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Detection of Circular Arcs in a Digital Image Using Chord and Sagitta Properties

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Book cover Graphics Recognition. Achievements, Challenges, and Evolution (GREC 2009)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 6020))

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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.

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References

  1. Bhowmick, P., Bhattacharya, B.B.: Fast polygonal approximation of digital curves using relaxed straightness properties. IEEE Trans. PAMI 29(9), 1590–1602 (2007)

    Google Scholar 

  2. Chen, T.C., Chung, K.L.: An efficient randomized algorithm for detecting circles. Computer Vision and Image Understanding 83(2), 172–191 (2001)

    Article  MATH  Google Scholar 

  3. Chiu, S.H., Liaw, J.J.: An effective voting method for circle detection. Pattern Recognition Letters 26(2), 121–133 (2005)

    Article  Google Scholar 

  4. Coeurjolly, D., et al.: An elementary algorithm for digital arc segmentation. Discrete Applied Mathematics 139, 31–50 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  5. Davies, E.R.: A modified Hough scheme for general circle location. PR 7(1), 37–43 (1984)

    Google Scholar 

  6. Gonzalez, R.C., Woods, R.E.: Digital Image Processing. Addison-Wesley, Reading (1993)

    Google Scholar 

  7. Ho, C.T., Chen, L.H.: A fast ellipse/circle detector using geometric symmetry. Pattern Recognition 28(1), 117–124 (1995)

    Article  Google Scholar 

  8. Illingworth, J., Kittler, J.: A survey of the Hough transform. CVGIP 44(1) (1988)

    Google Scholar 

  9. Kim, H.S., Kim, J.H.: A two-step circle detection algorithm from the intersecting chords. Pattern Recognition Letters 22, 787–798 (2001)

    Article  MATH  Google Scholar 

  10. Kimme, C., Ballard, D., Sklansky, J.: Finding circles by an array of accumulators. ACM Commun. 18(2), 120–122 (1975)

    Article  MATH  Google Scholar 

  11. Klette, R., Rosenfeld, A.: Digital Geometry: Geometric Methods for Digital Picture Analysis. Morgan Kaufmann, San Francisco (2004)

    MATH  Google Scholar 

  12. Klette, R., Rosenfeld, A.: Digital straightness: A review. Discrete Applied Mathematics 139(1-3), 197–230 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  13. Leavers, V.: Survey: Which Hough transform? 58(2), 250–264 (September 1993)

    Google Scholar 

  14. Rosin, P.L.: Techniques for assessing polygonal approximation of curves. IEEE Trans. PAMI 19(6), 659–666 (1997)

    Google Scholar 

  15. Wall, K., Danielsson, P.-E.: A fast sequential method for polygonal approximation of digitized curves. CVGIP 28, 220–227 (1984)

    Google Scholar 

  16. Weisstein, E.W.: Sagitta. From MathWorld—A Wolfram web resource (1993), http://mathworld.wolfram.com/Sagitta.html

  17. Xu, L., Oja, E.: Randomized Hough transform (RHT): Basic mechanisms, algorithms, and computational complexities. CVGIP 57(2), 131–154 (1993)

    Article  Google Scholar 

  18. 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)

    Article  Google Scholar 

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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

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  • 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)

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