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Splines and Wavelets: New Perspectives for Pattern Recognition

M. Unser

Plenary talk, Proceedings of the Twenty-Fifth Pattern Recognition Symposium (DAGM'03), Magdeburg (Sachsen-Anhalt), Federal Republic of Germany, September 10-12, 2003, [Pattern Recognition, Lecture Notes in Computer Science, vol. 2781, B. Michaelis, G. Krell, Eds., Springer, 2003], pp. 244-248.


We provide an overview of spline and wavelet techniques with an emphasis on applications in pattern recognition. The presentation is divided in three parts. In the first one, we argue that the spline representation is ideally suited for all processing tasks that require a continuous model of the underlying signals or images. We show that most forms of spline fitting (interpolation, least-squares approximation, smoothing splines) can be performed most efficiently using recursive digital filtering. We also discuss the connection between splines and Shannon's sampling theory. In the second part, we illustrate their use in pattern recognition with the help of a few examples: high-quality interpolation of medical images, computation of image differentials for feature extraction, B-spline snakes, image registration, and estimation of optical flow. In the third and last part, we discuss the fundamental role of splines in wavelet theory. After a brief review of some key wavelet concepts, we show that every wavelet can be expressed as a convolution product between a B-spline and a distribution. The B-spline constitutes the regular part of the wavelet and is entirely responsible for its key mathematical properties. We also describe fractional B-spline wavelet bases, which have the unique property of being continuously adjustable. As the order of the spline increases, these wavelets converge to modulated Gaussians which are optimally localized in time (or space) and frequency.

@INPROCEEDINGS(http://bigwww.epfl.ch/publications/unser0306.html,
AUTHOR="Unser, M.",
TITLE="Splines and Wavelets: {N}ew Perspectives for Pattern
	Recognition",
BOOKTITLE="Proceedings of the Twenty-Fifth Pattern Recognition Symposium
	({DAGM'03})",
YEAR="2003",
editor="Michaelis, B. and Krell, G.",
volume="2781",
series="Lecture Notes in Computer Science",
pages="244--248",
address="Magdeburg (Sachsen-Anhalt), Federal Republic of Germany",
month="September 10-12,",
organization="",
publisher="Springer",
note="Plenary talk")

© 2003 DAGM e. V. 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 DAGM e. V. 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.
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