Wiener Splines

Abstract

We describe an alternative way of constructing interpolating B-spline curves, surfaces or volumes in Fourier space which can be used for visualization. In our approach the interpolation problem is considered from a signal processing point of view and is reduced to finding an inverse B-spline filter sequence. The Fourier approach encompasses some advantageous features, such as successive approximation, compression, fast convolution and hardware support. In addition, optimal Wiener filtering can be applied to remove noise and distortions from the initial data points and to compute a smooth, least-squares fitting "lq Wiener spline". Unlike traditional fitting methods, the described algorithm is simple and easy to implement. The performance of the presented method is illustrated by some examples showing the restoration of surfaces corrupted by various types of distortions.