A stable and efficient algorithm for nonlinear orthogonal distance regression
SIAM Journal on Scientific and Statistical Computing
Practical methods of optimization; (2nd ed.)
Practical methods of optimization; (2nd ed.)
Least-squares fitting by circles
Computing
A trust region algorithm for parametric curve and surface fitting
Journal of Computational and Applied Mathematics - Special issue on scattered data
A comparison of orthogonal least squares fitting in coordinate metrology
Proceedings of the second international workshop on Recent advances in total least squares techniques and errors-in-variables modeling
Orthogonal least squares fitting by conic sections
Proceedings of the second international workshop on Recent advances in total least squares techniques and errors-in-variables modeling
Applications of orthogonal distance regression in metrology
Proceedings of the second international workshop on Recent advances in total least squares techniques and errors-in-variables modeling
Best-fit of implicit surfaces and plane curves
Mathematical Methods for Curves and Surfaces
The Reconstruction of Workpiece Surfaces from Probe Coordinate Data
Proceedings of the 5th IMA Conference on the Mathematics of Surfaces
Constrained curve fitting on manifolds
Computer-Aided Design
Application of gradient descent method to the sedimentary grain-size distribution fitting
Journal of Computational and Applied Mathematics
Extending the limits of feature-based SLAM with B-splines
IEEE Transactions on Robotics
Distance regression by Gauss–Newton-type methods and iteratively re-weighted least-squares
Computing - Geometric Modelling, Dagstuhl 2008
A revisit to least squares orthogonal distance fitting of parametric curves and surfaces
GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing
Journal on Computing and Cultural Heritage (JOCCH)
Unified Computation of Strict Maximum Likelihood for Geometric Fitting
Journal of Mathematical Imaging and Vision
Two-stage outlier elimination for robust curve and surface fitting
EURASIP Journal on Advances in Signal Processing - Special issue on robust processing of nonstationary signals
From unordered point cloud to weighted B-spline: a novel PCA-based method
AMERICAN-MATH'11/CEA'11 Proceedings of the 2011 American conference on applied mathematics and the 5th WSEAS international conference on Computer engineering and applications
Variational mesh segmentation via quadric surface fitting
Computer-Aided Design
Hi-index | 7.29 |
Given a family of curves or surfaces in Rs, an important problem is that of finding a member of the family which gives a "best" fit to m given data points. A criterion which is relevant to many application areas is orthogonal distance regression, where the sum of squares of the orthogonal distances from the data points to the surface is minimized. For certain types of fitting problem, attention has recently focussed on the use of an iteration process which forces orthogonality to hold at every iteration and uses steps of Gauss-Newton type. Within this framework a number of different methods has recently emerged, and the purpose of this paper is to place these methods into a unified framework and to make some comparisons.