A computer system executes hierarchical MK splines for scattered data approximation. The computer system constructs an image by generating a final approximation function that approximates a scattered data set with a hierarchy of control lattice from coarsest to densest. The method includes executing MK splines approximation to the scattered data set with the hierarchy of control lattice to iteratively obtain approximation functions. The image is constructed by generating the final approximation function to construct an interpolated surface.