Size invariant circle detection

The Circle Hough Transform (CHT) has become a common method for circle detection in numerous image processing applications. Various modifications to the basic CHT operation have been suggested which include: the inclusion of edge orientation, simultaneous consideration of a range of circle radii, use of a complex accumulator array with the phase proportional to the log of radius, and the implementation of the CHT as filter operations. However, there has also been much work recently on the definition and use of invariance filters for object detection including circles. The contribution of the work presented here is to show that a specific combination of modifications to the CHT is formally equivalent to applying a scale invariant kernel operator. This work brings together these two themes in image processing which have herewith been quite separate. Performance results for applying various forms of CHT filters incorporating some or all of the available modifications, along with results from the invariance kernel, are included. These are in terms of an analysis of the peak width in the output detection array (with and without the presence of noise), and also an analysis of the peak position in terms of increasing noise levels. The results support the equivalence between the specific form of the CHT developed in this work and the invariance kernel.

[1]  D. Kerbyson,et al.  Circle detection using Hough transform filters , 1995 .

[2]  O DudaRichard,et al.  Use of the Hough transformation to detect lines and curves in pictures , 1972 .

[3]  E. R. Davies.  Modelling peak shapes obtained by Hough transform , 1992 .

[4]  Josef Kittler,et al.  On the accuracy of the Sobel edge detector , 1983, Image Vis. Comput..

[5]  Herbert Jahn.  Crater detection by linear filters representing the Hough Transform , 1994, Other Conferences.

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

[7]  Josef Kittler,et al.  A Comparative Study of Hough Transform Methods for Circle Finding , 1989, Alvey Vision Conference.

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

[9]  W. Hoffman.  The Lie algebra of visual perception , 1966 .

[10]  Yehoshua Y. Zeevi,et al.  Recognition of distorted patterns by invariance kernels , 1991, Pattern Recognit..

[11]  Jack Sklansky,et al.  The Detection and Segmentation of Blobs in Infrared Images , 1981, IEEE Transactions on Systems, Man, and Cybernetics.

[12]  David A. Forsyth,et al.  Transformational invariance - a primer , 1990, BMVC.

[13]  John G. Proakis,et al.  Probability, random variables and stochastic processes , 1985, IEEE Trans. Acoust. Speech Signal Process..

[14]  JEFFREY WOOD,et al.  Invariant pattern recognition: A review , 1996, Pattern Recognit..

[15]  Charles W. Therrien,et al.  Discrete Random Signals and Statistical Signal Processing , 1992 .

[16]  Darren J. Kerbyson,et al.  The Coherent Circle Hough Transform , 1993, BMVC.

[17]  D. Kerbyson,et al.  Using phase to represent radius in the coherent circle Hough transform , 1993 .

[18]  Darren J. Kerbyson,et al.  Detection and segmentation of blobs using the Warwick multiple-SIMD architecture , 1990, Other Conferences.

[19]  J. Kittler,et al.  Comparative study of Hough Transform methods for circle finding , 1990, Image Vis. Comput..