Sampling and reconstruction

Abstract

How do we properly sample continuous data? Studying continuous phenomena using computer requires their discretization. The sampling strategy used impacts the quality and efficiency of the analysis. We study the advantages of different regular sampling patterns in 3D and higher dimensions and compare them to non-uniform sampling and reconstruction strategies. Applications range from rendering applications to experimental design and statistics.

 

Principal Investigators

• Torsten Möller
• Alireza Ghane
• Michael Phillips

 

Papers

Integrating Isosurface Statistics and Histograms
Duffy, Brian and Carr, Hamish and Möller, Torsten
pp. 263-277 ISSN 1077-2626 (2013)

Sparse PDF Maps for Non-linear Multi-resolution Image Operations
Hadwiger, Markus and Sicat, Ronell and Beyer, Johanna and Krüger, Jens and Möller, Torsten
ACM Trans. Graph., 31 (6). 133:1-133:12 ISSN 0730-0301 (2012)

Visual Comparability of 3D Regular Sampling and Reconstruction
Meng, Tai and Entezari, Alireza and Smith, Benjamin and Möller, Torsten and Weiskopf, Daniel and Kirkpatrick, Arthur E.
pp. 1420-1432 ISSN - (2011)

Sort-First Parallel Volume Rendering
Moloney, Brendan and Ament, Marco and Weiskopf, Daniel and Möller, Torsten
pp. 1164-1177 ISSN - (2011)

Quantitative Error Analysis for the Reconstruction of Derivatives
Condat, Laurent and Möller, Torsten
pp. 2965-2969 ISSN 1053-587X (2011)

Toward High-Quality Gradient Estimation on Regular Lattices
Hossain, Zahid and Alim, Usman R. and Möller, Torsten
pp. 426-439 ISSN 1077-2626 (2011)

Gradient Estimation Revitalized
Alim, Usman R. and Möller, Torsten and Condat, Laurent
pp. 1494-1503 ISSN 1077-2626 (2010)

Edge Aware Anisotropic Diffusion for 3D Scalar Data
Hossain, Zahid and Möller, Torsten
pp. 1375-1384 ISSN 1077-2626 (2010)

Efficient volume rendering on the body centered cubic lattice using box splines
Finkbeiner, Bernhard and Entezari, Alireza and Ville, Dimitri Van De and Möller, Torsten
pp. 409-423 ISSN - (2010)

ProbExplorer: Uncertainty-guided Exploration and Editing of Probabilistic Medical Image Segmentation
Saad, Ahmed and Möller, Torsten and Hamarneh, Ghassa
pp. 1113-1122 ISSN - (2010)

Estimation and Modeling of Actual Numerical Errors in Volume Rendering
Kronander, Joel and Unger, Jonas and Möller, Torsten and Ynnerman, Anders
pp. 893-902 ISSN - (2010)

Gabriel meshes and Delaunay edge flips
Dyer, Ramsay and Zhang, Hao and Möller, Torsten
In: SIAM/ACM Conference on Geometric and Physical Modeling, October 5 - 10, 2009, San Francisco, USA (2009)

Segmentation-based regularization of dynamic SPECT reconstruction
Humphries, T. and Saad, A. and Celler, A. and Hamarneh, G. and Möller, Torsten and Trummer, M.R.
In: IEEE Nuclear Science Symposium and Medical Imaging Conference 2009, Oct. 24 2009-Nov. 1 2009, Orlando, FL, USA (2009)

On Visualization and Reconstruction from Non-Uniform Point Sets using B-splines
Vuçini, Erald and Möller, Torsten and Gröller, M. Eduard
Computer Graphics Forum, 28 (3). pp. 1007-1014 ISSN 01677055 (2009)

High-Quality Volumetric Reconstruction on Optimal Lattices for Computed Tomography
Finkbeiner, Bernhard and Alim, Usman R. and Van De Ville, Dimitri and Möller, Torsten
Computer Graphics Forum, 28 (3). pp. 1023-1030 ISSN 01677055 (2009)

The Lattice-Boltzmann Method on Optimal Sampling Lattices
Alim, U.R. and Entezari, A. and Möller, Torsten
IEEE Transactions on Visualization and Computer Graphics, 15 (4). pp. 630-641 ISSN 1077-2626 (2009)

From Sphere Packing to the Theory of Optimal Lattice Sampling
Alireza Entezari, Ramsay Dyer, Torsten Möller
in Torsten Möller, Bernd Hamann, Robert Russell, (Eds.) Mathematical Foundations of Scientific Visualization, Computer Graphics, and Massive Data Exploration, Series: Mathematics and Visualization, pp. 227--255, June 2009. 

Mathematical Foundations of Scientific Visualization, Computer Graphics, and Massive Data Exploration
Torsten Möller, Bernd Hamann, Robert Russell, (Eds.)
Series: Mathematics and Visualization, June 2009. 

