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Mathematics Colloquium


Date:  Tuesday, November 01, 2011

Title:  Baldwin Prize Award Colloquium: Topics in PDE based image processing

Abstract:  In the first part of the talk, I will describe new, efficient and accurate algorithms for computing certain area preserving geometric motions of curves in the plane. These algorithms alternate two very simple and fast operations, namely convolution with the Gaussian kernel and construction of the signed distance function, to generate the desired geometric flow in an unconditionally stable manner. I will present applications to large scale simulations of coarsening, and to inverse problems from medical imaging. Joint work with Selim Esedoglu and Je rey Fessler. In the second part of the talk, I will present rigorous results on the coarsening rate of a class of high-order, ill-posed diffusion equations from image processing. The fourth order version of these equations constitutes the main motivation, since it corresponds to a well known model in the image denoising literature that was proposed by You and Kaveh: It is used to denoise images while maintaining sharp object boundaries (edges), and was intended to be an improved version of the famous Perona-Malik equation. I will follow a technique by Kohn and Otto to establish rigorous upper bounds on the coarsening rate of these high order equations in any space dimension, and for a large class of diff usivities.

Speaker:  Catherine  Kublik
Institution:  Univ of Teaxs


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