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Point Lattices in Computer Graphics and Visualization

Visualization 2005

Tutorial 4 - Monday 8:30 - 5:30

Minneapolis, Minnesota, October 24, 2005

Course Organizer
Lecturers
Torsten Möller
Simon Fraser University
Reza Entezari
Simon Fraser University

Jim Morey
The University of Western Ontario

Klaus Mueller
State University of New York at Stony Brook

Victor Ostromoukhov
University of Montreal

Dimitri Van De Ville
Swiss Federal Institute of Technology Lausanne

Contents

Abstract
Index to Course Materials
Presenter Information
Speaker Biographies

This DVD contains the content of the supplemental material of the tutorial Point Lattices in Computer Graphics and Visualizations given at the conference IEEE Visualization 2005 in October 2005. These materials were prepared before August 1st, 2005. Any additional material added after this production deadline can also be found in the online repository located at http://www.cs.sfu.ca/~torsten/Vis2005/


Abstract

This course is motivated by the deep connections and applications of point lattice theory in the mathematics of computer graphics and the role it plays in multidimensional signal processing and tilings. Next to an introduction to the theory and history of point lattices and the related sampling and group theories, we present an in-depth survey from two different perspectives:

  1. Signal processing --- Functional analysis and sampling theory

    All computational fields in science and engineering have to deal with discrete representations of continuous phenomena. Clearly, sampling theory is crucial to provide the essential link between the discrete and the continuous domain. Digital signal processing algorithms can only act on the discrete data, but should not loose sight of the continuous-domain aspect of their operations. As we will show, many interesting practical problems are best approached from this theoretic framework. Therefore, we will review general sampling theory in arbitrary dimensions and focus on recent developments for optimal lattices. This part will contain many examples and good-practice in image processing, medical imaging, and volume rendering. We survey reconstruction filter designs, wavelet techniques, medical reconstruction, discretization and rendering aspects for 2D, 3D, and 4D lattices. At the end, the attendee will comprehend how to put a proper discrete/continuous model for his/her application.

  2. Crystallography --- Geometry and group theory

    The study of the formation and structure of crystals has been the interest of scientists for many centuries. Consequently, the symmetries and translation invariant properties of point lattices have been studied and investigated thoroughly in the field of crystallography and solid-state physics. Group theory brought mathematical rigor to these fields. We take the opportunity in this course to migrate the most interesting results from this domain to the computer graphics community. Besides intricate mathematical concepts, regular structures have a strong aesthetic impact and have been incorporated into artistic expressions from ancient ornamental structures to famous works of Escher and general tiling patterns. In this part, we introduce fundamental group theory related to point lattices; we also effectively demonstrate geometric tools for the visualization of tilings and patterns in 2D, 3D, and 4D.


Index to Course Materials

Tutorial Slides

  1. Introduction by Torsten Möller
    [PDF, Color, 1 Slide per page], [PDF, Black/White, 1 Slides per page]
    [PDF, Color, 4 Slide per page], [PDF, Black/White, 4 Slides per page]

  2. Representation and History

  3. Applications

Additional Materials

I would like to see whether we can get something like a comprehensive bibliography together here. I started a litte bit and would appreciate your input. This could potentially be it's separate page.
  1. Representation and History

  2. Applications

Presenter Information

Reza Entezari
School Of Computing Science
Simon Fraser University
8888 University Drive
Burnaby, British Columbia, V5A 1S6
Canada
E-mail: aentezar@cs.sfu.ca
Home-page: http://gruvi.cs.sfu.ca/bio.php?id=282
Phone: +1-604-291-3610
GrUVi Logo SFU Logo
Klaus Mueller
State University of New York at Stony Brook, USA
Department of Computer Science
2428 Computer Science
Stony Brook, NY 11794-4400
USA
E-mail: muellerk@acm.org
Home-page: http://www.cs.sunysb.edu/~mueller/
Phone: +1-631-632-1524
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Jim Morey
Cognitive Engineering Lab
Department of Computer Science
Middlesex College
The University of Western Ontario
London, Ontario, N6A 5B7
Canada
E-mail: jim.morey@gmail.com
Home-page: http://www.csd.uwo.ca/~morey/
Phone: +1-519-661-3566
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Victor Ostromoukhov
University of Montreal, Dept.Comp.Sc.& Op.Res
2920, chemin de la Tour, office 2347/2153(secr)
C.P. 6128, Succ. Centre-Ville
Montreal, Quebec, H3C 3J7
Canada
E-mail: ostrom@iro.umontreal.ca
Home-page: http://www.iro.umontreal.ca/~ostrom/
Phone: +1-514-343-6509
U Montreal Logo
Torsten Möller
School Of Computing Science
Simon Fraser University
8888 University Drive
Burnaby, British Columbia, V5A 1S6
Canada
E-mail: torsten@sfu.ca
Home-page: http://www.cs.sfu.ca/~torsten/
Phone: +1-604-291-3774
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Dimitri Van De Ville
Swiss Federal Institute of Technology Lausanne, Switzerland
Biomedical Imaging Group
EPFL-IOA-LIB BM 4140; Station 17
CH-1015 Lausanne
Suisse
E-mail: Dimitri.VanDeVille@epfl.ch
Home-page: http://bigwww.epfl.ch/vandeville/
Phone: +41-21-6935142
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Speaker Biographies

Alireza Entezari is a PhD candidate at Simon Fraser University. He received his bachelor of science in Computing Science from Simon Fraser University in 2001. His current research focus lies in the interpolation and reconstruction issues on optimal sampling structures used in scientific computing and visualization.

Jim Morey received his PhD in computer science from the University of Western Ontario (2004), a MSc in pure mathematics from the University of British Columbia (1996), and a BSc in mathematics from the University of Guelph (1993). His work combines human computer interactions, mathematics, and theoretical computer science in designing tools for investigating repetitive geometric artifacts like tilings, crystal lattices, and polytopes. The tools have incorporated a number of novel interactive techniques, interactive representations, and repetitive artifacts. (for examples see http://www.csd.uwo.ca/~morey/CogEng)

Klaus Mueller is currently an Assistant Professor at the Computer Science Department at Stony Brook University, where he also holds co-appointments at the Biomedical Engineering and the Radiology Departments. He earned an MS degree in Biomedical Engineering in '91 and a PhD degree in Computer Science in '98, both from Ohio State University. His current research interests are computer graphics, visualization, medical imaging, and computer vision. He won the NSF CAREER award in 2001 and has served as a program co-chair at various conferences, such the Volume Graphics Workshop, IEEE Visualization, and the Symposium on Volume Visualization and Graphics. He has authored over 70 journal and conference papers.

Victor Ostromoukhov studied mathematics, physics and computer science at Moscow Institute of Physics and Technology (Psys-Tech, MFTI). After graduating in 1980, he spent several years with prominent European and American industrial companies (SG2, Paris; Olivetti, Paris and Milan; Canon Information Systems, Cupertino, CA) as a research scientist and/or computer engineer. He completed his Ph.D. in CS at Swiss Federal Institute of Technology (EPFL, Lausanne, 1995), where he continued to work as a lecturer and senior researcher. Invited professor at University of Washington, Seattle, WA, in 1997. Research scientist at Massachusetts Institute of Technology, Cambridge, MA, in 1999-2000. Associate Professor at University of Montreal, since August 2000. His research interests are mainly in computer graphics, and more specifically in non-photorealistic rendering, sampling, tiling theory, color science, halftoning, and digital art.

Dimitri Van De Ville received the Engineering and Ph.D. degrees in Computer Sciences in July 1998 and January 2002, respectively, from Ghent University, Belgium. He is now with the Biomedical Imaging Group at the Swiss Federal Institute of Technology Lausanne (EPFL). His current research interests include splines, wavelets, approximation and sampling theory, and biomedical signal and imaging applications such as fMRI and microscopy imaging. Dr. Van De Ville is associate editor of the IEEE Signal Processing Letters. He is also editor and webmaster of the Wavelet Digest, the electronic newsletter of the wavelet community.

Torsten Möller is an associate professor at the School of Computing Science at Simon Fraser University. His research interests include the fields of Scientific Visualization and Computer Graphics, especially the mathematical foundations of visualization and graphics. He is codirector of the Graphics, Usability and Visualization Lab and serves on the Board of Advisors for the Centre for Scientific Computing at Simon Fraser University. He has been appointed Vice Chair for Publications of the IEEE Technical Committee of Visualization and Graphics.