EPFL | Biomedical Imaging Group

Spline Kernels for Continuous-Space Image Processing

S. Horbelt, A. Muñoz Barrutia, T. Blu, M. Unser

Proceedings of the Twenty-Fifth IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'00), Istanbul, Turkey, June 5-9, 2000, vol. IV, pp. 2191–2194.

We present an explicit formula for spline kernels; these are defined as the convolution of several B-splines of variable widths h and degrees n. The spline kernels are useful for continuous signal processing algorithms that involve B-spline inner-products or the convolution of several spline basis functions. We apply our results for the derivation of spline-based algorithms for two classes of problems. The first is the resizing of images with arbitrary scaling factors. The second problem is the computation of the Radon transform and of its inverse; in particular, we present a new spline-based version of the filtered backprojection algorithm for tomographic reconstruction. In both case, our explicit kernel formula allows for the use high degree splines; these offer better approximation and performance than the conventional lower order formulations (e.g., piecewise constant or piecewise linear models).

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