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
Tuesday
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
Wednesday
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
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
Friday
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