Abstract
This paper presents a new technique for detection of digital circles and circular arcs using chord property and sagitta property. It is shown how a variant of the chord property of an Euclidean circle can be used to detect a digital circle or a circular arc. Based on this property, digital circular arcs are first extracted and then using the sagitta property, their centers and radii are computed. Several arcs are merged together to form a complete digital circle or a larger arc. Finally, a technique based on Hough transform is used to improve the accuracy of computing the centers and radii. Experimental results have been furnished to demonstrate the efficiency of the proposed method.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bhowmick, P., Bhattacharya, B.B.: Fast polygonal approximation of digital curves using relaxed straightness properties. IEEE Trans. PAMI 29(9), 1590–1602 (2007)
Chen, T.C., Chung, K.L.: An efficient randomized algorithm for detecting circles. Computer Vision and Image Understanding 83(2), 172–191 (2001)
Chiu, S.H., Liaw, J.J.: An effective voting method for circle detection. Pattern Recognition Letters 26(2), 121–133 (2005)
Coeurjolly, D., et al.: An elementary algorithm for digital arc segmentation. Discrete Applied Mathematics 139, 31–50 (2004)
Davies, E.R.: A modified Hough scheme for general circle location. PR 7(1), 37–43 (1984)
Gonzalez, R.C., Woods, R.E.: Digital Image Processing. Addison-Wesley, Reading (1993)
Ho, C.T., Chen, L.H.: A fast ellipse/circle detector using geometric symmetry. Pattern Recognition 28(1), 117–124 (1995)
Illingworth, J., Kittler, J.: A survey of the Hough transform. CVGIP 44(1) (1988)
Kim, H.S., Kim, J.H.: A two-step circle detection algorithm from the intersecting chords. Pattern Recognition Letters 22, 787–798 (2001)
Kimme, C., Ballard, D., Sklansky, J.: Finding circles by an array of accumulators. ACM Commun. 18(2), 120–122 (1975)
Klette, R., Rosenfeld, A.: Digital Geometry: Geometric Methods for Digital Picture Analysis. Morgan Kaufmann, San Francisco (2004)
Klette, R., Rosenfeld, A.: Digital straightness: A review. Discrete Applied Mathematics 139(1-3), 197–230 (2004)
Leavers, V.: Survey: Which Hough transform? 58(2), 250–264 (September 1993)
Rosin, P.L.: Techniques for assessing polygonal approximation of curves. IEEE Trans. PAMI 19(6), 659–666 (1997)
Wall, K., Danielsson, P.-E.: A fast sequential method for polygonal approximation of digitized curves. CVGIP 28, 220–227 (1984)
Weisstein, E.W.: Sagitta. From MathWorld—A Wolfram web resource (1993), http://mathworld.wolfram.com/Sagitta.html
Xu, L., Oja, E.: Randomized Hough transform (RHT): Basic mechanisms, algorithms, and computational complexities. CVGIP 57(2), 131–154 (1993)
Yip, R., Tam, P., Leung, D.: Modification of Hough transform for circles and ellipses detection using a 2-dimensional array. Pattern Recognition 25(9), 1007–1022 (1992)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bera, S., Bhowmick, P., Bhattacharya, B.B. (2010). Detection of Circular Arcs in a Digital Image Using Chord and Sagitta Properties. In: Ogier, JM., Liu, W., Lladós, J. (eds) Graphics Recognition. Achievements, Challenges, and Evolution. GREC 2009. Lecture Notes in Computer Science, vol 6020. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13728-0_7
Download citation
DOI: https://doi.org/10.1007/978-3-642-13728-0_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-13727-3
Online ISBN: 978-3-642-13728-0
eBook Packages: Computer ScienceComputer Science (R0)