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21 May 1993 Adaptive multidimensional interpolation using regularized linear splines
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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.
© (1993) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
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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