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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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