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Computación y Sistemas

Print version ISSN 1405-5546

Comp. y Sist. vol.17 n.4 México Oct./Dec. 2013

 

Artículos regulares

 

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

2 Centro de Ingeniería y Desarrollo Industrial, Querétaro, México. hugo.jimenez@cidesi.mx

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.

 

Resumen

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).

 

References

1. Ahn, S.J., Rauh, W. & Warnecke H.J. (2001). Least-squares orthogonal distances fitting of circle, sphere, ellipse, hyperbola, and parabola. Pattern Recognition, 34(12), 2283-2303.         [ Links ]

2. Almeida-Prieto, S., Blanco-Méndez, J. & Otero-Espinar, F. (2004). Image analysis of the shape of granulated powder grains. Journal of Pharmaceutical Sciences, 93(3), 621-634.         [ Links ]

3. Historical Standard: ASTM A247-67(1998) Standard Test Method for Evaluating the Microstructure of Graphite in Iron Castings.         [ Links ]

4. Artacho-Pérula, E., Roldán-Villalobos, R., Martínez-Cuevas J.F., & López-Rubio, F. (1994). Nuclear quantitative grading by discriminant analysis of renal cell carcinoma samples: a patient survival evaluation. The Journal of Pathology, 173(2), 105-114.         [ Links ]

5. Bose, P. & Morin, P. (2003). Testing the quality of manufactured disks and balls. Algorithmica, 38(1), 161 -177.         [ Links ]

6. Bottema, M.J. (2000). Circularity of objects in images. 2000 IEEE InternationalConference on Acoustics, Speech and Signal Processing (ICASSP'QQ). Istanbul, Turquia, 4, 2247-2250.         [ Links ]

7. Bouwman, A.M., Bosma, J.C, Vonk, P., Wesselingh, J.A. & Frijlink, H.W. (2004). Which shape factor (s) best describes granules? Powder Technology, 146(1-2), 66-72.         [ Links ]

8. Cenens, C., Jenne R. & Van. I.J. (2002). Evaluation of different shape parameters to distinguish between flocs and filaments in activated sludge images. Water Science Technology, 45(4-5), 85-91.         [ Links ]

9. Chaudhuri, D. (2010). A simple least squares method for fitting of ellipses and circles depends on border points of a two-tone image and their 3-D extensions. Pattern Recognition Letters, 31(9), 818-829.         [ Links ]

10. Chatzis, V., Kaburlasos, V.G., & Theodorides, M. (2005). An image processing method for particle size and shape estimation. 2nd International Scientific Conference on Computer Science, Chalkidiki, Greece, 7-12.         [ Links ]

11. Chen, M.C. (2002). Roundness measurements for discontinuous perimeters via machine visions. Computers in Industry, 47(2002), 185-197.         [ Links ]

12. Dasgupta, A. & Lahiri, P. (2000). Digital indicators for red cell disorder. Current Science, 78(10), 1250-1255.         [ Links ]

13. De Santis, A., Di Bartolomeo, O., lacoviello, D., & lacoviello, F. (2008). Quantitative shape evaluation of graphite particles in ductile iron. Journal of Materials Processing Technology, 196(1-3), 292-302.         [ Links ]

14. Di Ruperto, C. & Dempster, A. (2000). Circularity measures based on mathematical morphology. Electronics Letters, 36(20), 1691-1693.         [ Links ]

15. Foresto, P., D'Arrigo, M., Carreras, L., Cuezzo, R.E., Valverde, J. & Rasia, R. (2000). Evaluation of red blood cell aggregation in diabetes by computerized image analysis. Medicina (B. Aires), 60(5 pt. 1), 570-572.         [ Links ]

16. Frosio, I. & Borghese, N.A. (2008). Real time accurate circle fitting with occlusions. Pattern Recognition, 41(3), 1041 -1055.         [ Links ]

17. Giger, M.L., Doi, K., & MacMahon, H. (1988). Image feature analysis and computer-aided diagnosis in digital radiography, automated detection of nodules in peripheral lung fields. Medical Physics, 15(2), 158-166.         [ Links ]

18. Gordon, A., Colman-Lerner, A., Chin, T.E., Benjamin, K.R., Yu, R.C., & Brent, R. (2007). Single-cell quantification of molecules and rates using open-source microscope-based cytometry. Nature Methods, 4(2), 175-181.         [ Links ]

