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Polling an Image for Circles by Random Lines
January 2003 (vol. 25 no. 1)
pp. 125-130

Abstract—A new random sampling strategy, designed for retrieving subsets consisting of two edge pixels from an input image, is proposed as the sampling process for RANSAC circle detection using coaxal transform. The proposed strategy is shown to have the following advantages over the conventional random sampling strategy. First, a poll size can be planned in a principled manner. Second, once a poll size is set, the probability that a circle is missed by the sampling process is kept relatively constant regardless of noise. Third, the actual number of subsets taken is automatically adjusted for different image complexities. Experimental results in agreement with the claimed advantages are presented.

[1] M.A. Fischler and R.C. Bolles, “Random Sample Consensus: A Paradigm for Model Fitting with Applications to Image Analysis and Automated Cartography,” Graphics and Image Processing, vol. 24, no. 6, pp. 381–395, June 1981.
[2] G. Roth and M.D. Levine,“Extracting geometric primitives,” CVGIP: Image Understanding, vol. 58, no. 1, pp. 1-22, 1993.
[3] Y.C. Cheng and S.C. Lee, “A New Method for Quadratic Curve Detection Using K-RANSAC with Acceleration Techniques,” Proc. IEEE Int'l Symp. Speech, Image Processing, and Neural Networks, pp. 515-518, Apr. 1994.
[4] Y.C. Cheng and S.C. Lee, “A New Method for Quadratic Curve Detection Using K-RANSAC with Acceleration Techniques,” Pattern Recognition, vol. 28, no. 5, pp. 663-682, 1995.
[5] R.O. Duda and P.E. Hart, "Use of the Hough transforms to detect lines and curves in pictures," Comm. ACM, vol. 15, no. 1, pp. 11-15, 1972
[6] L. Xu, E. Oja, and P. Kultanen, “A New Curve Detection Method: Randomized Hough Transform (RHT),” Pattern Recognition Letters, vol. 11, pp. 331-338, May 1990.
[7] N. Kiryati, Y. Eldar, and A.M. Bruckstein, “A Probabilistic Hough Transform,” Pattern Recognition, vol. 24, no. 4, pp. 303-316, 1991.
[8] J.R. Bergen and H. Shvaytser, “A Probabilistic Algorithm for Computing Hough Transform,” J. Algorithms, vol. 12, pp. 639-656, 1991.
[9] V.F. Leavers, "The Dynamic Generalized Hough Transform: Its Relationship to the Probabilistic Hough Transforms and an Application to the Concurrent Detection of Circles and Ellipses," CVGIP: Image Understanding, vol. 56, no. 3, pp. 381-398, Nov. 1992.
[10] A. Ylä-Jääski and N. Kiryati, “Adaptive Termination of Voting in the Probabilistic Circular Hough Transform,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 16, no. 9, pp. 911-915, Sept. 1994.
[11] Y.C. Cheng and Y.-S. Liu, “A New Polling Method and Coaxal Transform for Robust Circle Detection,” Proc. Fourth Asian Conf. Computer Vision (ACCV-'00), vol. I, pp. 336-340, Jan. 2000.
[12] C.F. Olson, “Constrained Hough Transforms for Curve Detection,” Computer Vision and Image Understanding, vol. 73, no. 3, pp. 329-345, Mar. 1999.
[13] R. Jain, R. Kasturi, and B.G. Schunck, Machine Vision. New York: McGraw-Hill, 1995.

Index Terms:
Random sampling strategy, poll size determination, circle detection, RANSAC, Hough transform.
Citation:
Y.C. Cheng, Y.-S. Liu, "Polling an Image for Circles by Random Lines," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 25, no. 1, pp. 125-130, Jan. 2003, doi:10.1109/TPAMI.2003.1159952
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