Abstract
The circle is a useful morphological structure: in many situations, the importance is focused on the measuring of the similarity of a perfect circle against the object of interest. Traditionally, the well-known geometrical structures are employed as useful geometrical descriptors, but an adequate characterization and recognition are deeply affected by scenarios and physical limitations (such as resolution and noise acquisition, among others). Hence, this work proposes a new circularity measure which offers several advantages: it is not affected by the overlapping, incompleteness of borders, invariance of the resolution, or accuracy of the border detection. The propounded approach deals with the problem as a stochastic non-parametric task; the maximization of the likelihood of the evidence is used to discover the true border of the data that represent the circle. In order to validate the effectiveness of our proposal, we compared it with two recently effective measures: the mean roundness and the radius ratio.
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References
Bottema, M.J.: Circularity of objects in images. In: International Conference on Acoustic, Speech and Signal Processing. ICASSP, Istanbul, vol. 4, pp. 2247–2250 (2000)
Coeurjolly, D., Gérard, Y., Reveilles, J.P., Tougne, L.: An elementary algorithm for digital arc segmentation. Discrete Applied Mathematics 139(1-3), 31–50 (2004)
Cox, E.P.: A method of assigning numerical and percentage values to the degree of roundness of sand grains. Journal of Paleontology 1(3), 179–183 (1927)
Chapman, S.B., Rowe, R.C., Newton, J.M.: Characterization of the sphericity of particles by the one plane critical stability. Journal of Pharmacy and Pharmacology 40(7), 503–505 (1988)
Damaschke, P.: The linear time recognition of digital arcs. Pattern Recognition Letters 16(5), 543–548 (1995)
Dasgupta, A., Lahiri, P.: Digital indicators for red cell disorder. Current Science 78(10), 1250–1255 (2000)
Davies, E.R.: A modified Hough scheme for general circle location. Pattern Recognition Letters 7(1), 37–43 (1987)
Di Ruperto, C., Dempster, A.: Circularity measures based on mathematical morphology. Electronics Letters 36(20), 1691–1693 (2000)
Duda, R.O., Hart, P.E.: Use of the Hough transformation to detect lines and curves in pictures. Communications of the Association of Computing Machinery 15, 587–598 (1972)
Fisk, S.: Separating point sets by circles, and the recognition of digital disks. IEEE Transactions on Pattern Analysis and Machine Intelligence 8(4), 554–556 (1986)
Frosio, I., Borghese, N.A.: Real time accurate vectorization circle fitting with occlusions. Pattern Recognition 41, 890–904 (2008)
Grimmett, G.R., Stirzaker, D.R.: Probability and Random Processes, vol. 2. Clarendon Press (1992)
Haralick, R.M.: A measure for circularity of digital figures. IEEE Transactions on Systems, Man and Cybernetics 4(4), 394–396 (1974)
Hilaire, X., Tombre, K.: Robust and accurate vectorization of line drawings. IEEE Transactions on Pattern Analysis and Machine Intelligence 28(6), 217–223 (2006)
Kim, C.E., Anderson, T.A.: Digital disks and a digital compactness measure. In: Annual ACM Symposium on Theory of Computing, Proceedings of the Sixteenth Annual ACM Symposium on Theory of Computing, New York, USA, pp. 117–124 (1984)
Li, J., Lu, L., Lai, M.O.: Quantitative analysis of the irregularity of graphite nodules in cast iron. Materials Characterization 45, 83–88 (2000)
Lilliefors, H.: On the Kolmogorow-Smirnow test for normality with mean and variance unkown. Journal of the American Statistical Association 62, 399–402 (1967)
O’ Rourke, J., Kosaraju, S.R., Meggido, N.: Computing circular separability. Discrete and Computational Geometry 1, 105–113 (1986)
Peura, M., Livarinen, J.: Efficiency of simple shape descriptors. In: 3rd International Workshop on Visual Form, Capri, Italy, pp. 28–30 (1997)
Pegna, J., Guo, C.: Computational metrology of the circle. In: Proceedings of IEEE Computer Graphics International, pp. 350–363 (1998)
Ritter, N., Cooper, J.R.: New resolution independent measures of circularity. Journal of Mathematical Imaging and Visio 35(2), 117–127 (2009)
Rosin, P.L.: Measuring shape: ellipticity, rectangularity, and triangularity. Machine Vision and Applications 14(3), 172–184 (2003)
Sauer, P.: On the recognition of digital circles in linear time. Computational Geometry: Theory and Application 2(5), 287–302 (1993)
Whalley, W.B.: The description and measurement of sedimentary particles and the concept of form. Journal of Sedimentary Petrology 42(4), 961–965 (1972)
Worring, M., Smeulders, A.W.: Digitized circular arcs: characterization and parameter estimation. IEEE Transactions on Pattern Analysis and Machine Intelligence 17(6), 554–556 (1995)
Yip, R.K.K., Tam, P.K.S., Leung, D.N.K.: Modification of Hough transform for circles and ellipses detection using a 2-dimensional array. Pattern Recognition 25(9), 1007–1022 (1992)
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Herrera-Navarro, A.M., Jiménez-Hernández, H., Terol-Villalobos, I.R. (2012). A Probabilistic Measure of Circularity. In: Barneva, R.P., Brimkov, V.E., Aggarwal, J.K. (eds) Combinatorial Image Analaysis. IWCIA 2012. Lecture Notes in Computer Science, vol 7655. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34732-0_6
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DOI: https://doi.org/10.1007/978-3-642-34732-0_6
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