Lee, Lee, and Yoo propose a method for surface reconstruction based on scattered data, which is based on multilevel B-spline functions and quasi-interpolation. To be a bit more specific, the final approximation is a sum of spline functions, namely f = k &Sgr; f_i< i=0, where spline subspaces S_i (f_i ∈ S_i) are nested such that S₀ ⊂ S₁ ⊂ ... ⊂ S_k, and f_k approximates the deviation of the surface data &Dgr;^kz_i = &Dgr;^k-1z_i - f_k-1(x_i,y_i) = z_i - k-1 &Sgr; f_l(x_i,y_i) l=0 at grid point (x_i, y_i). To avoid costly global approximation, a local quasi-interpolation is suggested for each. Error estimates and computational cost are also briefly discussed. Finally, real-world examples are given showing the efficiency of multilevel approximations.

The real strength of the paper is its presentation of some interesting real-world examples of surface approximation that make multilevel approximation valuable. However, a reader will have to consult original papers on multilevel approximation and quasi-interpolation for more technical detail. Based on the same idea of using multilevel approximation, I would be interested in seeing a comparison between the suggested method (quasi-interpolation) and other local or even global approximation methods for performance and accuracy.