Strongly normal sets of contractible tiles in N dimensions

Authors:
T. Yung Kong;Punam Kumar Saha;Azriel Rosenfeld
Affiliations:
Department of Computer Science, Queens College, CUNY, Flushing, NY 11367-1597, USA;Laboratory for Structural NMR Imaging, Department of Radiology, University of Pennsylvania, Philadelphia, PA 19104-6021, USA;Center for Automation Research, University of Maryland, College Park, MD 20742-3275, USA
Venue:
Pattern Recognition
Year:
2007

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Abstract

The second and third authors and others have studied collections of (usually) convex ''tiles''-a generalization of pixels or voxels-in R^2 and R^3 that have a property called strong normality (SN): for any tile P, only finitely many tiles intersect P, and any nonempty intersection of those tiles also intersects P. This paper extends basic results about strong normality to collections of contractible polyhedra in R^n whose nonempty intersections are contractible. We also give sufficient (and trivially necessary) conditions on a locally finite collection of contractible polyhedra in R^2 or R^3 for their nonempty intersections to be contractible.