Abstract
For pattern recognition and computer vision, fitting of curves and surfaces to a set of given data points in space is a relevant subject. In this paper, we review the current orthogonal distance fitting algorithms for parametric model features, and, present two new algorithms in a well organized and easily understandable manner. Each of these algorithms estimates the model parameters which minimize the square sum of the shortest error distances between the model feature and the given data points. The model parameters are grouped and simultaneously estimated in terms of form, position, and rotation parameters. We give various examples of fitting curves and surfaces to a point set in space.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Ahn, S.J., Rauh, W., Warnecke, H.-J.: Least-squares orthogonal distances fitting of circle, sphere, ellipse, hyperbola, and parabola. Pattern Recognition 34 (2001) 2283–2303
Ahn, S.J., Rauh, W., Cho, H.S., Warnecke, H.-J.: Orthogonal Distance Fitting of Implicit Curves and Surfaces. IEEE Trans. Pattern Analy. Mach. Intell. 24 (2002) 620–638
Boggs, P.T., Byrd, R.H., Schnabel, R.B.: A stable and efficient algorithm for nonlinear orthogonal distance regression. SIAM J. Sci. Stat. Comput. 8 (1987) 1052–1078
Butler, B.P., Forbes, A.B., Harris, P.M.: Algorithms for Geometric Tolerance Assessment. Report No. DITC 228/94. NPL, Teddington, UK (1994)
Drieschner, R., Bittner, B., Elligsen, R., Wäldele, F.: Testing Coordinate Measuring Machine Algorithms: Phase II. BCR Report, EUR 13417 EN. Commission of the European Communities, Luxemburg (1991)
Gander, W., Golub, G.H., Strebel, R.: Least-squares fitting of circles and ellipses. BIT 34 (1994) 558–578
ISO 10360-6: Geometrical Product Specifications (GPS)-Acceptance and reverification test for coordinate measuring machines (CMM)-Part 6: Estimation of errors in computing Gaussian associated features. ISO, Geneva, Switzerland (2001)
Sourlier, D.: Three Dimensional Feature Independent Bestfit in Coordinate Metrology. Ph.D. Thesis, ETH Zurich, Switzerland (1995)
Sullivan, S., Sandford, L., Ponce, J.: Using Geometric Distance Fits for 3-D Object Modeling and Recognition. IEEE Trans. Pattern Analy. Mach. Intell. 16 (1994) 1183–1196
Turner, D.A.: The approximation of Cartesian coordinate data by parametric orthogonal distance regression. Ph.D. Thesis, University of Huddersfield, UK (1999)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ahn, S.J., Rauh, W., Westkämper, E. (2002). Fitting of Parametric Space Curves and Surfaces by Using the Geometric Error Measure. In: Van Gool, L. (eds) Pattern Recognition. DAGM 2002. Lecture Notes in Computer Science, vol 2449. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45783-6_66
Download citation
DOI: https://doi.org/10.1007/3-540-45783-6_66
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-44209-7
Online ISBN: 978-3-540-45783-1
eBook Packages: Springer Book Archive