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Fall 2000
IMA Workshop
Image Processing and Low Level Vision
October 16-20, 2000


Image Processing and Low Level Vision

October 16-20, 2000

with partial support by The Office of Naval Research

Organizers:

Allen Tannenbaum
Department of Computer and Electrical Engineering
University of Minnesota

tannenba@ee.umn.edu

Peter Olver
School of Mathematics
University of Minnesota

olver@math.umn.edu

Donald E. McClure
Department of Applied Mathematics
Brown University

Donald_McClure@Brown.edu

Pietro Perona
Department of Electrical Engineering
Caltech

perona@its.caltech.edu

 


Recent years have seen significant advances in the application of sophisticated mathematical theories to the problems arising in image processing. As yet, even very low level visual processing by computers remains a challenging problem. Both planar and three-dimensional images are of importance, and these arise in a wide variety of applications, including medical imagery---ultrasound, nuclear magnetic resonance, X-ray computed topography, etc.--- military and industrial imaging, and film restoration and animation. Basic issues include image smoothing and denoising, image enhancement, morphology, image compression, segmentation (determining boundaries of objects--- including problems of camera distortion and partial occlusion). Several mathematical approaches have emerged, including methods based on nonlinear partial differential equations, stochastic and statistical methods, and signal processing techniques, including wavelets and other transform theories. Partial differential equations are used to describe the evolution of shapes under curvature-controlled diffusions, providing a multi-scale representation that is based upon curvature flows of fundamental importance in differential geometry. These methods have proven successful in noise reduction while maintaining edge retention. Applications to segmentation are based on a variational formulation of the method of "snakes" or moving contours, in which an initial contour converges to the object boundary via a gradient descent flow based on a conformally Riemannian metric. Wavelets have applications to practical image compression methods, and texture characterization. Statistical methods such as the EM algorithm have been successfully applied to a variety of low level vision problems. A primary goal of this workshop is to educate and interest mathematicians in the mathematical and scientific problems that arise in basic image processing.

WORKSHOP SCHEDULE

Monday Tuesday
MONDAY, OCTOBER 16
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
8:30 am Coffee and Registration

Reception Room EE/CS 3-176

9:10 am Willard Miller, Fred Dulles, and Peter Olver Introduction
9:30 am Tony F. Chan
UCLA
A Level Set Framework for Active Contours and Mumford-Shah Segmentation
10:30 am Break Reception Room EE/CS 3-176
11:00 am-12:00 pm Alan S. Willsky
MIT
Multiresolution Stochastic Models and Their Use in Modeling and Analysis of Random Processes and Fields
2:00 pm-3:00 pm Donald E. McClure
Brown University
Restoration and Reformatting of Motion Images
4:00 pm IMA Tea IMA East, 400 Lind Hall A variety of appetizers and beverages will be served.
TUESDAY, OCTOBER 17
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
9:15 am Coffee Reception Room EE/CS 3-176
9:30 am Stanley Osher
UCLA
Level Set/PDE Based Algorithms for Image restoration, Surface Interpolation, and PDE's on General Manifolds
10:30 am Break Reception Room EE/CS 3-176
11:00 am-12:00 pm Stephane Mallat
Ecole Polytechnique, Courant Institute
Geometrical Image Representations with Bandelets
2:00 pm David Mumford
Brown University
Modeling the Full Statistics of Local Image Patches
3:00 pm Break Reception Room EE/CS 3-176
3:30-4:30 pm Anthony Yezzi
Georgia Institute of Technology
Variational Methods for Image Segmentation, Smoothing, Interpolation, Magnification, Stereo Matching, and Shape from Shading
WEDNESDAY, OCTOBER 18
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
9:15 am Coffee Reception Room EE/CS 3-176
9:30 am Olivier Faugeras
INRIA/MIT

Dynamic Shapes of Arbitrary Dimension: The Vector Distance Functions

Slides

10:30 am Break Reception Room EE/CS 3-176
11:00 am-12:00 pm David Donoho
Stanford University
Harmonic Analysis Perspective on Geometric Diffusions and Low level Vision
2:00 pm Stefano Soatto
UCLA and Washington University
Accommodation as a Low-Level Visual Cue
THURSDAY, OCTOBER 19
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
9:15 am Coffee Reception Room EE/CS 3-176
9:30 am Steven Haker
Yale University School of Medicine
Non-distorting Flattening for Virtual Colonoscopy
10:30 am Break Reception Room EE/CS 3-176
11:00 am-12:00 pm Ingrid C. Daubechies
Princeton University
Tree Approximation and Image Compression
2:00 pm Ilya Pollak
Purdue University
Some New Results on Optimality and Complexity of PDE-Based Segmentation Algorithms
2:40 pm Break Reception Room EE/CS 3-176
3:10-3:50 pm Marcelo Bertalmio
University of Minnesota
Image Inpainting and High Order PDE's in Image Processing
4:15-5:30 pm Tour
Daniel Kersten's Computational Vison Lab
518 Eliot Hall
6:00 pm Workshop Dinner Caspian Restaurant
FRIDAY, OCTOBER 20
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
9:15 am Coffee Reception Room EE/CS 3-176
9:30 am Bart M. ter Haar Romeny
Utrecht University
Front-End Vision and Multiscale Image Analysis (a new tutorial book.)
10:30 am Break Reception Room EE/CS 3-176
11:00-11:40 am Madjid Allili
Georgia Institute of Technology
Cubical Homology Theory and Applications in Image Processing and Computer Vision

