Surface approximation using weighted splines

The surface reconstruction problem is formulated as a two-stage reconstruction procedure. The first stage is a robust local fit to the data in a multiresolution scheme and the second is a regularized least squares fit, with the addition of an adaptive mechanism in the smoothness functional in order to make the solution well behaved. The authors present the details of the second stage in which they use the weighted bicubic spline as a surface representation in a regularization framework, with a Tikhonov stabilizer, as the smoothness norm. It is shown how the adaptive weights, in the stabilizer help the surface bend across discontinuities by varying the energy of the surface