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