A Statistical Examination of the Megalithic Sites in Britain

Thom, A.

doi:10.2307/2342494

Cited by 65 publications

(26 citation statements)

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“…It has applications in many areas of research including archaeology [1], geodesy [2], physics [3,4], microwave engineering [5] and computer vision and metrology [6].…”

Section: Introductionmentioning

confidence: 99%

A statistical analysis of the Delogne–Kåsa method for fitting circles

Zelniker¹,

Clarkson²

2006

Digital Signal Processing

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In this paper, we examine the problem of fitting a circle to a set of noisy measurements of points on the circle's circumference. Delogne (Proc. IMEKO-Symp. Microwave Measurements 1972, 117-123) has proposed an estimator which has been shown by Kåsa (IEEE Trans. Instrum. Meas. 25, 1976, 8-14) to be convenient for its ease of analysis and computation. Using Chan's circular functional model to describe the distribution of points, we perform a statistical analysis of the estimate of the circle's centre, assuming independent, identically distributed Gaussian measurement errors. We examine the existence of the mean and variance of the estimator for fixed sample sizes. We find that the mean exists when the number of sample points is greater than 3 and the variance exists when this number is greater than 4. We also derive approximations for the mean and variance for fixed sample sizes when the noise variance is small. We find that the bias approaches zero as the noise variance diminishes and that the variance approaches the Cramér-Rao lower bound.

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“…It has applications in many areas of research including archaeology [1], geodesy [2], physics [3,4], microwave engineering [5] and computer vision and metrology [6].…”

Section: Introductionmentioning

confidence: 99%

A statistical analysis of the Delogne–Kåsa method for fitting circles

Zelniker¹,

Clarkson²

2006

Digital Signal Processing

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“…The reasons for this range from quality inspection for mechanical parts [1] to fitting circles for particle trajectories [2], [3]. Circle fitting also has applications in archaeology [4], microwave engineering [5], and ball detection in robotic vision systems [6].…”

Section: Introductionmentioning

confidence: 99%

Maximum-likelihood estimation of circle parameters via convolution

Zelniker

Clarkson

2006

IEEE Trans. on Image Process.

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“…It has applications in many areas of research including archaeology [1], geodesy [2], microwave engineering [3] and computer vision and metrology [4].…”

Section: Introductionmentioning

confidence: 99%

“…The problem of obtaining an accurate circular fit, by which we mean the estimation of a circle's centre and its radius, appears to have been first studied by THOM [1] in connection with measurements of ancient stone circles in Britain. He proposes an approximate method of least squares solution.…”

Section: Introductionmentioning

confidence: 99%

A statistical analysis of least-squares circle-centre estimation

Zelniker

Clarkson

Proceedings of the 3rd IEEE International Symposium on Signal Processing and Information Technology (IEEE Cat. No.03EX795)

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In this paper, we examine the problem of fitting a circle to a set of noisy measurements of points on the circle's circumference. An estimator based on standard least-squares techniques has been proposed by DELOGNE which has been shown by KÅSA to be convenient for its ease of analysis and computation. Using CHAN's circular functional model to describe the distribution of points, we perform a statistical analysis of the estimate of the circle's centre, assuming independent, identically distributed Gaussian measurement errors. We examine the existence of the mean and variance of the estimator for fixed sample sizes. We find that the mean exists when the number of sample points is greater than 2 and the variance exists when this number is greater than 3. We also derive approximations for the mean and variance for fixed sample sizes when the noise variance is small. We find that the bias approaches zero as the noise variance diminishes and that the variance approaches the CRAMÉR-RAO lower bound. We also show this through Monte-Carlo simulations.

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A Statistical Examination of the Megalithic Sites in Britain

Cited by 65 publications

References 0 publications

A statistical analysis of the Delogne–Kåsa method for fitting circles

A statistical analysis of the Delogne–Kåsa method for fitting circles

Maximum-likelihood estimation of circle parameters via convolution

A statistical analysis of least-squares circle-centre estimation

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