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IMA Annual Program Year Workshop

New Mathematics and Algorithms for 3-D Image Analysis

January 9-12, 2006

Organizers:

Les G. Butler

Department of Chemistry
Louisiana State University
http://chemistry.lsu.edu/butler/

Gestur Olafsson

Department of Mathematics
Louisiana State University
http://www.math.lsu.edu/~olafsson/

Eric Todd Quinto

Department of Mathematics
Tufts University
http://www.tufts.edu/~equinto

Schedule Participants Program Application Feedback
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Abstracts and Talk Materials Dining Guide
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Description:

New mathematics and algorithms are needed for 3-D image acquisition and analysis. The 3-D images come from many disciplines: biomedicine, geology, chemistry, and microfabrication. The mathematics is wide-ranging and includes at least tomography and inverse problems, wavelets, PDE, and conformal mapping. The depth of the problem and the extent of the mathematics argue for developing long-term collaborations between mathematicians and scientists. This workshops is a step toward that end.

This workshop will focus on two topics:
  • the combination of multiple 3-D images into a reduced set of images; and
  • the analysis of images with simple geometric shapes.
  • A goal in the first area is to use multiple reconstructions of the raw data to better perform image segmentation. For example, edge images (e.g., using Λ-tomography) can be combined with composition images to derive a set of final images of much greater value to the experimentalists.

    The analysis of simple geometric shapes has received little attention and yet could illuminate entirely new strategies in 3-D image analysis. Many non-medical problems involve high-quality images of objects with simple shapes, and this is an excellent starting point for new mathematics and algorithms.

    Schedule
    Monday, January 9
    8:45a-9:00a Welcome and introduction Douglas N. Arnold (University of Minnesota Twin Cities) EE/CS 3-180
    9:30a-10:30a An introduction to the mathematics of tomography Eric Todd Quinto (Tufts University) EE/CS 3-180
    10:30a-11:00a coffee break   EE/CS 3-176
    11:00a-12:00p Recovery of the internal grain structure of polycrystals from X-ray diffaction data using discrete tomography Gabor T. Herman (City University of New York (CUNY)) EE/CS 3-180
    12:00p-2:30p lunch    
    2:30p-3:00p Image acquisition from a highly incomplete set of measurements Justin Romberg (California Institute of Technology) EE/CS 3-180
    3:00p-3:30p coffee break   EE/CS 3-176
    3:30p-4:00p Diffraction tomography using intensity measurements Mark A. Anastasio (Illinois Institute of Technology) EE/CS 3-180
    4:00p-4:40p Second Chances   EE/CS 3-180
    4:40p-4:45p Group photos    
    4:45p-6:00p Poster Session/Reception
    Lind Hall 400
    Image Reconstruction in Thermoacoustic Tomography Gaik Ambartsoumian (Texas A & M University)
    Peter Kuchment (Texas A & M University)
    Image Segmentation using a Modified Mumford-Shah Model Jung-Ha An (University of Minnesota Twin Cities)
    3D Image Acquisition and Image Analysis Algorithms Heath Barnett (Louisiana State University)
    Les G. Butler (Louisiana State University)
    Kyungmin Ham (Louisiana State University)
    Synchrotron micro computed tomography as a tool for the quantitative characterization of the structural changes during the ageing of metallic foams Oliver Brunke (Universität Bremen)
    Multiframe Dim Target Detection Using 3D Multiscale Geometric Analysis Boris Aharon Efros (Ben Gurion University of the Negev)
    Frame Isotropic Multiresolution Analysis for Micro CT Scans of Coronary Arteries Alex Gittens (University of Houston)
    Factorization method in inverse obstacle scattering Natalia Grinberg (Universität Fridericiana (TH) Karlsruhe)
    3D Shape Recognition and Reconstruction with Line Element Geometry Michael Hofer (Vienna University of Technology)
    Segmentation and Geometry of 3D Scenes form Unorganized Point Clouds George Kamberov (Stevens Institute of Technology)
    Measuring features in volumetric data sets using Blob3D Richard Ketcham (University of Texas)
    Zoomable PDEs Seongjai Kim (Mississippi State University)
    Unraveling the Mysteries of Grain Growth by X-Ray Tomography: Segmentation of the 3-D Microstructure of Polycrystalline Al-Sn Carl E. Krill III (Universität Ulm)
    Real Time Multi-Scale Geometric Segmentation of 3D Images Ofer Levi (Ben Gurion University of the Negev)
    Active Contours with Local Binary Fitting Energy Chunming Li (Vanderbilt University)
    Method of Background Subtraction for Medical Image Segmentation Hyeona Lim (Mississippi State University)
    TBA W. Brent Lindquist (Stony Brook University)
    A Unified Registration and Segmentation Framework for Medical Images Jundong Liu (Ohio University)
    An Active Regions approach for the segmentation of 3D biological tissue Gregory J. Randall (University of the Republic)
    Sobolev gradients and negative norms for image decomposition Walter Richardson Jr. (University of Texas)
    Total variation imaging followed by spectral decomposition using continuous wavelet transform Partha S. Routh (Boise State University)
    Orthogonal Wavelet Frames for Color Image Compression Eric S. Weber (Iowa State University)
    Structure-Preserving Filtering of DT-MRI Data: PDE and Discrete Approaches Martin Welk (Universität des Saarlandes)
    Common reflection angle imaging Graham A. Winbow (ExxonMobil)
    Sinogram decomposition for fan beam transform and its applications Alex Zamyatin (BIR, Inc.)
    Tuesday, January 10
    8:45a-9:00a Coffee   EE/CS 3-176
    9:00a-9:45a Dual-Modality Micro-CT with Poly-Capillary X-ray Optics Erik L. Ritman (Mayo Clinic) EE/CS 3-180
    9:45a-10:30a Grain maps and grain dynamics — a reconstruction challenge Henning Friis Poulsen (Riso National Laboratory) EE/CS 3-180
    10:30a-11:00a coffee break   EE/CS 3-176
    11:00a-11:45a On mathematics of thermoacoustic imaging Peter Kuchment (Texas A & M University) EE/CS 3-180
    11:45a-2:30p lunch    
    2:30p-3:00p Imaging Translational Water Diffusion with Magnetic Resonance for Fiber Mapping in the Central Nervous System Thomas H. Mareci (University of Florida) EE/CS 3-180
    3:00p-3:30p coffee break   EE/CS 3-176
    3:30p-4:30p Breakout groups
    EE/CSci 3-111, 3-115 and 3-320 
    Surface detection Richard Ketcham (University of Texas)
    segmentation W. Brent Lindquist (Stony Brook University)
    reconstructions in material science Henning Friis Poulsen (Riso National Laboratory)
    local tomography Eric Todd Quinto (Tufts University)
    4:30p-5:00p Second Chances   EE/CS 3-180
    Wednesday, January 11
    8:45a-9:00a Coffee   EE/CS 3-176
    9:00a-9:45a Thermoacoustic Tomography - Reconstruction of Data Measured under Clinical Constraints Sarah K. Patch (University of Wisconsin) EE/CS 3-176
    9:45a-10:30a Tomography and Sampling Theory Adel Faridani (Oregon State University) EE/CS 3-180
    10:30a-11:00a coffee break   EE/CS 3-176
    11:00a-12:00p Breakout groups
    EE/CSci 3-111, 3-115 and 3-320 
    sampling Adel Faridani (Oregon State University)
    Discrete tomography Gabor T. Herman (City University of New York (CUNY))
    line or path detection Thomas H. Mareci (University of Florida)
    de-noising Peter R. Massopust (Tuboscope Pipeline Services)
    12:00p-2:30p lunch    
    2:30p-3:00p 3D segmentation in tomography Guillermo R. Sapiro (University of Minnesota Twin Cities) EE/CS 3-180
    3:00p-3:30p Processing of Diffusion-Tensor Magnetic Resonance Images Akram Aldroubi (Vanderbilt University) EE/CS 3-180
    3:30p-4:00p coffee break   EE/CS 3-176
    4:00p-4:30p Ultrasound tomography Frank Natterer (Westfälische Wilhelms-Universität Münster) EE/CS 3-180
    4:30p-5:00p Second Chances   EE/CS 3-180
    5:00p-5:30p Poster session (same posters as on Monday)   Lind Hall 400
    6:30p-8:00p Workshop Dinner   Gardens of Solonika 
    Thursday, January 12
    8:45a-9:00a Coffee   EE/CS 3-176
    9:00a-9:45a Electron tomography. A short overview of methods and challenges Ozan Oktem (Sidec Technologies) EE/CS 3-180
    9:45a-10:30a Improved cone beam local tomography Alexander Katsevich (University of Central Florida) EE/CS 3-180
    10:30a-11:00a coffee break   EE/CS 3-176
    11:00a-12:00p Breakout groups
    EE/CSci 3-111, 3-115 and 3-320 
    Surface detection Richard Ketcham (University of Texas)
    segmentation W. Brent Lindquist (Stony Brook University)
    line or path detection Thomas H. Mareci (University of Florida)
    reconstructions in material science Henning Friis Poulsen (Riso National Laboratory)
    12:00p-2:30p lunch    
    2:30p-3:15p A Networked Framework for Visualization and Analysis of Volumetric Datasets Art W. Wetzel (Pittsburgh Supercomputing Center) EE/CS 3-180
    3:15p-3:30p coffee break   EE/CS 3-176
    3:30p-4:00p Summary session: What was accomplished? What's next? Les G. Butler (Louisiana State University), Eric Todd Quinto (Tufts University) EE/CS 3-180

    LIST OF CONFIRMED PARTICIPANTS

    Name Department Affiliation
    Iman Aganj Department of Electrical and Computer Engineering University of Minnesota Twin Cities
    Akram Aldroubi Mathematics Department Vanderbilt University
    Aisha Alwehebi Mathematics Department Mississippi State University
    Gaik Ambartsoumian Department of Mathematics Texas A & M University
    Jung-Ha An Institute for Mathematics and its Applications University of Minnesota Twin Cities
    Mark A. Anastasio Pritzker Institute of Medical Engineering Illinois Institute of Technology
    Fredrik Andersson Department of Mathematics Lund University
    D. Gregory Arnold AFRL/SNAT Air Force Research Laboratory
    Douglas N. Arnold Institute for Mathematics and its Applications University of Minnesota Twin Cities
    Donald G. Aronson Institute for Mathematics and its Applications University of Minnesota Twin Cities
    Heath Barnett Department of Chemistry Louisiana State University
    Evgeniy Bart Institute for Mathematics and its Applications University of Minnesota Twin Cities
    Aleksei Beltukov Department of Mathematics University of the South Pacific
    Francisco Blanco-Silva Department of Mathematics Purdue University
    Edward Howard Bosch Basic and Applied Research National Geospatial Intelligence Agency
    Oliver Brunke ZARM Universität Bremen
    Les G. Butler Department of Chemistry Louisiana State University
    Youngjoon Cha Department of Apllied Mathematics Sejong University
    Kyle Champley Department of Mathematics Oregon State University
    Guangliang Chen Department of Mathematics University of Minnesota Twin Cities
    Qianyong Chen Institute for Mathematics and its Applications University of Minnesota Twin Cities
    Jens Gerlach Christensen Department of Mathematics Louisiana State University
    Ivan Christov Department of Mathematics Texas A & M University
    Steven Benjamin Damelin Department of Mathematics Georgia Southern University
    Susanna Dann Department of Mathematics Louisiana State University
    Yves Defrenne Bio Based Products (CNR) University of Minnesota Twin Cities
    Brian DiDonna Institute for Mathematics and its Applications University of Minnesota Twin Cities
    Diane Eaker   Mayo Clinic
    Boris Aharon Efros Department of Industrial Engineering Ben Gurion University of the Negev
    Selim Esedoglu Department of Mathematics University of Michigan
    Adel Faridani Department of Mathematics Oregon State University
    Alex Gittens Department of Mathematics University of Houston
    Natalia Grinberg Department of Mathematics Universität Fridericiana (TH) Karlsruhe
    Changfeng Gui Department of Mathematics University of Connecticut
    Jooyoung Hahn Division of Applied Mathematics Korea Advanced Institute of Science and Technology (KAIST)
    Kyungmin Ham CAMD Louisiana State University
    Hazem Hamdan School of Mathematics University of Minnesota Twin Cities
    Gloria Haro Ortega Institute for Mathematics and its Applications University of Minnesota Twin Cities
    Gabor T. Herman Department of Computer Science City University of New York (CUNY)
    Michael Hofer Department of Mathematics and Geoinformation Vienna University of Technology
    Kathleen Hoffman Department of Mathematics and Statistics University of Maryland Baltimore County
    Xiang Huang Department of Mathematics University of Connecticut
    Steven Izen Department of Mathematics Case Western Reserve University
    Saurabh Jain Department of Mathematics University of Houston
    Sookyung Joo Institute for Mathematics and its Applications University of Minnesota Twin Cities
    Yoon Mo Jung School of Mathematics University of Minnesota Twin Cities
    George Kamberov Department of Computer Science Stevens Institute of Technology
    Sung Ha Kang Department of Mathematics University of Kentucky
    Alexander Katsevich Department of Mathematics University of Central Florida
    Richard Ketcham Department of Geological Science University of Texas
    Seongjai Kim Department of Mathematics and Statistics Mississippi State University
    SungWan Kim Department of Mathematics Yonsei University
    Carl E. Krill III Materials Division Universität Ulm
    Peter Kuchment Department of Mathematics Texas A & M University
    Matthias Kurzke Institute for Mathematics and its Applications University of Minnesota Twin Cities
    Song-Hwa Kwon Institute for Mathematics and its Applications University of Minnesota Twin Cities
    David Larson Department of Mathematics Texas A & M University
    Chang-Ock Lee Division of Applied Mathematics Korea Advanced Institute of Science and Technology (KAIST)
    Gilad Lerman Math Department University of Minnesota Twin Cities
    Ofer Levi Department of Industrial Engineering and Management Ben Gurion University of the Negev
    Stacey E. Levine Department of Mathematics and Computer Science Duquesne University
    Debra Lewis Institute for Mathematics and its Applications University of Minnesota Twin Cities
    Chunming Li   Vanderbilt University
    Hstau Liao Institute for Mathematics and its Applications University of Minnesota Twin Cities
    Hyeona Lim Department of Mathematics and Statistics Mississippi State University
    W. Brent Lindquist Department of Applied Mathematics and Statistics Stony Brook University
    Jundong Liu Electrical Engineering and Computer Science Ohio University
    Bradley J. Lucier Department of Mathematics Purdue University
    Alison Malcolm Institute for Mathematics and its Applications University of Minnesota Twin Cities
    Thomas H. Mareci Department of Biochemistry and Molecular Biology University of Florida
    Peter R. Massopust   Tuboscope Pipeline Services
    Olga Mendoza Sensors Directorate/Automatic Target Recognition Division Air Force Research Laboratory
    Willard Miller Jr. Institute for Mathematics and its Applications University of Minnesota Twin Cities
    Frank Natterer Fachbereich Mathematik Westfälische Wilhelms-Universität Münster
    Ozan Oktem Research and Development Sidec Technologies
    Gestur Olafsson Department of Mathematics Louisiana State University
    Peter J. Olver School of Mathematics University of Minnesota Twin Cities
    Winston Ou   University of Minnesota Twin Cities
    Manos Papadakis Department of Mathematics University of Houston
    Sarah K. Patch Department of Physics University of Wisconsin
    Thomas Posbergh Department of Electrical Engineering and Computer Science University of Minnesota Twin Cities
    Henning Friis Poulsen   Riso National Laboratory
    Eric Todd Quinto Department of Mathematics Tufts University
    Gregory J. Randall Instituto de Ingenieria Electrica University of the Republic
    Walter Richardson Jr. Department of Mathematical Sciences University of Texas
    Erik L. Ritman Department of Physiology and Biophysics Mayo Clinic
    Justin Romberg   California Institute of Technology
    Juan Romero Department of Mathematics University of Houston
    Partha S. Routh Department of Geosciences Boise State University
    Hans Rullgard Department of Mathematics University of Stockholm
    Steven Ruuth Mathematics Department Simon Fraser University
    Fadil Santosa School of Mathematics University of Minnesota Twin Cities
    Guillermo R. Sapiro Department of Electrical and Computer Engineering University of Minnesota Twin Cities
    Arnd Scheel Institute for Mathematics and its Applications University of Minnesota Twin Cities
    Jin Keun Seo Department of Mathematics Yonsei University
    Tatiana Soleski Institute for Mathematics and its Applications University of Minnesota Twin Cities
    Pablo Sprechmann Instituto de Ingenieria Electrica University of the Republic
    Peter Stiller Department of Mathematics Texas A & M University
    Nathaniel Kirk Strawn Department of Mathematics Texas A & M University
    Vladimir Sverak School of Mathematics University of Minnesota Twin Cities
    Carl Toews Institute for Mathematics and its Applications University of Minnesota Twin Cities
    Jing Wang   ViTAL Images, Inc.
    Jingyue Wang Department of Mathematics Purdue University
    Xiaoqiang Wang Institute for Mathematics and its Applications University of Minnesota Twin Cities
    Eric S. Weber Department of Mathematics Iowa State University
    Martin Welk Mathematical Image Analysis Group Universität des Saarlandes
    Art W. Wetzel Biomedical Initiative Group Pittsburgh Supercomputing Center
    Thomas Neil Williams Department of Mathematics Mississippi State University
    Graham A. Winbow Subsurface Imaging Division ExxonMobil
    Alex Zamyatin Research and Development BIR, Inc.
    Ofer Zeitouni School of Mathematics University of Minnesota Twin Cities