An improved riemannian metric approximation for graph cuts

Authors:
Ondřej Daněk;Pavel Matula
Affiliations:
Centre for Biomedical Image Analysis, Faculty of Informatics, Masaryk University, Brno, Czech Republic;Centre for Biomedical Image Analysis, Faculty of Informatics, Masaryk University, Brno, Czech Republic
Venue:
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
Year:
2011

Citing 12
Cited 0

Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations

Journal of Computational Physics
Geodesic active contours

ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
Geometric transforms for fast geometric algorithms

Geometric transforms for fast geometric algorithms
Computing Geodesics and Minimal Surfaces via Graph Cuts

ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
What Energy Functions Can Be Minimizedvia Graph Cuts?

IEEE Transactions on Pattern Analysis and Machine Intelligence
An Experimental Comparison of Min-Cut/Max-Flow Algorithms for Energy Minimization in Vision

IEEE Transactions on Pattern Analysis and Machine Intelligence
Multi-View Stereo via Volumetric Graph-Cuts

CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 2 - Volume 02
What Metrics Can Be Approximated by Geo-Cuts, Or Global Optimization of Length/Area and Flux

ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1 - Volume 01
Globally Minimal Surfaces by Continuous Maximal Flows

IEEE Transactions on Pattern Analysis and Machine Intelligence
Graph Cuts and Efficient N-D Image Segmentation

International Journal of Computer Vision
Maximum flows and minimum cuts in the plane

Journal of Global Optimization
Active contours without edges

IEEE Transactions on Image Processing

Quantified Score

Hi-index	0.00

Visualization

Abstract

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 [3]. In [9] 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.