IMA Annual Program Year Workshop

New Mathematics and Algorithms for 3-D Image Analysis

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.

• 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