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Proceedings Paper

Adaptive multidimensional interpolation using regularized linear splines
Author(s): Donald J. Bone
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Paper Abstract

An adaptive multi-dimensional interpolation technique for irregularly gridded data based on a regularized linear spline is described. The regularization process imposes a penalty or energy function which depends upon a sum of quadratic functions of the error at the data points and the gradient and curvature of the surface. The weighting of a given term in the penalty function is made to depend non-linearly on the first and second differences in the regularly gridded interpolation of the data. As a result the method is able to provide an interpolation which is sensitive to the local behavior of the data being interpolated. For example, data containing a discontinuity or crease can be smoothed to reduce noise without smoothing the discontinuity or crease. For the 2-D problem, the technique is analogous to a rectangular grid of stiff extensible rods defining an interpolation surface, with springs resisting: the displacement of the surface from the known data values; the extension of the rods, and the bending of one rod with respect to another. The weights in the penalty function are equivalent to a non-linear spring characteristic for which the spring constant is reduced at large displacements. For a given set of weights, the penalty function is quadratic. This leads to a set of linear equations which can be solved efficiently using iterative techniques. Implementations of the technique for irregular 2-D and 3-D data are described and results are presented.

Paper Details

Date Published: 21 May 1993
PDF: 11 pages
Proc. SPIE 1902, Nonlinear Image Processing IV, (21 May 1993); doi: 10.1117/12.144759
Show Author Affiliations
Donald J. Bone, CSIRO (Australia)

Published in SPIE Proceedings Vol. 1902:
Nonlinear Image Processing IV
Edward R. Dougherty; Jaakko T. Astola; Harold G. Longbotham, Editor(s)

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