Turning shape decision problems into measures

Martin, Ralph Robert and Rosin, Paul L. ORCID: https://orcid.org/0000-0002-4965-3884 2004. Turning shape decision problems into measures. International Journal of Shape Modeling 10 (01) , p. 83. 10.1142/S0218654304000614

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Abstract

This paper considers the problem of constructing shape measures; we start by giving a short overview of areas of practical application of such measures. Shapes can be characterised in terms of a set of geometric properties, some of which are Boolean in nature. We give two general principles for turning Boolean properties into continuous measures of that property. (For example, we may turn the Boolean property conves into a convexity value in the range [0–1].) We demonstrate how these principles can be applied to construct various shape measures, including ones for convexity, circularity, ellipticity, triangularity, rectilinearity, rectangularity and symmetry in two dimensions, and 2.5D-ness, stability, and imperforateness in three dimensions. Some of these measures are new; others are well known and we show how they fit into this general framework. We also show how such measures for a single shape can be generalised to multiple shapes, and consider as examples measures for containment, resemblance, congruence, and similarity.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Computer Science & Informatics
Subjects:	Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Uncontrolled Keywords:	Shape measures; shape properties; convexity; circularity; ellipticity; triangularity; rectilinearity; rectangularity; symmetry; containment; resemblance; congruence; similarity; 2.5D; stability; genus; hole
Publisher:	WorldSciNet
ISSN:	0218-6543
Last Modified:	24 Oct 2022 10:06
URI:	https://orca.cardiff.ac.uk/id/eprint/43149

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