Minimal non-simple sets in 4D binary images

Authors:
C. J. Gau;T. Yung Kong
Affiliations:
Department of Computer Science, Graduate School and University Center, City University of New York, New York, NY;Department of Computer Science, Queens College, City University of New York, Flushing, NY
Venue:
Graphical Models - Special issue: Discrete topology and geometry for image and object representation
Year:
2003

Citing 4
Cited 11

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Topology-Preserving Deletion of 1's from 2-, 3- and 4-Dimensional Binary Images

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Strongly normal sets of contractible tiles in N dimensions

Pattern Recognition
Two-Dimensional Parallel Thinning Algorithms Based on Critical Kernels

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Minimal non-deletable sets and minimal non-codeletable sets in binary images

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Minimal Simple Pairs in the 3-D Cubic Grid

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Skeletal curves of 3D astrocyte samples

Machine Graphics & Vision International Journal
On Parallel Thinning Algorithms: Minimal Non-simple Sets, P-simple Points and Critical Kernels

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An introduction to simple sets

Pattern Recognition Letters
New characterizations of simple points, minimal non-simple sets and P-simple points in 2D, 3D and 4D discrete spaces

DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
Minimal simple pairs in the cubic grid

DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
Minimal non-simple sets in 4-dimensional binary images with (8,80)-adjacency

IWCIA'04 Proceedings of the 10th international conference on Combinatorial Image Analysis
Minimal non-simple and minimal non-cosimple sets in binary images on cell complexes

DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery

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Abstract

One way to verify that a proposed parallel thinning algorithm "preserves topology" is to check that no iteration can ever delete a minimal non-simple ("MNS") set. This is a practical verification method because few types of set can be MNS without being a component. Ronse, Hall, Ma, and the authors have solved the problem of finding all such types of set for 2D and 3D Cartesian grids, 2D hexagonal grids, and 3D face-centered cubic grids. Here we solve this problem for a 4D Cartesian grid, in the case where 80-adjacency is used on 1's and 8-adjacency on 0's.