On sampling lattices with similarity scaling relationships
Steven Bergner, Dimitri Van De Ville, Thierry Blu, Torsten Möller
Proceedings of 8th International Conference on Sampling Theory and Applications 2009 (SampTA 2009), Marseille, France, May 2009. 

A Fast Fourier Transform with Rectangular Output on the BCC and FCC Lattices
Usman Alim, Torsten Möller
Proceedings of 8th International Conference on Sampling Theory and Applications 2009 (SampTA 2009), Marseille, France, May 2009. 

A tool to create illuminant and reflectance spectra for light-driven graphics and visualization
Steven Bergner, Mark S. Drew, Torsten Möller
ACM Transactions on Graphics, vol. 28, no. 1 (Jan. 2009), 1-11.

Statistical Analysis of Multi-Material Components using Dual Energy CT
Christoph Heinzl, Johann Kastner, Torsten Möller, Eduard Gröller
Vision, Modeling, and Visualization (VMV 2008), pp. 179--188, Konstanz, Germany, October 2008. 

Temporal Styles for Time-Varying Volume Data
Jean-Paul Balabanian, Ivan Viola, Torsten Möller, Eduard Gröller
Proceedings of 3D Data Processing, Visualization and Transmission, pp. 81--88, June 2008.

Recovery of Dynamic PET Regions via Simultaneous Segmentation and Deconvolution
Ben Smith, Ahmed Saad, Ghassan Hamarneh, Torsten Möller
MICCAI 2008 Workshop on Analysis of Functional Medical Images, pp. 33-40 New York, USA, September 2008

Surface sampling and the intrinsic Voronoi diagram
Ramsay Dyer, Hao Zhang, Torsten Möller
Computer Graphics Forum, Volume 27, Issue 4 (Special issue on Eurographics Symposium on Geometry Processing 2008), pp. 1393-1402, Copenhagen, July 2008.

Smooth Mixed-Resolution GPU Volume Rendering
Johanna Beyer, Markus Hadwiger, Torsten Möller, Laura Fritz
IEEE/EG Symposium on Volume and Point-Based Graphics 2008 pp. 163-170, Los Angeles, NY, August 2008.

Efficient Reconstruction from Non-uniform Point Sets
Erald Vuçini, Torsten Möller, Eduard Gröller
The Visual Computer, 24(7-9):555-563, July 2008. 

Practical Box Splines for Reconstruction on the Body Centered Cubic Lattice
Alireza Entezari, Dimitri Van De Ville, Torsten Möller
IEEE Transactions on Visualization and Computer Graphics, TVCG 14(2): 313-328, 2008.

Simultaneous Segmentation, Kinetic Parameter Estimation, and Uncertainty Visualization of Dynamic PET Images
Ahmed Saad, Ben Smith, Ghassan Hamarneh, Torsten Möller
Lecture Notes in Computer Science, Medical Image Computing and Computer-Assisted Intervention (MICCAI), 2007, pp. 726-733, Brisbane, Australia, November 2007. 

Delaunay mesh construction
Ramsay Dyer, Hao Zhang, Torsten Möller
Eurographics Symposium on Geometry Processing 2007, pp. 273-282, Barcelona, July 2007.

Voronoi-Delaunay duality and Delaunay meshes
Ramsay Dyer, Hao Zhang, Torsten Möller
ACM Solid and Physical Modeling Symposium 2007, pp. 415-420, Beijing, June 2007. 

On visual quality of optimal 3D sampling and reconstruction
Tai Meng, Benjamin Smith, Alireza Entezari, Arthur E. Kirkpatrick, Daniel Weiskopf, Leila Kalantari, Torsten Möller
Graphics Interface 2007, pp. 265-272, Montreal, May 2007. 

Feature peeling
M. Muddassir Malik, Torsten Möller, M. Eduard Gröller
Graphics Interface 2007, pp. 273-280, Montreal, May 2007. 

Visualization and exploration of time-varying medical image data sets
Zhe Fang, Torsten Möller, Ghassan Hamarneh, Anna Celler
Graphics Interface 2007, pp. 281-288, Montreal, May 2007. 

Scalable sort-first parallel direct volume rendering with dynamic load balancing
Brendan Moloney, Daniel Weiskopf, Torsten Möller, Markus Strengert
7th Eurographics Symposium on Parallel Graphics and Visualization 2007 (EGPGV'07), pp. 45-52, Lugano, Switzerland, May 2007. 

An Investigation of the Spectral Robustness of Mesh Laplacians
Ramsay Dyer, Hao Zhang, Torsten Möller, Andrew Clements
Technical Report, School of Computing Science, Simon Fraser University, (SFU-CMPT-17/07-TR2007-17), June 2007. 

