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.
Supported by the Austrian Science Fund under grants P18716-N13 and S9103-N04.
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Peltier, S., Ion, A., Haxhimusa, Y., Kropatsch, W.G., Damiand, G. (2007). Computing Homology Group Generators of Images Using Irregular Graph Pyramids. In: Escolano, F., Vento, M. (eds) Graph-Based Representations in Pattern Recognition. GbRPR 2007. Lecture Notes in Computer Science, vol 4538. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72903-7_26
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DOI: https://doi.org/10.1007/978-3-540-72903-7_26
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