Computing geodesics and minimal surfaces via graph cuts

Computing geodesics and minimal surfaces via graph cuts (2003)

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by Yuri Boykov

Venue:	in International Conference on Computer Vision
Citations:	123 - 14 self

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Datum	Value	Source
TITLE	Computing geodesics and minimal surfaces via graph cuts	INFERENCE
AUTHOR NAME	Yuri Boykov	SVM HeaderParse 0.2
AUTHOR AFFIL	Imaging & Visualization; Siemens Corp. Research	SVM HeaderParse 0.2
AUTHOR ADDR	Princeton, NJ 08540	SVM HeaderParse 0.2
ABSTRACT	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. 1.	SVM HeaderParse 0.2
YEAR	2003	INFERENCE
VENUE	in International Conference on Computer Vision	INFERENCE
VENUE TYPE	CONFERENCE	INFERENCE
PAGES	26--33	INFERENCE
VOLUME	1	INFERENCE
CITATIONS	29 found	ParsCit 1.0