Efficient application of B-Spline to enlargement or reduction of digital images

In order to realize the enlargement or reduction of digital images efficiency, an algorithm based on B-Spline is derived here. First the expressions for the z-transformation of the sampled B-Spline functions are determined and some convolution properties of these kernels are established. Based on these recursive convolution properties, then a fast recursive filtering algorithm for the efficient implementation of B-Spline interpolation and approximation is found. That is, a B-Spline interpolation is characterized by its transfer function and its impulse response. In terms of simplicity of realization and reduction of computational complexity, this algorithm is compared favourably with conventional matrix techniques. The cubic B-Spline is discussed in detail. By experiment we conclude that this B-Spline interpolation algorithm can be performed efficiently.