Parameter optimization in approximating curves and surfaces to measurement data

Sarkar, Biplab; Menq, Chia-Hsiang

doi:10.1016/0167-8396(91)90016-5

Cited by 110 publications

(25 citation statements)

References 16 publications

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“…We also considered constraints between nonadjacent surfaces as well as connectivity constraints. We satis£ed the constraints effectively using a numerical optimization process instead of an equation-solving approach [40], using the data projection method of [29]. While these buildings only have constrained planar surfaces, we have also developed techniques for constraints involving quadric and freeform surfaces [49,50].…”

Section: Constrained Building Reconstruction Buildings Have Standard mentioning

confidence: 99%

Solving architectural modelling problems using knowledge

Fisher¹

Fourth International Conference on 3-D Digital Imaging and Modeling, 2003. 3DIM 2003. Proceedings.

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Section: Constrained Building Reconstruction Buildings Have Standard mentioning

confidence: 99%

Solving architectural modelling problems using knowledge

Fisher¹

Fourth International Conference on 3-D Digital Imaging and Modeling, 2003. 3DIM 2003. Proceedings.

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“…We also considered constraints between non-adjacent surfaces as well as connectivity constraints. We satisfied the constraints effectively exactly using a numerical optimization process instead of an equation-solving approach [44], using the data projection method of [33]. One application is ensuring that the freeform surface is tangential or orthogonal to a planar surface at their common boundary.…”

Section: Constrained Reverse Engineeringmentioning

confidence: 99%

Applying knowledge to reverse engineering problems

Fisher

2004

Computer-Aided Design

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:This paper summarizes a series of recent research results made at Edinburgh University based on projects that apply domain knowledge of standard shapes and relationships to solve or improve reverse engineering problems. The problems considered are how to enforce known relationships when data fitting, how to extract features even in very noisy data, how to get better shape parameter estimates and how to infer data about unseen features.Keywords : range data, reverse engineering, constraints Copyright c 2004 by The University of Edinburgh. All Rights ReservedThe authors and the University of Edinburgh retain the right to reproduce and publish this paper for non-commercial purposes.Permission is granted for this report to be reproduced by others for non-commercial purposes as long as this copyright notice is reprinted in full in any reproduction. Applications to make other use of the material should be addressed in the first instance to Copyright Permissions, School of Informatics, The University of Edinburgh, 2 Buccleuch Place, Edinburgh EH8 9LW, Scotland. DRAFT: Applying knowledge to reverse engineering problemsRobert B. Fisher School of Informatics, University of Edinburgh rbf@inf.ed.ac.uk AbstractThis paper summarizes a series of recent research results made at Edinburgh University based on projects that apply domain knowledge of standard shapes and relationships to solve or improve reverse engineering problems. The problems considered are how to enforce known relationships when data fitting, how to extract features even in very noisy data, how to get better shape parameter estimates and how to infer data about unseen features.

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“…In the case of parametric surfaces, due to the influence of the parameterization, the fitting problem leads to a non-linear optimization problem. Different approaches for dealing with the effects of this nonlinearity have been developed, including various variants of Gauss-Newton type techniques [5,7,9,13,23,24,27,29,32,36].…”

Section: Surface Fittingmentioning

confidence: 99%

Robust fitting of implicitly defined surfaces using Gauss–Newton-type techniques

Aigner

Jüttler

2009

Vis Comput

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We describe Gauss-Newton type methods for fitting implicitly defined curves and surfaces to given unorganized data points. The methods are suitable not only for leastsquares approximation, but they can also deal with general error functions, such as approximations to the ℓ 1 or ℓ ∞ norm of the vector of residuals. Two different definitions of the residuals will be discussed, which lead to two different classes of methods: direct methods and data-based ones. In addition we discuss the continuous versions of the methods, which furnish geometric interpretations as evolution processes.It is shown that the data-based methods -which are less costly, as they work without the computation of the closest points -can efficiently deal with error functions that are adapted to noisy and uncertain data. In addition, we observe that the interpretation as evolution process allows to deal with the issues of regularization and with additional constraints.

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Parameter optimization in approximating curves and surfaces to measurement data

Cited by 110 publications

References 16 publications

Solving architectural modelling problems using knowledge

Solving architectural modelling problems using knowledge

Applying knowledge to reverse engineering problems

Robust fitting of implicitly defined surfaces using Gauss–Newton-type techniques

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