Topological models for boundary representation: a comparison with n-dimensional generalized maps
Computer-Aided Design - Beyond solid modelling
Efficiency of a Good But Not Linear Set Union Algorithm
Journal of the ACM (JACM)
A topologically consistent representation for image analysis: the Topological Graph of Frontiers
DCGA '96 Proceedings of the 6th International Workshop on Discrete Geometry for Computer Imagery
Topological Encoding of 3D Segmented Images
DGCI '00 Proceedings of the 9th International Conference on Discrete Geometry for Computer Imagery
Topological Map Based Algorithms for 3D Image Segmentation
DGCI '02 Proceedings of the 10th International Conference on Discrete Geometry for Computer Imagery
Delineating Homology Generators in Graph Pyramids
CIARP '08 Proceedings of the 13th Iberoamerican congress on Pattern Recognition: Progress in Pattern Recognition, Image Analysis and Applications
Directly computing the generators of image homology using graph pyramids
Image and Vision Computing
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
Computing homology generators for volumes using minimal generalized maps
IWCIA'08 Proceedings of the 12th international conference on Combinatorial image analysis
An iterative algorithm for homology computation on simplicial shapes
Computer-Aided Design
A fast algorithm to compute cohomology group generators of orientable 2-manifolds
Pattern Recognition Letters
Digital Imaging: A Unified Topological Framework
Journal of Mathematical Imaging and Vision
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In this paper, we present an algorithm which allows to compute efficiently generators of the first homology group of a closed surface, orientable or not. Starting with an initial subdivision of a surface, we simplify it to its minimal form (minimal refers to the number of cells), while preserving its homology. Homology generators can thus be directly deduced from the minimal representation of the initial surface. Finally, we show how this algorithm can be used in a 3D labelled image in order to compute homology of each region described by its boundary.