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A new convexity measure for polygons.
1Department of Computer Science, Exeter University, UK. J.Zunic@ex.ac.uk
Summary
This study introduces a new boundary-based convexity measure for polygons. It is more sensitive to boundary defects and advantageous for shapes with holes compared to existing methods.
Area of Science:
- Computational geometry
- Image analysis
- Shape analysis
Background:
- Convexity estimators are crucial for shape analysis.
- Existing area-based measures have limitations in detecting boundary defects.
Purpose of the Study:
- To define and evaluate a novel boundary-based convexity measure for planar polygonal regions.
- To address limitations of existing area-based convexity measures.
Main Methods:
- Development of a new "boundary-based" convexity measure.
- Comparison with traditional "area-based" measures and convex hull ratio methods.
Main Results:
- The new measure is more sensitive to boundary defects.
- It offers advantages for shapes with holes.
- The measure yields values in (0, 1], with 1 indicating convexity.
Conclusions:
- The proposed convexity measure is robust and efficient.
- It offers desirable properties including invariance under similarity transformations.
- A fast computation procedure is available.
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