BIOMEDICAL IMAGING GROUP (BIG)
Laboratoire d'imagerie biomédicale (LIB)

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). 

@INPROCEEDINGS(http://bigwww.epfl.ch/publications/horbelt0001.html,
AUTHOR="Horbelt, S. and Mu{\~{n}}oz Barrutia, A. and Blu, T. and
	Unser, M.",
TITLE="Spline Kernels for Continuous-Space Image Processing",
BOOKTITLE="Proceedings of the Twenty-Fifth {IEEE} International
	Conference on Acoustics, Speech, and Signal Processing
	({ICASSP'00})",
YEAR="2000",
editor="",
volume="{IV}",
series="",
pages="2191--2194",
address="Istanbul, Turkey",
month="June 5-9,",
organization="",
publisher="",
note="")

© 2000 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from IEEE. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.