Decomposition for efficient eccentricity transform of convex shapes

Authors:
Adrian Ion;Samuel Peltier;Yll Haxhimusa;Walter G. Kropatsch
Affiliations:
Pattern Recognition and Image Processing Group, Faculty of Informatics, Vienna University of Technology, Austria;Pattern Recognition and Image Processing Group, Faculty of Informatics, Vienna University of Technology, Austria;Pattern Recognition and Image Processing Group, Faculty of Informatics, Vienna University of Technology, Austria, Department of Psychological Sciences, Purdue University;Pattern Recognition and Image Processing Group, Faculty of Informatics, Vienna University of Technology, Austria
Venue:
CAIP'07 Proceedings of the 12th international conference on Computer analysis of images and patterns
Year:
2007

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Abstract

The eccentricity transform associates to each point of a shape the shortest distance to the point farthest away from it. It is defined in any dimension, for open and closed manyfolds. Top-down decomposition of the shape can be used to speed up the computation, with some partitions being better suited than others. We study basic convex shapes and their decomposition in the context of the continuous eccentricity transform. We show that these shapes can be decomposed for a more efficient computation. In particular, we provide a study regarding possible decompositions and their properties for the ellipse, the rectangle, and a class of elongated shapes.