Computing Homology Group Generators of Images Using Irregular Graph Pyramids

Abstract : 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.
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Graph-Based Representations in Pattern Recognition, Jun 2007, Alicante, Spain. Springer Berlin / Heidelberg, Lecture Notes in Computer Science, 4538, pp.283-294, 2007, Graph-Based Representations in Pattern Recognition. 〈10.1007/978-3-540-72903-7_26〉
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Samuel Peltier, Adrian Ion, Yll Haxhimusa, Walter Kropatsch, Guillaume Damiand. Computing Homology Group Generators of Images Using Irregular Graph Pyramids. Graph-Based Representations in Pattern Recognition, Jun 2007, Alicante, Spain. Springer Berlin / Heidelberg, Lecture Notes in Computer Science, 4538, pp.283-294, 2007, Graph-Based Representations in Pattern Recognition. 〈10.1007/978-3-540-72903-7_26〉. 〈hal-00348864〉

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