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Splines: A Perfect Fit for Signal Processing

M. Unser

Plenary talk, Tenth European Signal Processing Conference (EUSIPCO'00), Tampere, Finland, September 4-8, 2000.



Splines, which were invented by Schoenberg more than fifty years ago, constitute an elegant framework for dealing with interpolation and discretization problems. They are widely used in computer-aided design and computer graphics, but have been neglected in signal and image processing applications, mostly as a consequence of what I call the "bad press" phenomenon. Thanks to some recent research efforts in signal processing and wavelet-related techniques, the virtues of splines have been revived in our community there is now compelling evidence (several independent studies) that splines offer the best cost-performance tradeoff among available interpolation methods.

In this talk, I will argue that the spline representation is ideally suited for all processing tasks that require a continuous model of signals or images. I will show that most forms of spline fitting (interpolation, least squares approximation, smoothing splines) can be performed most efficiently using recursive digital filters. I will discuss the connection between splines and Shannon's sampling theory. I will also look at their multiresolution properties which make them prime candidates for constructing wavelet bases and computing image pyramids. I will provide multiple illustrations of their use in image processing; these include zooming and visualization, geometric transformation, registration, contour detection, as well as snakes and contour modeling.


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