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

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.

[1]  Laure Tougne,et al.  An elementary algorithm for digital arc segmentation , 2001, Electron. Notes Theor. Comput. Sci..

[2]  V. F. Leavers,et al.  Which Hough transform , 1993 .

[3]  Jong-Hwan Kim,et al.  A two-step circle detection algorithm from the intersecting chords , 2001, Pattern Recognit. Lett..

[4]  Ling-Hwei Chen,et al.  A fast ellipse/circle detector using geometric symmetry , 1995, Pattern Recognit..

[5]  Josef Kittler,et al.  A survey of the hough transform , 1988, Comput. Vis. Graph. Image Process..

[6]  E. R. Davies,et al.  A modified Hough scheme for general circle location , 1988, Pattern Recognit. Lett..

[7]  Jack Sklansky,et al.  Finding circles by an array of accumulators , 1975, Commun. ACM.

[8]  Karin Wall,et al.  A fast sequential method for polygonal approximation of digitized curves , 1984, Comput. Vis. Graph. Image Process..

[9]  Kuo-Liang Chung,et al.  An Efficient Randomized Algorithm for Detecting Circles , 2001, Comput. Vis. Image Underst..

[10]  Partha Bhowmick,et al.  Fast Polygonal Approximation of Digital Curves Using Relaxed Straightness Properties , 2007, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[11]  Jiun-Jian Liaw,et al.  An effective voting method for circle detection , 2005, Pattern Recognit. Lett..

[12]  Azriel Rosenfeld,et al.  Digital geometry - geometric methods for digital picture analysis , 2004 .

[13]  Paul L. Rosin.  Techniques for Assessing Polygonal Approximations of Curves , 1997, IEEE Trans. Pattern Anal. Mach. Intell..

[14]  Azriel Rosenfeld,et al.  Digital straightness - a review , 2004, Discret. Appl. Math..

[15]  Peter Kwong-Shun Tam,et al.  Modification of hough transform for circles and ellipses detection using a 2-dimensional array , 1992, Pattern Recognit..

[16]  Erkki Oja,et al.  Randomized hough transform (rht) : Basic mech-anisms, algorithms, and computational complexities , 1993 .

[17]  Erkki Oja,et al.  Randomized Hough Transform , 2009, Encyclopedia of Artificial Intelligence.