Surface shape and curvature scales
Image and Vision Computing
Data point selection for piecewise linear curve approximation
Computer Aided Geometric Design
Least squares surface approximation using multiquadrics and parametric domain distortion
Computer Aided Geometric Design
Repeated Knots in Least Squares Multiquadric Functions
Geometric Modelling, Dagstuhl, Germany, 1993
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Data reduction is a basic tool when a huge amount of data is given, and so it is extremely useful in surface approximation. In this paper we consider such a problem in the case of gridded data, and we propose the use of a two-stage approach in order to have a remarkable data reduction and, at the same time, a good approximation of the given data. In the first stage, a significant set of points is selected through a sampling strategy solving a suitable nonlinear system by means of the iterative Jacobi method. In the second stage, the least-squares approximating surface is computed using a "generalization" of the well known inverse multiquadric basis functions. Numerical results are given to show the performance of the method.