Distinguished speaker series: Professor Michael Unser
Title: Beyond the digital divide - Ten good reasons for using splines
"Think analog, act digital" is a motto that is relevant to scientific computing and algorithm design in a variety of disciplines, including numerical analysis, image/signal processing, and computer graphics. Here, we will argue that cardinal splines constitute a theoretical and computational framework that is ideally matched to this philosophy, especially when the data is available on a uniform grid. We show that multidimensional spline interpolation or approximation can be performed most efficiently using recursive digital filtering techniques.
We highlight a number of "optimal" aspects of splines (in particular, polynomial ones) and discuss fundamental relations with: (1) Shannon's sampling theory, (2) linear system theory, (3) wavelet theory, (4) regularization theory, (5) estimation theory, and (6) stochastic processes (in particular, fractals). The practicality of the spline framework is illustrated with concrete image processing examples; these include derivative-based feature extraction, high-quality rotation and scaling, and (rigid body or elastic) image registration.
About the speaker
Michael Unser is Professor and Director of EPFL's Biomedical Imaging Group, Lausanne, Switzerland. His main research area is biomedical image processing. He has a strong interest in sampling theories, multiresolution algorithms, wavelets, and the use of splines for image processing. He has published over 150 journal papers on those topics, and is one of ISI's Highly Cited authors in Engineering (http://isihighlycited.com).
From 1985 to 1997, he was with the Biomedical Engineering and Instrumentation Program, National Institutes of Health, Bethesda USA, conducting research on bioimaging and heading the Image Processing Group. Dr. Unser is a fellow of the IEEE, a member of the Swiss Academy of Engineering Sciences, and the recipients of three IEEE-SPS Best Paper Awards. He was recently elevated to EURASIP Fellow (2009) and selected to receive the Technical Achievement Award from the IEEE Signal Processing Society.