19. Hawkins, A.E. (1993). The shape of powder-particle outlines. Taunton: Research Studies Press.         [ Links ]

20. Hetzner, D.W. (2008). Comparing binary image analysis measurements-euclidean geometry, centroids and corners. Microscopy Today, 16(4), 10-15.         [ Links ]

21. Hilaire, X. & Tombre, K. (2006). Robust and accurate vectorization of line drawings. IEEE Transactions on Pattern Analysis and Machine Intelligence, 28(6), 890-904.         [ Links ]

22. Kovalevsky, V.A. (1990). New definition and fast recognition of digital straight segments and arcs. 10th International Conference on Pattern Recognition, Atlantic City, NJ, 2, 31-34.         [ Links ]

23. Li, J., Lu, L., & Lai, M.O. (2000). Quantitative analysis of the irregularity of graphite nodules in cast iron. Materials Characterization, 45(2), 83-88.         [ Links ]

24. Liew, L.H., Lee, B.Y. & Chan, M. (2010). Cell detection for bee comb images using circular Hough transformation. 2010 International Conference on Science and Social Research (CSSR), 191-195.         [ Links ]

25. Mohler, J.L., Partin, A.W., Epstein, J.I., Lohr, W.D., & Coffey, D.S. (2008). Nuclear roundness factor measurement for assessment of prognosis of patients with prostatic carcinoma. Standardization of methodology for histologic sections. The Journal of Urology, 139(5), 1085-1090.         [ Links ]

26. Montero, R.S. (2009). State of the Art of Compactness and Circularity Measures. International Mathematical Forum, 4(27), 1305-1335.         [ Links ]

27. Morales-Hernández, L.A., Terol-Villalobos, I.R., Domínguez-González, A., Manriquez-Guerrero, F., & Herrera-Ruíz, G. (2010). Spatial distribution and spheroidicity characterization of graphite nodules based on morphological tools. Journal of Materials Processing Technology, 210(2), 335-342.         [ Links ]

28. Peura, M. & livarinen, J. (1997). Efficiency of simple shape descriptors. 3rd International Workshop on Visual Form, Capri, Italy.         [ Links ]

29. Pegna, J. & Guo, C. (1998). Computational metrology of the circle. Proceedings of Computer Graphics International, Hannover, Germany, 350-363.         [ Links ]

30. Ritter, N. & Cooper, J. (2009). New resolution independent measures of circularity. Journal of Mathematical Imaging and Vision, 35(2), 117-127.         [ Links ]

31. Roussillon, T., Sivignon, I., & Tougne, L. (2010). Measure of circularity for parts of digital boundaries and its fast computation. Pattern Recognition, 43(1), 37-46.         [ Links ]

32. Sauer, P. (1993). On the recognition of digital circles in linear time. Computational Geometry, 2(5), 287-302.         [ Links ]

33. Swanson, K., Lee, D.T., & Wu, V.L. (1995). An optimal algorithm for roundness determination in convex polygons. Computational Geometry, 5(4), 225-235.         [ Links ]

34. Nguyen, T.P. & Debled-Rennesson, I. (2010). Circularity Measure in Linear Time. 20th International Conference on Pattern Recognition (ICPR 2010), Istanbul, Turkey, 2098-2101.         [ Links ]

35. Yip, R.K.K., Tam, P.K.S., & Leung, D.N.K. (1992). Modification of Hough transform for circles and ellipses detection using a 2-dimensional array. Pattern Recognition, 25(9), 1007-1022.         [ Links ]

36. Pan, L., Chu, W.-S., Saragih, J.M., & De la Torre, F. (1012). Fast and Robust Circular Object Detection with Probabilistic Pairwise Voting. lEEE Signal Processing Letters, 18(11), 639-642.         [ Links ]

37. Worring, M. & Smeulders, A.W.M. (1995). Digitized circular arcs: characterization and parameter estimation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 17(6). 587-598.         [ Links ]

38. Zunic, J., Hirota, K., Rosin, P.L. (2010). A Hu moment invariant as a shape circularity measure. Pattern Recognition, 43(1), 47-57.         [ Links ]

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