DAGM 2002: Pattern Recognition pp 548-556 | Cite as
Fitting of Parametric Space Curves and Surfaces by Using the Geometric Error Measure
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.
Keywords
Model Feature Geometric Distance Orthogonal Distance Generalize Newton Method Computing Time CostPreview
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References
- 1.Ahn, S.J., Rauh, W., Warnecke, H.-J.: Least-squares orthogonal distances fitting of circle, sphere, ellipse, hyperbola, and parabola. Pattern Recognition 34 (2001) 2283–2303MATHCrossRefGoogle Scholar
- 2.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) 620–638CrossRefGoogle Scholar
- 3.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) 1052–1078MATHCrossRefMathSciNetGoogle Scholar
- 4.Butler, B.P., Forbes, A.B., Harris, P.M.: Algorithms for Geometric Tolerance Assessment. Report No. DITC 228/94. NPL, Teddington, UK (1994)Google Scholar
- 5.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)Google Scholar
- 6.Gander, W., Golub, G.H., Strebel, R.: Least-squares fitting of circles and ellipses. BIT 34 (1994) 558–578MATHCrossRefMathSciNetGoogle Scholar
- 7.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)Google Scholar
- 8.Sourlier, D.: Three Dimensional Feature Independent Bestfit in Coordinate Metrology. Ph.D. Thesis, ETH Zurich, Switzerland (1995)Google Scholar
- 9.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) 1183–1196CrossRefGoogle Scholar
- 10.Turner, D.A.: The approximation of Cartesian coordinate data by parametric orthogonal distance regression. Ph.D. Thesis, University of Huddersfield, UK (1999)Google Scholar