The Mathematics of Images
PREP Workshop Outline


Monday

9:30-11:30 am
What is the field of vision and what is its mathematical side? Outline of topics to be presented. Round table introductions and forming working groups D.Mumford
1:30-3:00 pm Images as functions I: Edges and segmentation, filters, Fourier expansions and wavelets. Part lecture, part workshop with MatLab. Introducing two vision competitions, one with texture, one with shape K.Leonard
3:30-5:00 pm The geometry of imaging: multiple cameras, inferring 3D structure with stereoscopic images R.Romano
Tuesday

9:30-11:00 am Statistics as a tool for classifying images. Features and histograms, 3 fundamental tools in statistical pattern recognition (for use in the competition) D.Mumford
1:30-3:00 pm Images as functions II: evolving an image with ‘heat-type’ PDE’s and applications to image enhancement: Part lecture, part  workshop with MatLab J.Carter
3:30-5:00 pm The geometry inside images. The set of shapes as a metric space. K.Leonard
Wednesday

9:30-11:00 am Graph theory and linear algebra as tools for image analysis.  Use of the eigenvectors of the discrete graph Laplacian to segment an image TBA
AFTERNOON Free Time; Excursion to be proposed
Thursday

9:30-11:00 am More statistical methods, Bayes’s rule, likelihood ratios, inference M.Harrison
1:30-3:00 pm Shrink wrapping shapes, the variational approach known as ‘snakes’ TBA
3:00-? pm Free time to work on course material and the competition
Friday

9:30-11:00 am Information theory, signals and images, coding and counting bits D.Donoho
1:30-3:00 pm Idea of a diffeomorphism, ‘shortest path’ from one image to another, application to stereo 3D reconstruction and to morphing D.Mumford/K.Leonard
3:30 – 5:30 pm
General discussion of using images and matlab in courses, announce winners of competition