[en] Ellipse matching is the process of extracting (detecting and ﬁtting) elliptic shapes from digital images. This process typically requires the determination of 5 parameters, which can be obtained by using an Elliptic Hough Transform (EHT) algorithm.
In this paper, we focus on Elliptic Hough Transform (EHT) algorithms based on two edge points and their associated image gradients. For this set-up, it is common to ﬁrst reduce the dimension of the 5D EHT by means of some geometrical observations, and then apply a simpler HT.
We present an alternative approach, with its corresponding algebraic framework, based on the pencil of bi-tangent conics, expressed in two dual forms: the point or the tangential forms. We show that, for both forms, the locus of the ellipse parameters is a line in a 5D space.
With our framework, we can split the EHT into two steps. The ﬁrst step accumulates 2D lines, which are computed from planar projections of the parameter locus (5D line). The second part back-projects the peak of the 2D accumulator into the 5D space, to obtain the three remaining parameters that we then accumulate in a 3D histogram, possibly represented as three separated 1D histograms.
For the point equation, the ﬁrst step extracts parameters related to the ellipse orientation and eccentricity, while the remaining parameters are related to the center and a sizing parameter of the ellipse. For the tangential equation, the ﬁrst step is the known center extraction algorithm, while the remaining parameters are related to the ellipse half-axes and orientation.
Research center :
Telim Montefiore Institute - Montefiore Institute of Electrical Engineering and Computer Science - ULiège
Author, co-author :
Latour, Philippe ; Université de Liège - ULiège > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Dép. d'électric., électron. et informat. (Inst.Montefiore)
Van Droogenbroeck, Marc ; Université de Liège - ULiège > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Télécommunications
Dual Approaches for Elliptic Hough Transform: Eccentricity/Orientation vs Center based
Publication date :
Event name :
21st IAPR International Conference on Discrete Geometry for Computer Imagery
Event organizer :
Laboratoire d'Informatique Gaspard-Monge (LIGM) at ESIEE Paris, France
Kanatani, K., Sugaya, Y., Kanazawa, Y.: Ellipse Fitting for Computer Vision: Implementation and Applications. Synthesis Lectures on Computer Vision. Morgan & Claypool, San Rafael (2016)
Duda, R.O., Hart, P.E.: Use of the Hough transformation to detect lines and curves in pictures. Commun. ACM 15(1), 11–15 (1972)
Mukhopadhyay, P., Chaudhuri, B.: A survey of Hough transform. Pattern Recogn. 48(3), 993–1010 (2015)
Tsuji, S., Matsumoto, F.: Detection of ellipses by a modified Hough transformation. IEEE Trans. Comput. C-27(8), 777–781 (1978)
Yuen, H.K., Illingworth, J., Kittler, J.: Ellipse detection using the Hough transform. In: Proceedings of the Alvey Vision Conference, pp. 41.1–41.8. Alvey Vision Club (1988)
Guil, N., Zapata, E.L.: Lower order circle and ellipse Hough transform. Pattern Recogn. 30(10), 1729–1744 (1997)
Muammar, H.K., Nixon, M.: Tristage Hough transform for multiple ellipse extraction. IEE Proc. E Comput. Digit. Tech. 138(1), 27–35 (1991)
Yoo, J.H., Sethi, I.K.: An ellipse detection method from the polar and pole definition of conics. Pattern Recogn. 26(2), 307–315 (1993)
Bennett, N., Burridge, R., Saito, N.: A method to detect and characterize ellipses using the Hough transform. IEEE Trans. Pattern Anal. Mach. Intell. 21(7), 652– 657 (1999)
Forbes, A.B.: Fitting an Ellipse to Data. NPL Report DITC 95/87, National Physical Laboratory (1987)
Leavers, V.F.: The dynamic generalized Hough transform: its relationship to the probabilistic Hough transforms and an application to the concurrent detection of circles and ellipses. Comput. Vis. Graph. Image Process.: Image Underst. 56(3), 381–398 (1992)
Lu, W., Yu, J., Tan, J.: Direct inverse randomized Hough transform for incomplete ellipse detection in noisy images. J. Pattern Recogn. Res. 1, 13–24 (2014)