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
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