Bivariate splines on hexagonal lattice for digital image processing

In this paper, the applications of multi-variable spline functions in the digital signal processing was investigated further. Several two-dimensional spline functions were constructed for hexagonal lattice. They are actually variation of bivariate cardinal splines on regular triangular partition that were constructed earlier. Those bivariate cardinal splines have a number of desirable features which make it applicable for image processing and other areas. One feature lies in the fact that the coefficients of the interpolation representations with bivariate cardinal splines are basically the sample data at the interpolation points. The interpolations converge uniformly to the function being interpolated as the sampling increment approaches zero. Compare to the popular tensor product with the same degree of smoothness, our bivariate cardinal splines has the same degree of accuracy with smaller local support, lower degree of the polynomials. Therefore it should lead to the reduction of computation time and storage space.