Publication 2004 Issue No. 7 - July Abstract - A New Convexity Measure for Polygons
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A New Convexity Measure for Polygons
July 2004 (vol. 26 no. 7)
pp. 923-934
 ASCII Text x Jovisa Zunic, Paul L. Rosin, "A New Convexity Measure for Polygons," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 26, no. 7, pp. 923-934, July, 2004.
 BibTex x @article{ 10.1109/TPAMI.2004.19,author = {Jovisa Zunic and Paul L. Rosin},title = {A New Convexity Measure for Polygons},journal ={IEEE Transactions on Pattern Analysis and Machine Intelligence},volume = {26},number = {7},issn = {0162-8828},year = {2004},pages = {923-934},doi = {http://doi.ieeecomputersociety.org/10.1109/TPAMI.2004.19},publisher = {IEEE Computer Society},address = {Los Alamitos, CA, USA},}
 RefWorks Procite/RefMan/Endnote x TY - JOURJO - IEEE Transactions on Pattern Analysis and Machine IntelligenceTI - A New Convexity Measure for PolygonsIS - 7SN - 0162-8828SP923EP934EPD - 923-934A1 - Jovisa Zunic, A1 - Paul L. Rosin, PY - 2004KW - ShapeKW - polygonsKW - convexityKW - measurement.VL - 26JA - IEEE Transactions on Pattern Analysis and Machine IntelligenceER -

Abstract—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.

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Index Terms:
Shape, polygons, convexity, measurement.
Citation:
Jovisa Zunic, Paul L. Rosin, "A New Convexity Measure for Polygons," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 26, no. 7, pp. 923-934, July 2004, doi:10.1109/TPAMI.2004.19