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Definition
Fit one or more ellipses to a set of image points.
Background
Fitting geometric primitives to image data is a basic task in pattern recognition and computer vision. The fitting allows reduction and simplification of image data to a higher level with certain physical meanings. One of the most important primitive models is ellipse, which, being a projective projection of a circle, is of great importance for a variety of computer vision-related applications.
Ellipse fitting methods can be roughly divided into two categories: least square fitting and voting/clustering. Least square fitting, though usually fast to implement, requires the image data pre-segmented and is sensitive to outliers. On the other hand, voting techniques can detect multiple ellipses at once and exhibit some robustness against noise, but suffers from a heavier computational and memory load....
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References
Voss K, Suesse H (1997) Invariant fitting of planar objects by primitives. IEEE Trans Pattern Anal Mach Intell 19(1):80–84
Roth G, Levine MD (1994) Geometric primitive extraction using a genetic algorithm. IEEE Trans Pattern Anal Mach Intell 16(9):901–905
Ahn SJ, Rauh W, Warnecke HJ (2001) Least-squares orthogonal distances fitting of circle, sphere, ellipse, hyperbola, and parabola. Pattern Recognit 34:2283–2302
Liu ZY, H Qiao (2009) Multiple ellipses detection in noisy environments: a hierarchical approach. Pattern Recognit 42:2421–2433
Spath H (1997) Orthogonal distance fitting by circles and ellipses with given data. Comput Stat 12:343–354
Cui Y, Weng J, Reynolds H (1996) Estimation of ellipse parameters using optimal minimum variance estimator. Pattern Recognit Lett 17:309–316
Fitzgibbon AW, Pilu M, Fisher RB (1999) Direct least-squares fitting of ellipses. IEEE Trans Pattern Anal Mach Intell 21(5):476–480
Taubin G (1991) Estimation of planar curves, surfaces and non-planar space curves defined by implicit equations with applications to edge and range image segmentation. IEEE Trans Pattern Anal Mach Intell 13(11):1115–1138
Halir R, Flusser J (1998) Numerically stable direct least squares fitting of ellipses. In: WSCG’98 conference proceedings
Yuen HK, Illingworth J, Kittler J (1989) Detecting partially occluded ellipses using the hough transform. Image Vis Comput 7:31–37
Ho CT, Chen LH (1995) A fast ellipse/circle detector using geometric sysmetry. Pattern Recognit 28: 117–124
Guil N, Zapata EL (1997) Lower order circle and ellipse hough transform. Pattern Recognit 30:1729–1744
McLaughlin RA (1998) Randomized hough transform: improved ellipse detection with comparison. Pattern Recognit Lett 19:299–305
Tsuji S, Matsumoto F (1978) Detection of ellipses by a modified hough transformation. IEEE Trans Comput 25:777–781
Yipa KK, Tama KS, Leung NK (1992) Modification of hough transform for circles and ellipses detection using a 2-dimensional array. Pattern Recognit 25:1007–1022
Kim E, Haseyama M, Kitajima H (2002) Fast and robust ellipse extraction from complicated images. In: Proceedings of IEEE international conference on information technology and applications
Mai F, Hung YS, Zhong H, Sze WF (2008) A hierarchical approach for fast and robust ellipse extraction. Pattern Recognit 8(41):2512–2524
Kanatani K (1994) Statistical bias of conic fitting and renormalization. IEEE Trans Pattern Anal Mach Intell 16(3):320–326
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Liu, ZY. (2020). Ellipse Fitting. In: Computer Vision. Springer, Cham. https://doi.org/10.1007/978-3-030-03243-2_318-1
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DOI: https://doi.org/10.1007/978-3-030-03243-2_318-1
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