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GRAPH CUTS AND APPROXIMATION OF THE EUCLIDEAN METRIC ON ANISOTROPIC GRIDSTopics: Computational Geometry; Early Vision and Image Representation; Segmentation and Grouping

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Ontology
Subjects/Areas/Topics:Computational Geometry
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Computer Vision, Visualization and Computer Graphics
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Early Vision and Image Representation
;
Image and Video Analysis
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Image Formation and Preprocessing
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Segmentation and Grouping

Abstract: Graph cuts can be used to find globally minimal contours and surfaces in 2D and 3D space, respectively. To achieve this, weights of the edges in the graph are set so that the capacity of the cut approximates the contour length or surface area under chosen metric. Formulas giving good approximation in the case of the Euclidean metric are known, however, they assume isotropic resolution of the underlying grid of pixels or voxels. Anisotropy has to be simulated using more general Riemannian metrics. In this paper we show how to circumvent this and obtain a good approximation of the Euclidean metric on anisotropic grids directly by exploiting the well-known Cauchy-Crofton formulas and Voronoi diagrams theory. Furthermore, we show that our approach yields much smaller metrication errors and most interestingly, it is in particular situations better even in the isotropic case due to its invariance to mirroring. Finally, we demonstrate an application of the derived formulas to biomedical image segmentation.(More)

Graph cuts can be used to find globally minimal contours and surfaces in 2D and 3D space, respectively. To achieve this, weights of the edges in the graph are set so that the capacity of the cut approximates the contour length or surface area under chosen metric. Formulas giving good approximation in the case of the Euclidean metric are known, however, they assume isotropic resolution of the underlying grid of pixels or voxels. Anisotropy has to be simulated using more general Riemannian metrics. In this paper we show how to circumvent this and obtain a good approximation of the Euclidean metric on anisotropic grids directly by exploiting the well-known Cauchy-Crofton formulas and Voronoi diagrams theory. Furthermore, we show that our approach yields much smaller metrication errors and most interestingly, it is in particular situations better even in the isotropic case due to its invariance to mirroring. Finally, we demonstrate an application of the derived formulas to biomedical image segmentation.

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Daněk O. and Matula P. (2010). GRAPH CUTS AND APPROXIMATION OF THE EUCLIDEAN METRIC ON ANISOTROPIC GRIDS.In Proceedings of the International Conference on Computer Vision Theory and Applications - Volume 2: VISAPP, (VISIGRAPP 2010) ISBN 978-989-674-029-0, pages 68-73. DOI: 10.5220/0002833000680073

@conference{visapp10, author={Ondřej Daněk and Pavel Matula}, title={GRAPH CUTS AND APPROXIMATION OF THE EUCLIDEAN METRIC ON ANISOTROPIC GRIDS}, booktitle={Proceedings of the International Conference on Computer Vision Theory and Applications - Volume 2: VISAPP, (VISIGRAPP 2010)}, year={2010}, pages={68-73}, publisher={SciTePress}, organization={INSTICC}, doi={10.5220/0002833000680073}, isbn={978-989-674-029-0}, }

TY - CONF

JO - Proceedings of the International Conference on Computer Vision Theory and Applications - Volume 2: VISAPP, (VISIGRAPP 2010) TI - GRAPH CUTS AND APPROXIMATION OF THE EUCLIDEAN METRIC ON ANISOTROPIC GRIDS SN - 978-989-674-029-0 AU - Daněk O. AU - Matula P. PY - 2010 SP - 68 EP - 73 DO - 10.5220/0002833000680073