Mathematical Sciences Research Institute - Introductory Workshop in Mathematical, Computational and Statistical Aspects of Image Analysis

The introductory workshop will be a week long and concentrate on problems in what is typically described as ``early vision'' or ``low-level vision''. By this, people mean whatever you can understand about an image as a function or a signal without introducing explicitly the origin of the image on the basis of the physics and the specific objects present in the world. We have in mind the following themes, each of which will be introduced in a series of tutorial lectures, intended at a level that could be understood by mathematicians, physical scientists or engineers with no previous background in vision
and image analysis.

1. Harmonic analysis applied to images. The last few years have seen a great deal interest in the computational harmonic analysis community on developing
approximations and expansions specifically oriented to problems in dealing with
images, for example edges and textures in images. The resulting multiscale
processing tools start with wavelets and go considerably beyond (bandelets,
curvelets, ridgelets, brushlets, etc.). There are numerous applications to
compression, denoising etc. (Candes, Mallat, Meyer, Saito, Donoho)

2. Statistics of natural images at the signal as well as morphological levels. Because of its data intensive nature, a deep study of the statistics of images lagged some 20 years behind the statistical study of speech. However, many groups are now working out many types of statistics and constructing stochastic models for various aspects of natural images. (Malik, Grenander, Ruderman, Simoncelli, Olshausen, Gousseau, Lee, van Hateren, Freeman, Mumford)

3. Contours, textures, and perceptual organization. The gestalt school of
psychophysics, from the 20.s through the 60.s, systematized in a qualitative way
the rules by which the elements of images are grouped into larger structures.
Vision scientists are now beginning to formalize these rules quantitatively. (Malik, Zhu, Morel, Moisan, Desolneux, Geman, Williams).

4. Variational approaches, partial differential equations for image analysis. These techniques date from the 80.s (Mumford-Shah/Blake-Zisserman functional, the .snakes. of Terzopoulos, Perona-Malik non-linear diffusion) and have been one of the main mathematical approaches to image processing, esp. in the schools of Osher and Morel. (Osher, Chan, Shah, Tannenbaum, Morel, Guichard, Faugeras,
Mumford, Sethian).

Lectures
Tutorial/Introductory/Survey

David Donoho (Stanford)
1. Natural Image Statistics and Bayesian Statistics, Information Theory vs. Computer Vision Perspectives
2. Image Manifolds and Image Complexes
3. Harmonic Analysis Analogies to Early Vision.
Olivier Faugeras (INRIA)
1. Fundamental PDE's of Computer Vision
2. Approaches to Image Warping and Matching
3. Shape Topologies and Applications to Segmentation
David Mumford (Brown)
1. Pattern theory: Grenander's ideas and examples.
2. Modeling shape: comparing metrics, L^1, L^2 and L^\infty techniques, the solid, liquid and conformal approaches.

Research/Advanced

1. Image representation: Eero Simoncelli (NYU)
2. Biological vision: Bruno Olshausen (Davis/RNI)
3. Seeing as Statistical Inference: Song Chun Zhu (UCLA)
4. Statistics of Grouping and Figure/Ground in Natural images: J.Malik
5. Modern Classifier design: Trevor Hastie (Stanford)
6. Towards Unsupervised Learning of Categories: Pietro Perona (Caltech)
7. Strategies for visual recognition: Donald Geman (JHU/ENS Cachan)
8. Ecological optics: Jan Koenderink
9. Energy minimization and "u+v" models: Luminita Vese (UCLA)

Schedule of Talks

Currently Available Videos

David Mumford , Pattern Theory: Grenander's Ideas and Examples January 24,2005, 09:00 AM to 10:00 AM
Olivier Faugeras , Variational Principles and PDE's of Computer Vision January 24,2005, 10:30 AM to 11:30 AM
Trevor Hastie , Modern Classifier Design January 24,2005, 10:30 AM to 11:30 AM
Pietro Perona , An Invitation to Visual Recognition January 25,2005, 09:00 AM to 10:00 AM
Donald Geman , Strategies for Visual Recognition January 25,2005, 10:30 AM to 11:30 AM
Edward Adelson , Image Statistics and Surface Perception January 25,2005, 01:30 PM to 02:30 PM
Richard Baraniuk , Multiscale Geometric Analysis for Images January 25,2005, 03:00 PM to 04:00 PM
David Mumford , Modeling Shape January 26,2005, 09:00 AM to 10:00 AM
Olivier Faugeras , Variational Methods for Multimodal Image Matching: Theory and Applications January 26,2005, 10:30 AM to 11:30 AM
David Donoho , Appearance Manifolds 2 January 26,2005, 01:30 PM to 02:30 PM
Luminita Vese , Energy Minimization for Cartoon & Texture Separation :U+V Models January 26,2005, 03:00 PM to 04:00 PM
Eero Simoncelli , Statistical Image Models January 27,2005, 09:00 AM to 10:00 AM
Bruno Olshausen , What We Know and Don't Know About Biological Vision January 27,2005, 10:30 AM to 11:30 AM
Song Chun Zhu , Seeing as Statistical Inference January 27,2005, 01:30 PM to 02:30 PM
Jitendra Malik , Ecological Statistics of Grouping and Figure-Ground Cues January 27,2005, 03:00 PM to 04:00 PM
Jan Koenderink , Ecological Optics January 28,2005, 09:00 AM to 10:00 AM
Olivier Faugeras , Variations on Image and Shape Warping, Statistics and Segmentation January 28,2005, 10:30 AM to 11:30 AM
Joachim Buhmann , Learning and Image Segmentation January 28,2005, 01:30 PM to 02:30 PM
David Donoho , More Interactions January 28,2005, 03:30 PM to 04:30 PM

You can find videos of other workshops and events on our VMath - Streaming Video page.

For more information:
Questions about this workshop should be sent either by email to

270@msri.org

or by regular mail to:

Intro Image Analysis Workshop Mathematical Sciences Research Institute 17 Gauss Way, Berkeley, CA 94720-5070. USA

The Institute is committed to the principles of Equal Opportunity and Affirmative Action.

Back to Workshop Listing

Want to be kept updated on upcoming events? Then Click Here to Subscribe to Our Newsletters!