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Splines: A Unifying Framework for Signal and Image Processing

M. Unser

Plenary talk, Fifth IASTED International Conference on Signal Processing, Pattern Recognition, and Applications (SPPRA'08), Innsbruck, Republic of Austria, February 13-15, 2008.



Our purpose is to justify the use splines in signal processing and imaging applications, emphasizing their ease of use, as well as their fundamental properties. In particular, we will describe efficient digital filtering algorithms for the interpolation and spline-based processing of signals and images. We will show that splines are intimately linked to differentials and identify B-splines as the exact mathematical translators between the discrete and continuous versions of the (scale-invariant) operator. This partly explains why these functions play such a fundamental role in wavelet theory. Splines may also be justified on variational and/or statistical grounds; e.g., they provide Wiener (i.e, MMSE) estimators for fractal processes such as fractional Brownian motion. We will illustrate spline processing with applications in biomedical imaging where its impact has been the greatest so far. Specific tasks include high-quality interpolation, snakes, and various types of image registration.


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