Authors: Žunić, Joviša 
Rosin, Paul
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: A new convexity measure for polygons
Journal: IEEE Transactions on Pattern Analysis and Machine Intelligence
Volume: 26
Issue: 7
First page: 923
Last page: 934
Issue Date: 1-Jan-2004
Rank: M21a
ISSN: 0162-8828
DOI: 10.1109/TPAMI.2004.19
Convexity estimators are commonly used in the analysis of shape. In this paper, we define and evaluate a new convexity measure for planar regions bounded by polygons. The new convexity measure can be understood as a "boundary-based" measure and in accordance with this it is more sensitive to measured boundary defects than the so called "area-based" convexity measures. When compared with the convexity measure defined as the ratio between the Euclidean perimeter of the convex hull of the measured shape and the Euclidean perimeter of the measured shape then the new convexity measure also shows some advantages - particularly for shapes with holes. The new convexity measure has the following desirable properties: 1) the estimated convexity is always a number from (0,1], 2) the estimated convexity is 1 if and only if the measured shape is convex, 3) there are shapes whose estimated convexity is arbitrarily close to 0, 4) the new convexity measure is invariant under similarity transformations, and 5) there is a simple and fast procedure for computing the new convexity measure.
Keywords: Convexity | Measurement | Polygons | Shape
Publisher: IEEE

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