UCL logo

UCL Discovery

UCL home » Library Services » Electronic resources » UCL Discovery

Computing geodesics and minimal surfaces via graph cuts

Boykov, Y; Kolmogorov, V; (2003) Computing geodesics and minimal surfaces via graph cuts. In: NINTH IEEE INTERNATIONAL CONFERENCE ON COMPUTER VISION, VOLS I AND II, PROCEEDINGS. (pp. 26 - 33). IEEE COMPUTER SOC

Full text not available from this repository.


Geodesic active contours and graph cuts are two standard image segmentation techniques. We introduce a new segmentation method combining some of their benefits. Our main intuition is that any cut on a graph embedded in some continuous space can be interpreted as a contour (in 2D) or a surface (in 3D). We show how to build a grid graph and set its edge weights so that the cost of cuts is arbitrarily close to the length (area) of the corresponding contours (surfaces)for any anisotropic Riemannian metric.There are two interesting consequences of this technical result. First, graph cut algorithms can be used to find globally minimum geodesic contours (minimal surfaces in 3D) under arbitrary Riemannian metric for a given set of boundary conditions. Second, we show how to minimize metrication artifacts in existing graph-cut based methods in vision. Theoretically speaking, our work provides an interesting link between several branches of mathematics differential geometry, integral geometry, and combinatorial optimization. The main technical problem is solved using Cauchy-Crofton formula from integral geometry.

Type: Proceedings paper
Title: Computing geodesics and minimal surfaces via graph cuts
Event: 9th IEEE International Conference on Computer Vision
Location: NICE, FRANCE
Dates: 2003-10-13 - 2003-10-16
ISBN: 0-7695-1950-4
URI: http://discovery.ucl.ac.uk/id/eprint/123708
Downloads since deposit
Download activity - last month
Download activity - last 12 months
Downloads by country - last 12 months

Archive Staff Only

View Item View Item