# Mathematical Sciences Research Institute

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# Workshop

Introductory Workshop in Mathematical, Computational and Statistical Aspects of Image Analysis January 24, 2005 - January 28, 2005
 Registration Deadline: January 28, 2005 about 10 years ago October 24, 2004 over 10 years ago
Parent Program: Mathematical, Computational and Statistical Aspects of Image Analysis
Organizers David Donoho, Olivier Faugeras, David B Mumford
Speaker(s)

## Show List of Speakers

Description

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

Funding & Logistics

## Show Funding

To apply for funding, you must register by the funding application deadline displayed above.

Students, recent Ph.D.'s, women, and members of underrepresented minorities are particularly encouraged to apply. Funding awards are typically made 6 weeks before the workshop begins. Requests received after the funding deadline are considered only if additional funds become available.

## Show Lodging

A block of rooms has been reserved at the Rose Garden Inn. Reservations may be made by calling 1-800-992-9005 OR directly on their website. Click on Corporate at the bottom of the screen and when prompted enter code MATH (this code is not case sensitive). By using this code a new calendar will appear and will show MSRI rate on all room types available.

A block of rooms has been reserved at the Hotel Durant. Reservations may be made by calling 1-800-238-7268. When making reservations, guests must request the MSRI preferred rate. If you are making your reservations on line, please go to this link and enter the promo/corporate code MSRI123. Our preferred rate is \$129 per night for a Deluxe Queen/King, based on availability.

Additional lodging options (short term housing page - Short Term Housing

## Show Visa/Immigration

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