A New Measure of Circularity Based on Distribution of the Radius

Una nueva medida de circularidad basada en la distribución de radios

Ana M. Herrera-Navarro¹, Hugo Jiménez Hernández², Hayde Peregrina-Barreto¹, Federico Manríquez- Guerrero³, Iván R. Terol-Villalobos³

¹ Facultad de Ingeniería, Universidad Autónoma de Querétaro, Querétaro, México. anaherreranavarro@gmail.com, hperegrina@ieee.org

³ Centro de Investigación y Desarrollo Tecnológico en Electroquímica, Querétaro, México. fmanriquez@cideteq.mx, famter@ciateq.mx

Article received on 02/02/2012
Accepted on 23/01/2013.

Abstract

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.

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

Las medidas de circularidad más utilizadas en la literatura actual para calcular la redondez de objetos digitales son derivaciones del factor de forma, que se basa en el área y perímetro. Sin embargo, estas medidas son altamente dependientes de la resolución de la imagen y sensibles a variaciones de forma. En este artículo se propone una nueva medida de circularidad que considera la geometría dominante de los objetos, evitando el uso de parámetros como área, perímetro y diámetro de Ferret. La medida propuesta tiene una complejidad computacional baja, y debido a que es basada en la distribución de probabilidad de los radios, no es afectada por cambios bruscos en los contornos o forma de resolución. Para mostrar el comportamiento de la medida, esta es comparada con otras tres medidas recientemente propuestas: factor de forma, la cual es recomendada por la medición de estándar americano de pruebas y materiales, redondez media y la relación de radio.

Palabras clave: Medida, forma, circularidad, función de densidad de probabilidad, centro, radio, media, moda.

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Acknowledgments

We would like to thank the anonymous reviewers for their valuable comments. The author Ana Marcela Herrera-Navarro thanks the government agency CONACyT (133697).

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