Simple Algorithms and Architectures for B-spline Interpolation

We prove that the Toeplitz binary value matrix inversion associated with mth order E-spline interpolation can be implemented using only 2 (m + 1) additions. We develop pipelined architectures for real time B-spline interpolation based on simple running average filters. We also show that an ideal interpolating function, which is approximated by a truncated sinc function with M half cycles, can be implemented using B-splines with M + 2 multiplies. With insignificant loss of performance, the coefficients at the knots of the truncated sinc function can be approximated using coefficients which are powers of two. The resulting implementation requires only M + 4m + 6 additions. We believe that the truncated sinc function approximated by zero order B-spline functions actually achieves the best visual performance.