Applied Mathematics Seminar | Dominique Brunet, Image processing in metric spaces with applications to weather forecasting

Several tasks in image processing and in pattern recognition involve either the computation of the distance between two objects or the averaging of two or more objects. The k-means algorithm is the perfect prototype which combines the two tasks. A general method of performing these tasks is (image) registration. In the variational setting, registration translates to a non-linear energy minimization problem whose solution is a deformation (or velocity) field. Minimal energy provides a measure of distance whereas warping objects according to the deformation field leads to an averaging procedure. We will illustrate this framework as applied to sets in the plane,  showing four applications related to weather forecasting: computing the uncertainty of a forecast, interpolating manually drawn contours in space and time, tracking and "nowcasting" thunderstorm cells and performing object-based verification.

This talk provides the mathematical framework of Dr. Brunet's CPAMI Seminar entitled, "The MetObject approach:  Enabling man and machine intellgence,'' to be presented earlier in the day (11:00 a.m. in E5 5106/5128).  An informal working session on this and related problems in image processing is planned for after the afternoon talk.  Everyone is welcome.

Biography

Dominique Brunet received the B.Sc. (2005) and M.Sc. (2007) degrees in Mathematics from Laval University in Québec City and the Ph.D. (2012) degree in Applied Mathematics from University of Waterloo. He is currently a NSERC Visiting Fellow at the Cloud Physics and Severe Weather Research Section in Environment Canada, working at the weather radar station in King City. Previously he was a Postdoctoral Fellow in the Department of Radiation Physics at the Princess Margaret Cancer Centre in Toronto. He also briefly pursued a Postdoctoral Fellowship in the Department of Electrical and Computer Engineering at the University of Waterloo. His research interests include mathematical and statistical image processing, image approximation and compression, image quality assessment, computer vision and pattern recognition, image-guided radiation therapy, and meteorological data analysis. Dr. Brunet is a member of the SIAM Imaging Sciences group (2012-), of the SIAM Geosciences group (2015-) and of the IEEE SIgnal Processing Society (2013-).