A fast method for global surface interpolation

A fast algorithm is presented for a globally smooth interpolation for a visual surface from scattered range data. This method is based on matching lower order spatial moments, where the reconstructed surface is given by a linear combination of Legendre polynomials. This method can handle data that do not lie on a regular grid. The value of the function at points where the grid is not defined, or where the original data is missing, can be approximated from the constituent polynomials. Some simulation experiments evaluate the performance of the proposed scheme. An arbitrarily shaped surface is shown on a 35×35 grid, and the depth information is available only at a few selected grid points. The result of the implementation of Grimson´s (1981) algorithm where the surface is constrained to pass through the given data set is given. The proposed method runs much faster than Grimson´s algorithm. The coefficients of the Legendre polynomials can be precomputed