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The Mathematics of Images

THE MATHEMATICS OF IMAGES

Co-Sponsored by the MSRI (Mathematical Sciences Research Institute)

Kathryn Leonard, David Mumford
March 14-18, 2005
Mathematical Sciences Research Institute
Berkeley, CA



Present-day challenges in image analysis draw on a wide range of mathematical theories including harmonic analysis, variational calculus and PDE, geometry, statistical learning theory, and stochastic modeling. These are employed to address many issues arising in image analysis, including efficient image decomposition, image segmentation and restoration, understanding distributions of empirical image data, and formulating grammars for image construction. This subject touches many parts of the undergraduate mathematics curriculum without requiring extensive prerequisites, and thus it is natural to adapt some of the recent research in this area for presentation in those courses, as visually appealing illustrations of the basic material, and as an invitation to enter the subject.

Examples from image analysis capture the imaginations of students and naturally integrate into many mathematics courses, including differential geometry, real analysis, linear algebra, PDE, and multivariate statistics, as well as courses in signal processing, computer graphics and numerical methods. In this workshop, the organizers will provide background and seminal ideas in several initial lectures, moving on to particular problems and projects in image analysis which are accessible to students in the appropriate undergraduate courses. Additional presentations will be given by participants at a concurrent MSRI image
analysis program.

Throughout, emphasis will be placed on dealing with real data while being guided by theoretical results. As lead-in to the program, participants will be required to learn and work with Matlab, exploring image data and specific problems provided by the organizers. For more information, see the Mathematics of Images Workshop Page.



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