A New Measure of Circularity Based on Distribution of the Radius

Ana M. Herrera-Navarro, Hugo Jiménez Hernández, Hayde Peregrina-Barreto, Federico Manríquez- Guerrero, Iván R. Terol-Villalobos


The measures most commonly used in current literature to compute the roundness of digital objects are derivations of the form factor based on area and perimeter computations. However, these measures are highly dependent on image resolution and sensitive to shape variations. In this article, a new measure is proposed. This measure takes into consideration the dominant geometry of objects, avoiding the use of such parameters as area, perimeter and Ferret's diameter. The proposed measure is easy to compute, and since it is a distribution of probability based on the radius, it is invariant to abrupt changes in contours or to shape resolution. In order to show the performance of this measure, it is compared with three other recently proposed measures: factor shape, which is recommended by the American Standard Test Measurement, mean roundness and radius ratio.


Measure, shape, circularity, probability density function, center, radius, medium, mode.

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