Image processing based on partial differential equations
Speaker:Prof. Xue-cheng Tai
Professor
Department of Mathematics
University of Bergen
Date & Time:14 Mar 2011 (Monday) 10:30 - 11:30
Venue:N402
Organized by:Department of Mathematics

Abstract

In this talk, we first introduce models for image processing based on partial differential equations. This part will cover the well-known models related to ROF (total variation model), Mumford-shah model, and Euler's elastic model. Then we will give some details in using these models for image processing include: image restoration, image segmentation, noise removal and image inpainting.

In order to use these models for real industrial applications, fast numerical methods are needed. We start with the traditional gradient decent algorithms. Afterwards, we will go through some modern fast numerical schemes including: Dual algorithms, Alternating minimization algorithms, Augmented Lagrangian methods, graph cuts schemes, and some fast iterative algorithms that have been proposed recently.

Biography

Prof. Xue-cheng Tai is currently Professor of the Department of Mathematics of the University of Bergen. He obtained his PhD. Degree at the University of Jyvaskyla, Finland in 1991. Prof. Tai's research interests are in numerical mathematics, scientific computing and industrial applications. His research activities are related to Numerical PDEs (partial differential equations), optimization techniques, inverse problems, and image processing.