References
- R.J. Adcock, “Note on the method of least squares, ” The Analyst, Des Moines, Iowa, vol.4, pp.183-184, 1877 https://doi.org/10.2307/2635777
- S.J. Ahn, W. Rauh, H.S. Cho, H.-J. Warnecke, “Orthogonal Distance Fitting of Implicit Curves and Surfaces,” IEEE Trans. Pattern Analy. Mach. Intell, vol.24, no.5, pp.620-638, 2002 https://doi.org/10.1109/34.1000237
- S.J. Ahn, E. Westkamper, W. Rauh, “Orthogonal Distance Fitting of Parametric Curves and Surfaces, ” Proc. 4th Int'l Symp. Algorithms for Approximation, J. Levesley et al. (eds.), U.K.: Univ. of Huddersfield, pp.122-129, 2002
- P.T. Boggs, R.H. Byrd, R.B. Schnabel, “A stable and efficient algorithm for nonlinear orthogonal distance regression,” SIAM J. Sci. Stat. Compt., vol.8, pp. 1052-1078, 1987 https://doi.org/10.1137/0908085
- P.T. Boggs, J.R. Donaldson, R.H. Byrd, R.B. Schnabel, “Algorithm 676 – ODRPACK: Software for Weighted Orthogonal Distance Regression,” ACM Trans. Math. Softw., vol.15, no.4, pp.348-364, 1989 https://doi.org/10.1145/76909.76913
- F.L. Bookstein, “Fitting conic sections to scattered data,” Comput. Graph. Image Process., vol.9, no.1, pp.56-71, 1979 https://doi.org/10.1016/0146-664X(79)90082-0
- B.P. Butler, A.B. Forbes, P.M. Harris, “Algorithms for Geometric Tolerance Assessment,” Report no. DITC 228/94, Teddington, U.K.: NPL, 1994
- X. Cao, N. Shrikhande, G. Hu, “Approximate orthogonal distance regression method for fitting quadric surfaces to range data,” Pattern Recogn. Lett., vol.15, no.8, pp. 781-796, 1994 https://doi.org/10.1016/0167-8655(94)90006-X
- A. Fitzgibbon, M. Pilu, R.B. Fisher, “Direct Least Square Fitting of Ellipses,” IEEE Trans. Pattern Analy. Mach. Intell, vol.21, no.5, pp.476-480, 1999 https://doi.org/10.1109/34.765658
- H.-P. Helfrich and D. Zwick, “A trust region method for implicit orthogonal distance regression,” Numer. Algorithms, vol.5, pp.535-545, 1993 https://doi.org/10.1007/BF02108668
- H.-P. Helfrich and D. Zwick, “A trust region algorithm for parametric curve and surface fitting,” J. Comput. Appl. Math., vol.73, pp.119-134, 1996 https://doi.org/10.1016/0377-0427(96)00039-8
- J. Hoschek, F.-J. Schneider, P. Wassum, “Optimal approximate conversion of spline surfaces”, Comput. Aided Geom. Design, vol.6, pp.293-306, 1989 https://doi.org/10.1016/0167-8396(89)90030-7
- 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,” Geneva, Switzerland: ISO, Dec. 2001
- D. Marshall, G. Lukacs, R. Martin, “Robust Segmentation of Primitives from Range Data in the Presence of Geometric Degeneracy,” IEEE Trans. Pattern Analy. Mach. Intell, vol.23, no.3, pp.304-314, 2001 https://doi.org/10.1109/34.910883
- K. Pearson, “On Lines and Planes of Closest Fit to Systems of Points in Space,” The Philos. Mag., ser.6, vol.2, no.11, pp.559-572, 1901 https://doi.org/10.1080/14786440109462720
- L. Piegl and W. Tiller, “The NURBS Book,” 2nd Ed., Berlin: Springer, 1997
- F. Solina and R. Bajcsy, “Recovery of Parametric Models from Range Images: The Case for Superquadrics with Global Deformations,” IEEE Trans. Pattern Analy. Mach. Intell, vol.12, no.2, pp.131-147, 1990 https://doi.org/10.1109/34.44401
- D. Sourlier, “Three Dimensional Feature Independent Bestfit in Coordinate Metrology,” Ph.D. Thesis, no. 11319, Zurich, Switzerland: ETH Zurich, 1995
- S. Sullivan, L. Sandford, J. Ponce, “Using Geometric Distance Fits for 3-D Object Modeling and Recognition,” IEEE Trans. Pattern Analy. Mach. Intell, vol.16, no.12, pp.1183-1196, 1994 https://doi.org/10.1109/34.387489
- 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, vol.13, no. 11, pp.1115-1138, 1991 https://doi.org/10.1109/34.103273
- D.A. Turner, “The approximation of Cartesian coordinate data by parametric orthogonal distance regression,” Ph.D. Thesis, U.K.: Univ. of Huddersfield, 1999
Cited by
- Ellipse Fitting Using the Finite Rate of Innovation Sampling Principle vol.25, pp.3, 2016, https://doi.org/10.1109/TIP.2015.2511580
- Surface fitting in geomorphology — Examples for regular-shaped volcanic landforms vol.221, 2014, https://doi.org/10.1016/j.geomorph.2014.06.009
- Development of an ellipse fitting method with which to analyse selected area electron diffraction patterns vol.160, 2016, https://doi.org/10.1016/j.ultramic.2015.10.009