B-Spline Signal Processing: Part II - Efficient Design and Applications

Abstract

This paper describes a class of recursive filtering algorithms for the efficient implementation of B-spline interpolation and approximation techniques. In terms of simplicity of realization and reduction of computational complexity, these algorithms compare favorably with conventional matrix approaches. A filtering interpretation (low-pass filter followed by an exact polynomial spline interpolator) of smoothing spline and least squares approximation methods is proposed. These techniques are applied to the design of digital filters for cubic spline signal processing. An efficient implementation of a smoothing spline edge detector is proposed. It is also shown how to construct a cubic spline image pyramid that minimizes the loss of information in passage from one resolution level to the next. In terms of common measures of fidelity (e.g., visual quality, SNR), this data structure appears to be superior to the widely used Gaussian/Laplacian pyramid.