Topology for Computing (Cambridge Monographs on Applied and Computational Mathematics)
Topology for Computing (Cambridge Monographs on Applied and Computational Mathematics)
On the cohomology of 3D digital images
Discrete Applied Mathematics - Special issue: Advances in discrete geometry and topology (DGCI 2003)
Digital Products, Wedges, and Covering Spaces
Journal of Mathematical Imaging and Vision
Computing homology group generators of images using irregular graph pyramids
GbRPR'07 Proceedings of the 6th IAPR-TC-15 international conference on Graph-based representations in pattern recognition
GD'07 Proceedings of the 15th international conference on Graph drawing
Computing homology for surfaces with generalized maps: application to 3d images
ISVC'06 Proceedings of the Second international conference on Advances in Visual Computing - Volume Part II
Irregular Graph Pyramids and Representative Cocycles of Cohomology Generators
GbRPR '09 Proceedings of the 7th IAPR-TC-15 International Workshop on Graph-Based Representations in Pattern Recognition
Invariant representative cocycles of cohomology generators using irregular graph pyramids
Computer Vision and Image Understanding
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Computation of homology generators using a graph pyramid can significantly increase performance, compared to the classical methods. First results in 2D exist and show the advantages of the method. Generators are computed on the upper level of a graph pyramid. Top-level graphs may contain self loops and multiple edges, as a side product of the contraction process. Using straight lines to draw these edges would not show the full information: self loops disappear, parallel edges collapse. This paper presents a novel algorithm for correctly visualizing graph pyramids, including multiple edges and self loops which preserves the geometry and the topology of the original image. New insights about the top-down delineation of homology generators in graph pyramids are given.