A Spectral Analysis of Function Composition and its Implications for Sampling in Direct Volume Visualization
Steven Bergner, Torsten Möller, Daniel Weiskopf, David Muraki
IEEE Transactions on Visualization and Computer Graphics (Proceedings Visualization / Information Visualization 2006), vol. 12, no. 5, pp. 1353--1360, Sep.-Oct. 2006. 

Extensions of the Zwart-Powell Box Spline for Volumetric Data Reconstruction on the Cartesian Lattice
Alireza Entezari, Torsten Möller
IEEE Transactions on Visualization and Computer Graphics (Proceedings Visualization / Information Visualization 2006), vol. 12, no. 5, pp. 1337--1344, Sep.-Oct. 2006. 

A Granular Three Dimensional Multiresolution Transform
Alireza Entezari, Tai Meng, Steven Bergner, Torsten Möller
Proceedings of Eurographics/IEEE-VGTC Symposium on Visualization 2006 (EuroVis 2006), pp. 267-274, Lisbon, Portugal, May 2006. 

Improving the Quality of Multi-resolution Volume Rendering
Hamid Younesy, Torsten Möller, Hamish Carr
Proceedings of Eurographics/IEEE-VGTC Symposium on Visualization 2006 (EuroVis 2006), pp. 251-258, Lisbon, Portugal, May 2006. 

Artifacts Caused By Simplicial Subdivision
Hamish Carr, Torsten Möller, Jack Snoeyink
IEEE Transactions on Visualization and Computer Graphics, TVCG 12(2): 231-242, March 2006.

Using the Physics-based Rendering Toolkit for Medical Reconstruction
Steven Bergner, Eric Dagenais, Anna Celler, Torsten Möller
Proceedings of 2005 IEEE Nuclear Science Symposium and Medical Imaging Conference, pp. 3022-3026, Puerto Rico, October 2005. 

Visualization of Time-Varying Volumetric Data using Differential Time-Histogram Table
Hamid Younesy, Torsten Möller, Hamish Carr
Workshop on Volume Graphics 2005 (VG05), pp. 21-29, Stony Brook, NY, June 2005. 

A Practical Approach to Spectral Volume Rendering
Steven Bergner, Torsten Möller, Melanie K. Tory, Mark Drew
IEEE Transactions on Visualization and Computer Graphics, TVCG 11(2): 207-216, March 2005.

Linear and Cubic Box Splines for the Body Centered Cubic Lattice
Alireza Entezari, Ramsay Dyer, Torsten Möller
Proceedings of IEEE Visualization 2004 (Vis04), pp. 11-18, Austin, TX, October 2004.

Subsampling Matrices for Wavelet Decompositions on Body Centered Cubic Lattices
Alireza Entezari, Torsten Möller, Jacques Vaisey
IEEE Signal Processing Letters, Vol. 11, No. 9, pp. 733-735, September 2004. 

A Spectral Engine for Visualization
Steven Bergner, Torsten Möller, Mark Drew
Technical Report, School of Computing Science, Simon Fraser University, (SFU-CMPT-06/04-TR2004-06), June 2004. 

Transfer Functions on a Logarithmic Scale for Volume Rendering
Simeon Potts, Torsten Möller
Graphics Interface 2004, pp. 57-63, London, May 2004. 

Curvature-Based Transfer Functions for Direct Volume Rendering: Methods and Applications
Gordon Kindlmann, Ross Whitaker, Tolga Tasdizen, Torsten Möller
Proceedings of IEEE Visualization 2003 (Vis03), pp. 513-520, Seattle, October 2003. 

A Parallel Coordinates Interface for Exploratory Volume Visualization
Simeon Potts, Melanie Tory, Torsten Möller 
presented at IEEE Conference on Visualization (Vis03), Seattle, October 2003. 

Voxelization in Common Sampling Lattices
Haris Widjaya, Torsten Möller, Alireza Entezari 
Proceedings of Pacific Graphics 2003 (PG03), pp. 497-501, Canmore, Alberta, October 2003. 

Rapid Emission Tomography Reconstruction
Ken Chidlow, Torsten Möller
Workshop on Volume Graphics 2003 (VG03), Tokio, July 2003.

Isosurfaces on Optimal Regular Samples
Hamish Carr, Thomas Theußl, Torsten Möller
Joint EUROGRAPHICS - IEEE TCVG Symposium on Visualization (VisSym 2003), pp. 39-48, Grenoble, May 2003.

Scatter segmentation in dynamic SPECT images using principal component analysis
Klaus D. Toennies, Anna Celler, Stephan Blinder, Torsten Möller, Ronald Harrop
Proceedings of SPIE International Symposium on Medical Imaging. Proc. SPIE Int. Soc. Opt. