WORKSHOP ON

DISCRETE TOMOGRAPHY
AND ITS APPLICATIONS
 June 13-15, 2005
New York City

 





Organizers

Gabor T. Herman
Department of Computer Science
The Graduate Center
City University of New York
365 Fifth Avenue
New York, NY 10016
USA
e-mail: gabortherman at yahoo.com

Attila Kuba
Department of Computer Graphics and Image Processing
University of Szeged
Árpád tér 2.
H-6720 Szeged
Hungary
e-mail: kuba at inf.u-szeged.hu

 




Administrator

Lajos Rodek
Department of Computer Science
The Graduate Center
City University of New York
365 Fifth Avenue
New York, NY 10016
USA
e-mail: rodek at inf.u-szeged.hu

 




Venue

The meeting took place at the The Graduate Center of the City University of New York 
(365 Fifth Avenue, New York, NY 10016, USA, on the opposing corner from the Empire State Building)
in the well-equiped and beautifully appointed Elebash Recital Hall.

 


Subject Matter

We assume that there is a domain, which may itself be discrete (such as a set of ordered pairs of integers)
or continuous (such as Euclidean space). We further assume that there is an unknown function f whose
range is known to be a given discrete set (usually of real numbers). The problems of discrete tomography,
as we perceive the field, have to do with determining f (perhaps only partially, perhaps only approximately)
from weighted sums over subsets of its domain in the discrete case and from weighted integrals over
subspaces of its domain in the continuous case. In many applications these sums or integrals may be known
only approximately. From this point of view, the most essential aspect of discrete tomography is that knowing
the discrete range of f may allow us to determine its value at points where without this knowledge it could not
be determined. Discrete tomography is full of mathematically fascinating questions and it has many interesting
applications.

Further details can be obtained by looking at
DISCRETE TOMOGRAPHY: Foundations, Algorithms and Applications
(Edited by Gabor T. Herman and Attila Kuba)
Birkhäuser Boston, 1999


Schedule

The workshop reception was held in the Lobby of the Elebash Recital Hall on June 13 between 6:00 PM - 7:00 PM.

 

There was an optional conference dinner on June 14 from 7:00 PM in the razil Brazil Churrascaria at the cost of $75 per person, including drinks..
 
June 13
 
registration and opening (9:30 - 10:00)
 

Foundations of DT I.

 
10:00 - 10:30
1. Gardner: Discrete Point X-Rays of Convex Lattice Sets
10:30 - 11:00
2. Hajdu: Unique Reconstruction of Bounded Sets in Discrete Tomography
 
coffee (11:00 - 11:30)
 

Foundations of DT II.

 
11:30 - 12:00
3. Kaneko: Structure of Total Reconstructed Sets from Given Two Projection Data
12:00 - 12:30
4. Zopf: Reconstruction of Measurable Sets from Two Generalized Projections
12:30 - 1:00
5. Daurat: Determination of Q-convex Bodies by X-Rays
 
lunch (1:00 - 2:00)
 

Foundations of DT III.

 
2:00 - 2:30
6. Dahl: Matrices of Zeros and Ones with Given Line Sums and a Zero Block
2:30 - 3:00
7. Picouleau: Reconstructing a Binary Matrix under Timetabling Constraints
3:00 - 3:30
8. Vallejo: Minimal Matrices and Discrete Tomography
 
coffee ( 3:30 - 4:00)
 

Connections of DT with Other Mathematical Fields I.

 
4:00 - 4:30
9. D'Ariano: Quantum Tomography for Imaging
4:30 - 5:00
10. Grassl: Tomography of Quantum States in Small Dimensions
5:00 - 5:30
11. Roetteler: Solution to the Mean King's Problem in Prime Power Dimensions using Discrete Tomography
5:30 - 6:00
12. Huck/Langfeld: Discrete Tomography of Mathematical Quasicrystals: A Primer
 
reception in the Lobby of the Elebash Recital Hall (6:00 - 7:00)
 
 
 
June 14
 

Connections of DT with Other Mathematical Fields II.

 
9:30 - 10:00
13. Severini: On the X-rays of Permutations
10:00 - 10:30
14. Kazantsev: Optimal Ordering of Projections using Permutation Matrices and Angles between Projection Subspaces
10:30 - 11:00
15. Imiya: Tomography on Finite Graphs
 
coffee (11:00 - 11:30)
 

DT Reconstruction Algorithms I.

 
11:30 - 12:00
16. Brimkov: Exact Image Reconstruction from a Single Projection through Real Computation
12:00 - 12:30
17. Batenburg: A New Algorithm for 3D Binary Tomography
12:30 - 1:00
18. Capricelli: Parallel Block-Iterative Reconstruction Algorithms for Binary Tomography
 
lunch ( 1:00 - 2:00)
 

DT Reconstruction Algorithms II.

 
2:00 - 2:30
19. Costa: Reconstruction of Binary Matrices under Adjacency Constraints
2:30 - 3:00
20. Ruskó: Multi-Resolution Method for Binary Tomography
3:00 - 3:30
21. Weber: Prior Learning and Convex-Concave Regularization of Binary Tomography
 
coffee ( 3:30 - 4:00)
 

DT Reconstruction Algorithms III.

 
4:00 - 4:30
22. Balázs: Reconstruction of Discrete Sets from Four Projections: Strong Decomposability
4:30 - 5:00
23. Kuba: An Efficient Algorithm for Reconstructing Binary Matrices from Horizontal and Vertical Absorbed Projections
5:00 - 5:30
24. Schüle: Adaptive Reconstruction of Discrete-Valued Objects from Few Projections
5:30 - 6:00
25. Kiss: DIRECT: DIscrete REConstruction Techniques
 
dinner ( 7:00 - )
 
 
 
June 15
 

Applications of DT I.

 
9:30 - 10:00
26. Liao: Discrete Tomography with a Very Few Views, using Gibbs Priors and a Marginal Posterior Mode Approach
10:00 - 10:30
27. Alpers: Resolving Ambiguities in Reconstructed Grain Maps using Discrete Tomography
10:30 - 11:00
28. Herman: Discrete Tomographic Reconstruction of 2D Polycrystal Orientation Maps From X-Ray Diffraction Projections Using Gibbs Priors
 
coffee (11:00 - 11:30)
 

Applications of DT II.

 
11:30 - 12:00
29. Krimmel: Discrete Tomography for Reconstruction from Limited View Angles in Non-Destructive Testing
12:00 - 12:30
30. Rodek: Reconstruction of Pixel-Based and Geometric Objects by Discrete Tomography. Simulation and Physical Experiments
12:30 - 1:00
31. Schillinger: Proposed Combination of CAD Data and Discrete Tomography for the Detection of Coking and Lubricants in Turbine Blades or Engines
 
lunch ( 1:00 - 2:00)
 

Applications of DT III.

 
2:00 - 2:30
32. Gérard: Application of a Discrete Tomography Algorithm to Computerized Tomography
2:30 - 3:00
33. Nagy, A.: Reconstruction of Factor Structures using Discrete Tomography Method
3:00 - 3:30
34. Zdunek: Detection of Subsurface Bubbles with Discrete Electromagnetic Geotomography
 
coffee ( 3:30 - 4:00)
 

Connections of DT with Other Mathematical Fields III.

 
4:00 - 4:30
35. Sharif: Discrete Tomography in Discrete Deconvolution: Deconvolution of Binary Images using Ryser's Algorithm
4:30 - 5:00
36. Nagy, B.: An Algorithm to Find the Number of the Digitizations of Discs with a Fixed Radius
5:00 - 5:30
37. Servières: The Mojette Transform: Discrete Angles for Tomography
 
closing ( 5:30 - 5:40)



Special session after the closing (science in action, as captured by Barbara Langfeld)




 


Registrants

Name

University/Company

Town

Country

A. Alpers

Cornell Univ.

Ithaca, NY

USA

P. Balázs

Univ. Szeged

Szeged

Hungary

R.P. Barneva

State Univ. New York

Fredonia, NY

USA

K.J. Batenburg

Leiden Univ.

Leiden

The Netherlands

V.E. Brimkov

Fairmont State University

Fairmont, WV

USA

L.G. Butler

Louisiana State Univ.

Baton Rouge, LA

USA

T.D. Capricelli

Univ. Paris 6

Paris

France

L. Cavalier

Univ. Provence

Marseille

France

M.T. Chan

GE Global Research

Niskayuna, NY

USA

W. Chen

Grad. Center, CUNY

New York, NY

USA

P.L. Combettes

Univ. Paris 6

Paris

France

M.-C. Costa

Cedric-CNAM

Paris

France

G. Dahl

Univ. Oslo

Oslo

Norway

G.M. D'Ariano

Univ. Pavia

Pavia

Italy

A. Daurat

Univ. Strasbourg

Strasbourg

France

R. Davidi

Grad. Center, CUNY

New York, NY

USA

J. Dubowy

Grad. Center, CUNY

New York, NY

USA

R.J. Gardner

Western Washington Univ.

