Faster graph-theoretic image processing via small-world and quadtree topologies

Authors:
Leo Grady;Eric L. Schwartz
Affiliations:
Imaging and Visualization Department of Siemens Corporate Research, Princeton, NJ;Departments of Cognitive and Neural Systems and Electrical and Computer Engineering, Boston University, Boston, MA
Venue:
CVPR'04 Proceedings of the 2004 IEEE computer society conference on Computer vision and pattern recognition
Year:
2004

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Abstract

Numerical methods associated with graph-theoretic image processing algorithms often reduce to the solution of a large linear system. We show here that choosing a topology that yields a small graph diameter can greatly speed up the numerical solution. As a proof of concept, we examine two image graphs that preserve local connectivity of the nodes (pixels} while drastically reducing the graph diameter. The first is based on a "small-world" modification of a standard 4-connected lattice. The second is based on a quadtree graph. Using a recently described graph-theoretic image processing algorithm we show that large speed-up is achieved with a minimal Perturbation of the solution when these graph topologies are utilized. We suggest that a variety of similar algorithms may also benefit from this approach.