Finite topology as applied to image analysis
Computer Vision, Graphics, and Image Processing
Computer Vision, Graphics, and Image Processing
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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
Computation of homology groups and generators
Computers and Graphics
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ISVC'06 Proceedings of the Second international conference on Advances in Visual Computing - Volume Part II
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Integral Operators for Computing Homology Generators at Any Dimension
CIARP '08 Proceedings of the 13th Iberoamerican congress on Pattern Recognition: Progress in Pattern Recognition, Image Analysis and Applications
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CIARP '08 Proceedings of the 13th Iberoamerican congress on Pattern Recognition: Progress in Pattern Recognition, Image Analysis and Applications
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SSPR & SPR '08 Proceedings of the 2008 Joint IAPR International Workshop on Structural, Syntactic, and Statistical Pattern Recognition
Directly computing the generators of image homology using graph pyramids
Image and Vision Computing
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IWANN '09 Proceedings of the 10th International Work-Conference on Artificial Neural Networks: Part I: Bio-Inspired Systems: Computational and Ambient Intelligence
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GbRPR'11 Proceedings of the 8th international conference on Graph-based representations in pattern recognition
P systems and computational algebraic topology
Mathematical and Computer Modelling: An International Journal
Multi-resolution cell complexes based on homology-preserving euler operators
DGCI'13 Proceedings of the 17th IAPR international conference on Discrete Geometry for Computer Imagery
Topological modifications and hierarchical representation of cell complexes in arbitrary dimensions
Computer Vision and Image Understanding
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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, and 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. We show that the new method produces valid homology generators and present some experimental results.