A new free-form surface fitting method for precision coordinate metrology

Free-form surfaces are widely used in advanced optical and mechanical devices. In order to assess the form accuracy of free-form surfaces, it is needed to fit the measurement surface with the design template. To improve the fitting efficiency and accuracy, the fitting procedure is divided into two stages, rough fitting and final fitting. A new rough fitting method, called structured region signature is proposed. Structured region signature is a generalised global feature which represents the surface shape by a one-dimensional function. The template location occupying the best fitting signature is considered to be the correct initial position of the measurement surface. In the final fitting, the motion parameters are calculated iteratively using the Levenberg-Marquardt algorithm. Simulation and experiments are given to identify the validity of this method. It is demonstrated that the fitting accuracy is as high as 1:106.

[1]  Les A. Piegl,et al.  The NURBS book (2nd ed.) , 1997 .

[2]  Andrew W. Fitzgibbon.  Robust registration of 2D and 3D point sets , 2003, Image Vis. Comput..

[3]  T. C. Chang,et al.  Graph-based heuristics for recognition of machined features from a 3D solid model , 1988 .

[4]  Lisa M. Brown,et al.  A survey of image registration techniques , 1992, CSUR.

[5]  H. Groemer.  Geometric Applications of Fourier Series and Spherical Harmonics , 1996 .

[6]  William H. Press,et al.  Numerical recipes in C , 2002 .

[7]  Chin Seng Chua,et al.  Point Signatures: A New Representation for 3D Object Recognition , 1997, International Journal of Computer Vision.

[8]  Martin D. Buhmann,et al.  Radial Basis Functions: Theory and Implementations: Preface , 2003 .

[9]  Naoufel Werghi,et al.  Aligning Arbitrary Surfaces using Pairwise Geometric Histograms , 1998, NMBIA.

[10]  Sreenivas Rangan Sukumar,et al.  Curvature Variation as Measure of Shape Information , 2004 .

[11]  J. Mason,et al.  Algorithms for approximation , 1987 .

[12]  Sandy To,et al.  Measuring ultra-precision freeform surfaces using a robust form characterization method , 2006 .

[13]  W. Grimson,et al.  Model-Based Recognition and Localization from Sparse Range or Tactile Data , 1984 .

[14]  Les A. Piegl,et al.  The NURBS Book , 1995, Monographs in Visual Communication.

[15]  Leonidas J. Guibas,et al.  Robust global registration , 2005, SGP '05.

[16]  Russell H. Taylor,et al.  Automatic Synthesis of Fine-Motion Strategies for Robots , 1984 .