Performance evaluation of iterative geometric fitting algorithms

Kanatani, Kenichi; Sugaya, Yasuyuki

doi:10.1016/j.csda.2007.05.013

Cited by 39 publications

(32 citation statements)

References 17 publications

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“…It is known that the most challenging scenario for ellipse fitting is when an ellipse needs to be fit to data coming from a short segment with high eccentricity [17]. Such a situation may arise in the case of fitting an ellipse to a face region, where the data lie on the chin line.…”

Section: Real Datamentioning

confidence: 99%

Guaranteed Ellipse Fitting with the Sampson Distance

Szpak

Chojnacki

Hengel

2012

Computer Vision – ECCV 2012

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Abstract. When faced with an ellipse fitting problem, practitioners frequently resort to algebraic ellipse fitting methods due to their simplicity and efficiency. Currently, practitioners must choose between algebraic methods that guarantee an ellipse fit but exhibit high bias, and geometric methods that are less biased but may no longer guarantee an ellipse solution. We address this limitation by proposing a method that strikes a balance between these two objectives. Specifically, we propose a fast stable algorithm for fitting a guaranteed ellipse to data using the Sampson distance as a data-parameter discrepancy measure. We validate the stability, accuracy, and efficiency of our method on both real and synthetic data. Experimental results show that our algorithm is a fast and accurate approximation of the computationally more expensive orthogonal-distance-based ellipse fitting method. In view of these qualities, our method may be of interest to practitioners who require accurate and guaranteed ellipse estimates.

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Section: Real Datamentioning

confidence: 99%

Guaranteed Ellipse Fitting with the Sampson Distance

Szpak

Chojnacki

Hengel

2012

Computer Vision – ECCV 2012

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“…(16), for which eigenvectors θ have scale indeterminacy, we can adopt normalization θ = 1 rather than Eq. (13). Then, the solution θ is always a unit vector.…”

Section: Algebraic Fittingmentioning

confidence: 99%

“…where the true data valuesx α in the definition of V , and the projective GaussNewton iteration 13) .…”

Section: Error Analysismentioning

confidence: 99%

HyperLS for Parameter Estimation in Geometric Fitting

Kanatani

Rangarajan

Sugaya

et al. 2011

IPSJ Transactions on Computer Vision and Applications

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We present a general framework of a special type of least squares (LS) estimator, which we call "HyperLS," for parameter estimation that frequently arises in computer vision applications. It minimizes the algebraic distance under a special scale normalization, which is derived by a detailed error analysis in such a way that statistical bias is removed up to second order noise terms. We discuss in detail many theoretical issues involved in its derivation. By numerical experiments, we show that HyperLS is far superior to the standard LS and comparable in accuracy to maximum likelihood (ML), which is known to produce highly accurate results but may fail to converge if poorly initialized. We conclude that HyperLS is a perfect candidate for ML initialization.

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“…All these methods are robust to occlusion and outliers, but are slow, heavy from the memory allocation point of view and not so accurate. In the second group we can find methods based on the Maximum Likelihood (ML) estimation (Chojnacki et al, 2000;Kanatani & Sugaya, 2007;Leedan & Meer, 2000;Matei & Meer, 2006). These are the most accurate methods, whose solution already achieves the theoretical accuracy Kanatani-Cramer-Rao (KCR) limit.…”

Section: Ellipse Fitting On the Image Plane 41 Pupil Ellipse Fittingmentioning

confidence: 99%