Least Squares Fitting of Circles

Chernov, N.; Lesort, Claire

doi:10.1007/s10851-005-0482-8

Cited by 251 publications

(201 citation statements)

References 29 publications

Supporting

Mentioning

189

Contrasting

Unclassified

Order By: Relevance

“…It is known [16,28,31] that, under certain general conditions, the minimum of (6) exists and is unique. But the minimization of (6) is a nonlinear problem that has no closed form solution.…”

Section: Curve Fitting Methods In Errors-in-variables Modelsmentioning

confidence: 99%

“…by representing a line as Ax + By + C = 0 under a natural constraint A 2 + B 2 = 1; then the MLEÂ andB of the new parameters A and B would obviously have finite moments. But when one fits circles or ellipses, it is harder to find convenient parameters whose estimates would have finite moments; see some attempts in [16]. Besides in many applications the estimates of the center and radius are of natural interest and then one has to deal with their infinite moments.…”

Section: Curve Fitting Methods In Errors-in-variables Modelsmentioning

confidence: 99%

“…In the nonlinear regression, there are several popular circle fitting methods (by Kåsa, Pratt, and Taubin; see references in [2,16]). It turns out that they all (!)…”

Section: Curve Fitting Methods In Errors-in-variables Modelsmentioning

confidence: 99%

“…Now the estimates (â,b,R) constitute a map from R 2n to R 3 , which is defined provided the best fitting circle exists and is unique. It has been pointed out by several authors [16,28,31] that the set of 'data' (x 1 , . .…”

Section: Appendixmentioning

confidence: 99%

See 3 more Smart Citations

Untitled

2012

Theor. Probability and Math. Statist.

View full text Add to dashboard Cite

Abstract. Regression models in which all variables are subject to errors are known as errors-in-variables (EIV) models. The respective parameter estimates have many unusual properties: their exact distributions are very hard to determine, and their absolute moments are often infinite (so that their mean and variance do not exist). In our paper, Error analysis for circle fitting algorithms, Electr. J. Stat. 3 (2009), 886-911, we developed an unconventional statistical analysis that allowed us to effectively assess EIV parameter estimates and design new methods with superior characteristics. In this paper we validate our approach in a series of numerical tests. We also prove that in the case of fitting circles, the estimates of the parameters are absolutely continuous (have densities).

show abstract

Section: Curve Fitting Methods In Errors-in-variables Modelsmentioning

confidence: 99%

Section: Curve Fitting Methods In Errors-in-variables Modelsmentioning

confidence: 99%

“…In the nonlinear regression, there are several popular circle fitting methods (by Kåsa, Pratt, and Taubin; see references in [2,16]). It turns out that they all (!)…”

Section: Curve Fitting Methods In Errors-in-variables Modelsmentioning

confidence: 99%

Section: Appendixmentioning

confidence: 99%

See 2 more Smart Citations

Untitled

2012

Theor. Probability and Math. Statist.

View full text Add to dashboard Cite

show abstract

“…Très rapide, ils sont souvent utilisés en vision industrielle. De nombreuses implémentations sont possibles et Les auteurs ont implémenté l'algorithme proposé dans [5,6].…”

Section: Estimation Par Moindres Carrésunclassified

Mesurage de perçages imparfaits au défilé par vision industrielle

Mairesse

Sliwa

Voisin

2013

16th International Congress of Metrology

View full text Add to dashboard Cite

Résumé. Cet article traite de la mesure sur chaînes de production par vision industrielle et plus particulièrement du mesurage de perçages sur panneaux manufacturés. Pour cela, nous nous intéressons au contour de ces usinages à la surface du panneau. Ces formes sont communément considérées, en première approche, comme des cercles ou des ellipses ce qui peut être assez éloigné de la réalité notamment pour des matériaux compressés. D'autres phénomènes tels que l'environnement industriel et la chaîne d'acquisition interfèrent également sur la qualité de l'image obtenue. Afin de répondre à cette problématique, les auteurs présentent une comparaison de différentes méthodes d'estimation de cercles dans le cadre de déformations de formes. Une méthode de correction de formes est proposée dans le but d'améliorer la mesure. Les résultats obtenus montrent une amélioration significative de l'estimation des perçages pour certains estimateurs et notamment dans les cas de perçages de faible diamètre apparent.Abstract. This article deals with measurement on production lines by industrial vision. More precisely, it concerns the measurement of drillings on manufactured panels. We are interested in the contour of drillings in the panel plan. These forms can be considered, in a first approach, as circles or ellipses that are not true notably in compressed material. Others phenomena such as industrial environment and acquisition chain can also interfere on the image quality. In order to answer this problematic, the authors present a comparison of several measurement methods on distort circles. A method to regularize forms is proposed in order to increase measure quality. The results indicate that the validity of the measure obviously depends on the computation methods but also on the diameter of the drilling.

show abstract