1. A method executed by a computer system to construct an image by generating a final approximation function f that approximates a scattered data set V, the method comprising: setting, by the computer system, a hierarchy of control lattices R 0 , R 1 ,. .. , R h , wherein R 0 is a coarsest control lattice and R h is a densest control lattice defined by a user, R k is a control lattice at level k of the hierarchy of control lattices, a spacing between control points in the control lattices is smaller from one lattice to the next; executing, by the computer system, Many-Knot (MK) Splines approximation to V with the coarsest control lattice R 0 to obtain approximation function f 0 that is a most smooth approximation function of V; calculating, by the computer system, a first deviation Δ 1 z c of f 0 for each point in V to generate a deviation data set V 1 ; performing, by the computer system, iteration steps for the control lattices from R 1 to R h to generate a sequence of approximation functions from f 1 to f h , the iteration steps comprising: for the level k of the hierarchy of control lattices, summing, by the computer system, f 0 to f k−1 to yield a smaller deviation Δ k z c for each point in V to generate a deviation data set V k ; executing, by the computer system, the Many-Knot (MK) Splines approximation with the control lattice R k to the deviation data set V k to obtain approximation function f k ; generating, by the computer system, the final approximation function f by summing f 0 to f h to construct an interpolated surface; and constructing, by the computer system, the image from the interpolated surface.