A Stable and Efficient Algorithm for Nonlinear Orthogonal Distance Regression

Boggs, Paul T.; Byrd, Richard H.; Schnabel, Robert B.

doi:10.1137/0908085

Cited by 328 publications

(160 citation statements)

References 14 publications

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“…For a unified treatment of these methods, and some comparisons, see [1]. The direct solution of (3) trades the subproblems for t i (a) for an increase in the number of variables, and generates orthogonal distances only in the limit: methods which exploit the structure of the Jacobian in Gauss-Newton (or Levenberg-Marquardt) methods are given in [6,10]. Which approach should be used depends mainly on whether or not the points x(a, t i (a)) are easy to calculate.…”

Section: C189mentioning

confidence: 99%

“…(7) (2) (1) (7) (2) (1) (7) (2) (1) (7) (2) Now consider the l p distance regression problem (3). For the case p = 2 the structure of the Jacobian matrix in (9) can be exploited as in odrpack or funke [5,6,10]. But in this more general case, this structure can also be exploited in the least squares subproblem which, as shown, gives the GaussNewton step asymptotically.…”

Section: This Is a Descent Step For F (A) Ifmentioning

confidence: 99%

See 1 more Smart Citation

Use of lp norms in fitting curves and surfaces to data

Atieg¹,

Watson

2004

ANZIAMJ

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Section: C189mentioning

confidence: 99%

Section: This Is a Descent Step For F (A) Ifmentioning

confidence: 99%

Use of lp norms in fitting curves and surfaces to data

Atieg¹,

Watson

2004

ANZIAMJ

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“…(ODR) algorithm (Boggs et al 1987(Boggs et al , 1992 6 , we determined the three parameters, that are shown in Table 1. The ODR uses the uncertainties on both variables to determine the best fit.…”

Section: Color-metallicity Relationmentioning

confidence: 99%

On the relation between metallicity and RGB color in HST/ACS data

Streich

Jong

Bailin

et al. 2014

A&A

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Context. The determination of stellar metallicity and its gradient in external galaxies is a difficult task, but crucial for the understanding of galaxy formation and evolution. Aims. The color of the Red Giant Branch (RGB) can be used to determine metallicities of stellar populations that have only shallow photometry. We will quantify the relation between metallicity and color in the widely used HST/ACS filters F606W and F814W. Methods. We use a sample of globular clusters from the ACS Globular Cluster Survey and measure their RGB color at given absolute magnitudes to derive the color-metallicity relation. We especially investigate the scatter and the uncertainties in this relation and show its limitations.Results. There is a clear relation between metallicity and RGB color. A comparison with isochrones shows reasonably good agreement with BaSTI models, a small offset to Dartmouth models, and a larger offset to Padua models. Conclusions. Even for the best globular cluster data available, the metallicity of a simple stellar population can be determined from the RGB alone only with an accuracy of 0.3 dex for [M/H] −1, and 0.15 dex for [M/H] −1. For mixed populations, as they are observed in external galaxies, the uncertainties will be even larger due to uncertainties in extinction, age, etc. Therefore caution is necessary when interpreting photometric metallicities.

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“…Fitzgibbon fitted 3D complex surfaces using the LevenbergMarquardt algorithm by minimising the Huber estimator in the z direction [30]. Boggs et al proposed an algorithm to minimize the mean squared orthogonal distance for explicit complex surfaces [31]. Sourlier [32] discussed the fitting of parametric surfaces based on orthogonal distance regression.…”

Section: Review Of Related Workmentioning

confidence: 99%

Template matching of freeform surfaces based on orthogonal distance fitting for precision metrology

Jiang

Zhang

Scott

2010

Meas. Sci. Technol.

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Abstract. Freeform surfaces are widely used in advanced optical and mechanical devices. In order to assess the form quality of a freeform surface, it is required to match the measurement surface with the design template. To improve the matching efficiency and accuracy, the whole procedure is divided into two stages, rough matching and final fitting. A new rough matching method, called the structured region signature is proposed. The structured region signature is a generalized global feature which represents the surface shape by a one dimensional function. The template location occupying the best matching signature is considered to be the correct rough position of the measurement surface. After that the motion parameters are updated iteratively based on the orthogonal distance fitting. The dependency between the foot-point parameters of the projection points and the motion parameters is derived from the closestdistance relationship between correspondance point pairs. Numerical experiments are given to demonstrate the validity of this approach.

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A Stable and Efficient Algorithm for Nonlinear Orthogonal Distance Regression

Cited by 328 publications

References 14 publications

Use of lp norms in fitting curves and surfaces to data

Use of lp norms in fitting curves and surfaces to data

On the relation between metallicity and RGB color in HST/ACS data

Template matching of freeform surfaces based on orthogonal distance fitting for precision metrology

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