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Math of Images Outline

The Mathematics of Images
PREP Workshop Outline


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
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
The geometry of imaging: multiple cameras, inferring 3D structure with stereoscopic images R.Romano

Statistics as a tool for classifying images. Features and histograms, 3 fundamental tools in statistical pattern recognition (for use in the competition) D.Mumford
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
The geometry inside images. The set of shapes as a metric space. K.Leonard

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

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

Information theory, signals and images, coding and counting bits D.Donoho
Idea of a diffeomorphism, ‘shortest path’ from one image to another, application to stereo 3D reconstruction and to morphing D.Mumford/K.Leonard
General discussion of using images and matlab in courses, announce winners of competition