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Biometrika 1994 81(2):247-258; doi:10.1093/biomet/81.2.247
© 1994 by Biometrika Trust
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Fast computation of a discretized thin-plate smoothing spline for image data

M. J. BUCKLEY

CSIRO Division of Mathematics and Statistics, Locked Bag 17 North Ryde, New South Wales 2113, Australia

This paper describes a fast method of computation for a discretized version of the thin-plate spline for image data. This method uses the Discrete Cosine Transform and is contrasted with a similar approach based on the Discrete Fourier Transform. The two methods are similar from the point of view of speed, but the errors introduced near the edge of the image by use of the Discrete Fourier Transform are significantly reduced when the Discrete Cosine Transform is used. This is because, while the Discrete Fourier Transform implicitly assumes periodic boundary conditions, the Discrete Cosine Transform uses reflective boundary conditions. It is claimed that the Discrete Cosine Transform may profitably be used in place of the Discrete Fourier Transform in a variety of image processing applications besides spline smoothing.

Key Words: Diagonalization • Discrete Cosine Transform • High-dimensional smoothing • Image smoothing • Laplacian spline • Thin-plate spline


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