Talk    pdf    postscript

Contributed Talks
Lind Hall 409

2:00 pm Eric Pauwels
CWI (Netherlands)
Segmentation Based on Distribution-free Statistics
2:30 pm Josh Zeevi
Technion
Generalized Gabor-type and Wavelet-type Schemes and their Applications
3:00 pm

Nir Sochen
Tel Aviv University

Gabor-type Snakes
3:30 pm Selim Esedoglu
IMA
An Analysis of the Peron-Malik Scheme
4:00-4:30 pm Haomin Zhou
UCLA
Adaptive ENO-wavelets for Image Compression
Monday Tuesday

LIST OF CONFIRMED PARTICIPANTS

as of 10/13/2000
Name Department Affiliation
Mark Alber Mathematics University of Notre Dame
Madjid Allili Mathematics Georgia Institute of Technology
Ery Arias-Castro Statistics Stanford University
Amir Averbuch Computer Science Tel Aviv University
Piero Barone Istituto per le Applicazioni del Calcolo Consiglio Nazionale delle Ricerche (CNR)
Sebastiano Battiato AST - Catania Lab STMicroelectronics
Bertalmio Marcelo Electrical and Computer Engineering University of Minnesota
Antonin Chambolle CEREMADE Universite de Paris-Dauphine
Tony F.C. Chan Mathematics UCLA
Alessandro Chiuso Electrical Engineering University of Padova
Shuli Cohen Shwartz U.C.G. Technologies Ltd. The Technion Enterpreneurial Incubator Co.
Nicholas Coult Mathematics Augsburg College
Ingrid C. Daubechies Mathematics Princeton University
David Donoho Statistics Stanford University
Fred Dulles   Institute for Mathematics & its Applications
Olivier Faugeras Sophia Antipolis Research Unit INRIA
Juan Gispert Medical Imaging Laboratory Hospital Universitario Gregorio Maranon
Jack Goldfeather Mathematics and Computer Science Carleton College
Bernard Goulard Centre de Recherches Mathematiques Universite de Montreal
Steven Haker Image Processing and Analysis Group Yale University School of Medicine
John Hoffman Maritime Surveillance Aircraft Lockheed Martin
David Jacobs   NEC Research Institute
Josef Keller Engineering Tel Aviv University
Jean-Marc Lina Centre de Recherches Mathematiques University of Montreal
Bradley Love Laboratory of Survival and Longevity Max Planck Institute for Demographic Research
Stephane Mallat   Ecole Polytechnique
Massimo Mancuso AST - Catania Lab STMicroelectronics
Riccardo March Istituto per le Applicasioni del Calcolo (IAC) Consiglio Nazionale delle Ricerche (CNR)
Donald E. McClure Applied Mathematics Brown University
Peter McCoy Mathematics U.S. Naval Academy
Willard Miller   Institute for Mathematics & its Applications
David Mumford Applied Mathematics Brown University
Peter Olver Mathematics University of Minnesota
Stanley Osher Mathematics UCLA
Daniel N. Ostrov   Santa Clara University
Javier Pascau Medical Imaging Laboratory Hospital Universitario Gregorio Maranon
Eric Pauwels PNA4 Centre for Mathematics and Information Science
Ilya Pollak Electrical and Computer Engineering Purdue University
Fadil Santosa   IMA and MCIM
Otmar Scherzer Institute for Industrial Mathematics University of Linz
Erik Schlicht Psychology University of Minnesota
Kevin Schweiker Engineering Freestyle Technologies, Inc.
Michael Israel Sigal Mathematics University of Toronto
Stefano Soatto Electrical Engineering Washington University
Nir Sochen Applied Mathematics Tel-Aviv University
Allen Tannenbaum Electrical & Computer Engineering Georgia Institute of Technology
Bart M. ter Haar Romeny Image Sciences Institute University Medical Center
Richard Tsai Mathematics UCLA
Ranga Vatsavai Remote Sensing & GIS Lab University of Minnesota
Luminita Aura Vese Mathematics University of California
Curtis Vogel Mathematical Science Montana State University
Alan S. Willsky Electrical Engineering & Computer Science MIT
Anthony Yezzi Electrical Engineering & Computer Science Georgia Institute of Technology
Y.Y. Zeevi Computer Science & Eolectrical Eng. Technion-Israel Institute of Technology
Haomin Zhou Applied Mathematics Caltech

 

2000-2001 Program: Mathematics in Multimedia

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