Strange discrete operators - A tour concerning meshless methods and image processing

12 October 2006
Prof Thomas Sonar

One of the oldest approach in meshless methods for PDEs is the Interpolating Moving Least Squares (IMLS) technique developed in the 1980s. Although widely accepted by users working in fields as diverse as geoinformatics and crack dynamics I shall take a fresh look at this method and ask for the equivalent difference operators which are generated implicitly. As it turns out, these operators are optimal only in trivial cases and are "strange" in general. I shall try to exploit two different approaches for the computation of these operators.

On the other hand (and very different from IMLS), Total Variation Flow (TVF) PDEs are the most recent developments in image processing and have received much attention lately. Again I shall show that they are able to generate "strange" discrete operators and that they easily can behave badly although they may be properly implemented.

  • Computational Mathematics and Applications Seminar