Geometric Fitting of Parametric Curves and Surfaces
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This paper deals with the geometric fitting algorithms for parametric curves and surfaces in 2-D/3-D space, which estimate the curve/surface parameters by minimizing the square sum of the shortest distances between the curve/surface and the given points. We identify three algorithmic approaches for solving the nonlinear problem of geometric fitting. As their general implementation we describe a new algorithm for geometric fitting of parametric curves and surfaces. The curve/surface parameters are estimated in terms of form, position, and rotation parameters. We test and evaluate the performances of the algorithms with fitting examples.
Abstract
This paper deals with the geometric fitting algorithms for parametric curves and surfaces in 2-D/3-D space, which estimate the curve/surface parameters by minimizing the square sum of the shortest distances between the curve/surface and the given points. We identify three algorithmic approaches for solving the nonlinear problem of geometric fitting. As their general implementation we describe a new algorithm for geometric fitting of parametric curves and surfaces. The curve/surface parameters are estimated in terms of form, position, and rotation parameters. We test and evaluate the performances of the algorithms with fitting examples.
참고문헌 (21)
- R.J. Adcock, "on the method of least squares", The Analyst Des Moines Iowa, 4, pp.183~184 (1877)
- S.J. Ahn, "Orthogonal Distance Fitting of Implicit Curves and Surfaces", IEEE Trans. Pattern Analy. Mach. Intell, 24(5), pp.620~638 (2002)
- S.J. Ahn, "Orthogonal Distance Fitting of Parametric Curves and Surfaces", Proc. 4th Int'l Symp. Algorithms for Approximation, pp.122~129 (2002)
- P.T. Boggs, "A stable and efficient algorithm for nonlinear orthogonal distance regression", SIAM J. Sci. Stat. Compt, 8, pp.1052~1078 (1987)
- P.T. Boggs, "Algorithm 676 – ODRPACK: Software for Weighted Orthogonal Distance Regression", ACM Trans. Math. Softw, 15(4), pp.348~364 (1989)
- F.L. Bookstein, "Fitting conic sections to scattered data", Comput. Graph. Image Process, 9(1), pp.56~71 (1979)
- Algorithms for Geometric Tolerance Assessment, "B.P. Butler", NPL, ~, pp.Report no. DITC 228 (1994), 94
- X. Cao, "Approximate orthogonal distance regression method for fitting quadric surfaces to range data", Pattern Recogn. Lett, 15(8), pp.781~796 (1994)
- A. Fitzgibbon, "Direct Least Square Fitting of Ellipses", IEEE Trans. Pattern Analy. Mach. Intell, 21(5), pp.476~480 (1999)
- H.-P. Helfrich, "trust region method for implicit orthogonal distance regression", Numer. Algorithms, 5, pp.535~545 (1993)
- H.-P. Helfrich, "A trust region algorithm for parametric curve and surface fitting", J. Comput. Appl. Math, 73, pp.119~134 (1996)
- J. Hoschek, "Optimal approximate conversion of spline surfaces", Comput. Aided Geom. Design, 6, pp.293~306 (1989)
- "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", ~ (2001)
- D. Marshall, "Robust Segmentation of Primitives from Range Data in the Presence of Geometric Degeneracy", IEEE Trans. Pattern Analy. Mach. Intell, 23(3), pp.304~314 (2001)
- K. Pearson, "On Lines and Planes of Closest Fit to Systems of Points in Space", The Philos. Mag. ser.6, 2(11), pp.559~572 (1901)
- L. Piegl, "The NURBS Book" (1997), Springer
- F. Solina, "Recovery of Parametric Models from Range Images: The Case for Superquadrics with Global Deformations", IEEE Trans. Pattern Analy. Mach. Intell, 12(2), pp.131~147 (1990)
- D. Sourlier, "Three Dimensional Feature Independent Bestfit in Coordinate Metrology", 박사, pp.1995
- S. Sullivan, "Using Geometric Distance Fits for 3-D Object Modeling and Recognition", IEEE Trans. Pattern Analy. Mach. Intell, 16(12), pp.1183~1196 (1994)
- G. Taubin, "Estimation of Planar Curves, Surfaces, Nonplanar Space Curves Defined by Implicit Equations with Applications to Edge and Range Image Segmentation", IEEE Trans. Pattern Analy. Mach. Intell, 13(11), pp.1115~1138 (1991)
- D.A. Turner, "The approximation of Cartesian coordinate data by parametric orthogonal distance regression", 박사, pp.1999