Finite topology as applied to image analysis
Computer Vision, Graphics, and Image Processing
Computer Vision, Graphics, and Image Processing
Graphs: theory and algorithms
Near optimal algorithms for computing Smith normal forms of integer matrices
ISSAC '96 Proceedings of the 1996 international symposium on Symbolic and algebraic computation
A Pyramid Framework for Early Vision: Multiresolutional Computer Vision
A Pyramid Framework for Early Vision: Multiresolutional Computer Vision
Image Processing, Analysis, and Machine Vision
Image Processing, Analysis, and Machine Vision
Contains and inside relationships within combinatorial pyramids
Pattern Recognition
Computation of homology groups and generators
Computers and Graphics
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
Extending the notion of AT-model for integer homology computation
GbRPR'07 Proceedings of the 6th IAPR-TC-15 international conference on Graph-based representations in pattern recognition
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
Topological map: an efficient tool to compute incrementally topological features on 3d images
IWCIA'06 Proceedings of the 11th international conference on Combinatorial Image Analysis
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
Homological Computation Using Spanning Trees
CIARP '09 Proceedings of the 14th Iberoamerican Conference on Pattern Recognition: Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications
Invariant representative cocycles of cohomology generators using irregular graph pyramids
Computer Vision and Image Understanding
Cup products on polyhedral approximations of 3D digital images
IWCIA'11 Proceedings of the 14th 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
Removal operations in nd generalized maps for efficient homology computation
CTIC'12 Proceedings of the 4th international conference on Computational Topology in Image Context
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We introduce a method for computing homology groups and their generators of a 2D image, using a hierarchical structure, i.e. irregular graph pyramid. Starting from an image, a hierarchy of the image is built by two operations that preserve homology of each region. Instead of computing homology generators in the base where the number of entities (cells) is large, we first reduce the number of cells by a graph pyramid. Then homology generators are computed efficiently on the top level of the pyramid, since the number of cells is small. A top down process is then used to deduce homology generators in any level of the pyramid, including the base level, i.e. the initial image. The produced generators fit on the object boundaries. A unique set of generators called the minimal set, is defined and its computation is discussed. We show that the new method produces valid homology generators and present some experimental results.