A digital fundamental group

doi:10.1016/0097-8493(89)90058-7

Computers & Graphics

Volume 13, Issue 2, 1989, Pages 159-166

https://doi.org/10.1016/0097-8493(89)90058-7 Get rights and content

Abstract

A group analogous to the fundamental group is defined for binary digital pictures based on almost arbitrary lattices and adjacency relations. This digital fundamental group has an immediate application to image processing—it can be used to give a precise statement of what it means for a three-dimensional image thinning algorithm to preserve topology. Given any suitably well-behaved digital picture, it is possible to construct a polyhedral set whose fundamental groups are naturally isomorphic to the digital fundamental groups of the digital picture. This result confirms that the digital fundamental group has been appropriately defined.

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^∗: On leave during the 1988–1989 academic year. Current address: Department of Mathematics, City College of New York, CUNY, New York, NY 10031.

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3D voxel-based graphicsA digital fundamental group

Abstract

Pattern Recognition Letters

Motion, deformation and homotopy in finite spaces

Characterizations of simply-connected finite polyhedra in 3-space

Bulletin of the London Mathematical Society

Algebraic Topology

Classical Topology and Combinatorial Group Theory

Some parallel thinning algorithms for digital pictures

J. ACM

Hexagonal parallel pattern transformations

IEEE Trans.

Linear skeletons from square cupboards

Local properties of binary images in two dimensions

IEEE Trans.

Multidimensional logical transforms

IEEE Trans.

3D voxel-based graphics
A digital fundamental group