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Projection-based polygonality measurement.

Thanh Phuong Nguyen, Thai V Hoang

    IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
    |November 22, 2014
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    Summary
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    This study introduces a novel method to measure how closely shapes resemble polygons, offering robust and invariant measurements. This approach enhances shape analysis and approximation for various applications.

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    Area of Science:

    • Computer Vision
    • Image Analysis
    • Computational Geometry

    Background:

    • Quantifying shape resemblance to polygons (polygonality) is challenging due to shape variations from digitization and transformations.
    • Existing measures for polygonality often lack generality or robustness against noise and distortions.

    Purpose of the Study:

    • To propose a generic and robust framework for measuring polygonality.
    • To develop measures invariant to similarity transformations and robust to noise and boundary distortions.
    • To enable approximation of shapes by analytical polygons using measurements in projection space.

    Main Methods:

    • A novel approach measuring polygonality in the projection space using Radon images of shape primitives.
    • Development of measures ranging from (0, 1], with 1 indicating analytical polygons.
    • Demonstration of invariance to similarity transformations and robustness to noise and boundary distortion.

    Main Results:

    • The proposed method provides a generalized measure of polygonality, encompassing existing metrics like triangularity and quadrangularity.
    • Measures are robust to noise and boundary distortions, and invariant to similarity transformations.
    • The framework facilitates the approximation of complex shapes using analytical polygons.

    Conclusions:

    • The developed projection space approach offers a versatile and effective method for quantifying polygonality.
    • This framework advances shape analysis by providing robust, invariant measures and enabling shape approximation.
    • Experimental validation on synthetic and real data confirms the efficiency and applicability of the proposed method.