Finite topology as applied to image analysis
Computer Vision, Graphics, and Image Processing
A topological approach to digital topology
American Mathematical Monthly
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]
| Hi-index | 0.00 |
The paper presents a new method of investigating topological properties of three-dimensional manifolds by means of computers. Manifolds are represented as finite cell complexes. The paper contains definitions and a theorem necessary to transfer some basic knowledge of the classical topology to finite topological spaces. The method is based on subdividing the given set into blocks of simple cells in such a way, that a k-dimensional block be homeomorphic to a k-dimensional ball. The block structure is described by the data structure known as "cell list" which is generalized here for the three-dimensional case. Some experimental results are presented.