A doubly optimal ellipse fit

Al-Sharadqah, Ali; Chernov, N.

doi:10.1016/j.csda.2012.02.028

Cited by 20 publications

(10 citation statements)

References 19 publications

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“…In this paper, we expound this principle in detail and modify renormalization so that it outperforms the standard reprojection error minimization. Doing a precise high order error analysis using the perturbation technique of Kanatani [11] and Al-Sharadqah and Chernov [1], we derive a formula that maximizes the accuracy of the solution; we call it hyper-renormalization. Partly, this has already been done in the single constraint case, such as ellipse fitting, by Kanatani et al [12].…”

Section: Introductionmentioning

confidence: 99%

“…The best known approach is maximum likelihood (ML), which minimizes the negative log-likelihood l = − N α=1 log p θ (x α ). Recently, an alternative approach is more 1 Professor Emeritus, Okayama University, Okayama 700-8530, Japan alsharadqaha@ecu.edu c) sugaya@iim.cs.tut.ac.jp and more in use: one directly solves specified equations, called estimating equations [5], in the form of g(x 1 , . .…”

Section: Introductionmentioning

confidence: 99%

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Hyper-renormalization: Non-minimization Approach for Geometric Estimation

Kanatani

Al-Sharadqah

Chernov

et al. 2014

IPSJ Transactions on Computer Vision and Applications

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Abstract:The technique of "renormalization" for geometric estimation attracted much attention when it appeared in early 1990s for having higher accuracy than any other then known methods. The key fact is that it directly specifies equations to solve, rather than minimizing some cost function. This paper expounds this "non-minimization approach" in detail and exploits this principle to modify renormalization so that it outperforms the standard reprojection error minimization. Doing a precise error analysis in the most general situation, we derive a formula that maximizes the accuracy of the solution; we call it hyper-renormalization. Applying it to ellipse fitting, fundamental matrix computation, and homography computation, we confirm its accuracy and efficiency for sufficiently small noise. Our emphasis is on the general principle, rather than on individual methods for particular problems.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Hyper-renormalization: Non-minimization Approach for Geometric Estimation

Kanatani

Al-Sharadqah

Chernov

et al. 2014

IPSJ Transactions on Computer Vision and Applications

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“…However, as the authors noted in their original work, the method suffered from substantial bias problems. Other algebraic fitting methods have focused on minimizing the bias, but no longer guaranteed that the resulting estimate will be an ellipse [2,16].…”

Section: Introductionmentioning

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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“…Halif et al [13] provided improvements towards numerical stability. Newer ellipse fitting methods proved to achieve higher accuracies [3,16,17,20,29,34]. Nevertheless, most of these approaches do not guarantee that the final result is an ellipse, rather hyperbolas or parabolas might occur.…”

Section: Related Workmentioning

confidence: 96%

“…Our constrained ellipse fitting approach is based on the Fitzgibbon method because it is the only method that always guarantees an ellipse fit in a non-iterative and therefore fast way. Other methods which proved to be superior in accuracy in free conic fitting require a post hoc procedure to ensure an ellipse fit [3,17].…”

Section: Related Workmentioning

confidence: 99%

Constrained Ellipse Fitting with Center on a Line

2015

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Fitting an ellipse to given data points is a common optimization task in computer vision problems. However, the possibility of incorporating the prior constraint "the ellipse's center is located on a given line" into the optimization algorithm has not been examined so far. This problem arises, for example, by fitting an ellipse to data points representing the path of the image positions of an adhesion inside a rotating vessel whose position of the rotational axis in the image is known. Our new method makes use of a constrained algebraic cost function with the incorporated "ellipse center on given line"-prior condition in a global convergent onedimensional optimization approach. Further advantages of the algorithm are computational efficiency and numerical stability.

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A doubly optimal ellipse fit

Cited by 20 publications

References 19 publications

Hyper-renormalization: Non-minimization Approach for Geometric Estimation

Hyper-renormalization: Non-minimization Approach for Geometric Estimation

Guaranteed Ellipse Fitting with the Sampson Distance

Constrained Ellipse Fitting with Center on a Line

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