Abstract
In this paper, we draw on Spielman and Srivastava’s method for graph sparsification in order to simplify shape representations. The underlying principle of graph sparsification is to retain only the edges which are key to the preservation of desired properties. In this regard, sparsification by edge resistance allows us to preserve (to some extent) links between protrusions and the remainder of the shape (e.g. parts of a shape) while removing in-part edges. Applying this idea to alpha shapes (abstract representations which have a huge number of edges) opens up a way of introducing a hierarchy of the edge strength, thus being relevant for shape analysis and interpretation.
Notes
- 1.
In this paper, the parameter \(\epsilon \) controls the number of samples needed by the process, whereas the weight for choosing the edges is given by effective resistances.
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Acknowledgments
F. Escolano and M. Curado are funded by Project TIN2015-69077-P of the Spanish Government.
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Escolano, F., Curado, M., Biasotti, S., Hancock, E.R. (2017). Shape Simplification Through Graph Sparsification. In: Foggia, P., Liu, CL., Vento, M. (eds) Graph-Based Representations in Pattern Recognition. GbRPR 2017. Lecture Notes in Computer Science(), vol 10310. Springer, Cham. https://doi.org/10.1007/978-3-319-58961-9_2
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