Spline kernels for continuous-space image processing

We present an explicit formula for spline kernels; these are defined as the convolution of several B-splines of variable widths hi and degrees ni. The spline kernels are useful for continuous signal processing algorithms that involve Bspline inner-products or the convolution of several spline basis functions. We apply our results to the derivation of spline-based algorithms for two classes of problems. The first is the resizing of images with arbitrary scaling factors. The second 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 cases, our explicit kernel formula allows for the use of high-degree splines; these offer better approximation performance than the conventional lower-order formulations (e.g., piecewise constant or piecewise linear models). keywords: spline kernel, anti-aliasing, resizing, Radon transform, filtered back-projection