Surface smoothing with finite elements

摘要

Spline smoothing is a very good technique to fit a surface to a noisy scattered data set. Surface splines are obtained while minimizing a rotation invariant inner product in an Hilbert space. When the sampling size N is very large, the surface splines are very hard to determine numerically and don't provide any data compression. An approximate solution of the spline smoothing problem, given by finite elements can be very useful to reduce the dimension. Bicubic splines are, for this problem, very efficient piecewise bicubic rectangular finite elements.