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@inproceedings{898468,
author = {Daněk, Ondřej and Matula, Pavel},
address = {Berlin, Heidelberg},
booktitle = {16th International Conference on Discrete Geometry for Computer Imagery},
doi = {http://dx.doi.org/10.1007/978-3-642-19867-0_6},
keywords = {graph cuts; metric approximation; Riemannian metrics; image segmentation},
howpublished = {tištěná verze "print"},
language = {eng},
location = {Berlin, Heidelberg},
isbn = {978-3-642-19866-3},
note = {LNCS 6607},
pages = {71-82},
publisher = {Springer-Verlag},
title = {An Improved Riemannian Metric Approximation for Graph Cuts},
url = {http://www.springerlink.com/content/g64286w402h4v1p6/},
year = {2011}
}
TY - JOUR
ID - 898468
AU - Daněk, Ondřej - Matula, Pavel
PY - 2011
TI - An Improved Riemannian Metric Approximation for Graph Cuts
PB - Springer-Verlag
CY - Berlin, Heidelberg
SN - 9783642198663
N1 - LNCS 6607
KW - graph cuts
KW - metric approximation
KW - Riemannian metrics
KW - image segmentation
UR - http://www.springerlink.com/content/g64286w402h4v1p6/
L2 - http://www.springerlink.com/content/g64286w402h4v1p6/
N2 - Boykov and Kolmogorov showed that it is possible to find globally minimal contours and surfaces via graph cuts by embedding an appropriate metric approximation into the graph edge weights and derived the requisite formulas for Euclidean and Riemannian metrics. In [2] we have proposed an improved Euclidean metric approximation that is invariant under (horizontal and vertical) mirroring, applicable to grids with anisotropic resolution and with a smaller approximation error. In this paper, we extend our method to general Riemannian metrics that are essential for graph cut based image segmentation or stereo matching. It is achieved by the introduction of a transformation reducing the Riemannian case to the Euclidean one and adjusting the formulas from [9] to be able to cope with non-orthogonal grids. We demonstrate that the proposed method yields smaller approximation errors than the previous approaches both in theory and practice.
ER -
DANĚK, Ondřej and Pavel MATULA. An Improved Riemannian Metric Approximation for Graph Cuts. In \textit{16th International Conference on Discrete Geometry for Computer Imagery}. Berlin, Heidelberg: Springer-Verlag, 2011, p.~71-82. ISBN~978-3-642-19866-3. Available from: https://dx.doi.org/10.1007/978-3-642-19867-0\_{}6.
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