Masaryk University, Czech Republic
Graph cuts, Euclidean metric approximation, Anisotropic grids, Voronoi diagrams, Image segmentation.
Computer Vision, Visualization and Computer Graphics
Early Vision and Image Representation
Image and Video Analysis
Image Formation and Preprocessing
Segmentation and Grouping
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 imag