Bellingham, WA

USA

E. Garduno

Univ. of California

San Diego, CA

USA

Y. Gerard

Univ. Auvergne

Aubiere

France

M. Grassl

Univ. Karlsruhe

Karlsruhe

Germany

L. Hajdu

Univ. Debrecen

Debrecen

Hungary

G.T. Herman

Grad. Center, CUNY

New York, NY

USA

C. Huck

Univ. Bielefeld

Bielefeld

Germany

A. Imiya

Chiba Univ.

Chiba

Japan

A. Jain

Johns Hopkins Univ.

Baltimore, MD

USA

A. Kaneko

Ochanomizu Univ.

Tokyo

Japan

I. Kazantsev

Univ. Pennsylvania

Philadelphia, PA

USA

Z. Kiss

Univ. Szeged

Szeged

Hungary

A. Klappenecker

Texas A&M Univ.

College Station, TX

USA

E. Knudsen

Riso Natl. Lab.

Roskilde

Denmark

K. Koto

Ochanomizu Univ.

Tokyo

Japan

S. Krimmel

Technical Univ. of Munich/Siemens AG

Garching-Munich

Germany

A. Kuba

Univ. Szeged

Szeged

Hungary

B. Langfeld

Techn. Univ. of Munich

Garching-Munich

Germany

H. Liao

Grad. Center, CUNY

New York, NY

USA

K. Lord

Techn. Univ. of Munich

Garching-Munich

Germany

R. Luke

Univ. Delaware

Newark, DE

USA

S. Matej

Univ. of Pennsylvania

Philadelphia, PA

USA

K. Mueller

Stony Brook Univ.

Stony Brook, NY

USA

R. Nagahama

Ochanomizu Univ.

Tokyo

Japan

A. Nagy

Univ. Szeged

Szeged

Hungary

B. Nagy

Univ. Debrecen

Debrecen

Hungary

C. Picouleau

Cedric-CNAM

Paris

France

H.F. Poulsen

Riso Natl. Lab.

Roskilde

Denmark

C.V.S. Rao

Inst. Plasma Research

Bhat, Gandhinagar

India

L. Rodek

Grad. Center, CUNY

New York, NY

USA

M. Roetteler

NEC Laboratories America, Inc.

Princeton, NJ

USA

S. Rowland

Grad. Center, CUNY

New York, NY

USA

L. Ruskó

Univ. Szeged

Szeged

Hungary

M. Santoyo Mondragón

Univ. Mich. de San Nicolás de Hidalgo

Morelia, Michoacán

Mexico

D. Sarioz

Grad. Center, CUNY

New York, NY

USA

B. Schillinger

Techn. Univ. of Munich

Garching-Munich

Germany

C. Schnörr

Univ. Mannheim

Mannheim

Germany

T. Schüle

Univ. Mannheim

Mannheim

Germany

M. Servières

Univ. Nantes

Nantes

France

S. Severini

Univ. York

York

U.K.

B. Sharif

Univ. Illinois

Urbana, IL

USA

M. Tajine

Univ. Strasbourg

Strasbourg

France

E. Vallejo

Univ. Nac. Autónoma de México

Morelia, Michoacán

Mexico

E. Vardi-Gonen

Grad. Center, CUNY

New York, NY

USA

S. Weber

Univ. Mannheim

Mannheim

Germany

C.E. Yarman

Rensselaer Polytechnic Institute

Troy, NY

USA

R. Zdunek

Wroclaw Univ. Technology

Wroclaw

Poland

S. Zopf

SVS-Vistek GmbH

Munich

Germany

 


Publications

The talks presented at the workshop have been published as a special  issue of  the Electronic Notes in Discrete Mathematics (Elsevier),

 

Furthermore, based on some of these talks we will edit a book entitled Advances in Discrete Tomography and Its Applications that will be published by Birkhäuser Boston (in 2006).


Supported by

National Science Foundation

Doctoral Program in Computer Science, City University of New York


Last updated: August 3, 2005