Adaptive multidimensional interpolation using regularized linear splines

Donald J. Bone

doi:10.1117/12.144759

21 May 1993 Adaptive multidimensional interpolation using regularized linear splines

Donald J. Bone

Proceedings Volume 1902, Nonlinear Image Processing IV; (1993) https://doi.org/10.1117/12.144759
Event: IS&T/SPIE's Symposium on Electronic Imaging: Science and Technology, 1993, San Jose, CA, United States

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.

Citation Download Citation

Donald J. Bone "Adaptive multidimensional interpolation using regularized linear splines", Proc. SPIE 1902, Nonlinear Image Processing IV, (21 May 1993); https://doi.org/10.1117/12.144759

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