Abstract
We consider an optimization version of the image segmentation problem, in which we are given a grid graph with weights on the grid cells. We are interested in finding the maximum weight subgraph such that the subgraph can be decomposed into two ”star-shaped” images. We show that this problem can be reduced to the problem of finding a maximum-weight closed set in an appropriately defined directed graph which is well known to have efficient algorithms which run very fast in practice. We also show that finding a maximum-weight subgraph that is decomposable into m star-shaped objects is NP-hard for some m > 2.
This material is based upon work supported by the National Science Foundation under Grant No. CCF-0830402 and Grant No. CCF-0844765 as well as by the National Institute of Health under Grant No. R01-EB004640.
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Gibson, M., Han, D., Sonka, M., Wu, X. (2011). Maximum Weight Digital Regions Decomposable into Digital Star-Shaped Regions. In: Asano, T., Nakano, Si., Okamoto, Y., Watanabe, O. (eds) Algorithms and Computation. ISAAC 2011. Lecture Notes in Computer Science, vol 7074. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25591-5_74
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DOI: https://doi.org/10.1007/978-3-642-25591-5_74
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