The paper demonstrates that in an n-dimensional digital space only those of the (a, b)-adjacencies commonly used in computer imagery have analogs among the LF spaces, in which a and b are different and one of the adjacencies is the "maximal" one, corresponding to 3 n 驴 1 neighbors. Even these (a, b)-adjacencies have important limitations and drawbacks. The most important one is that they are applicable only to binary images. The way of easily using LF spaces in computer imagery on standard orthogonal grids containing only pixels or voxels and no cells of lower dimensions is suggested.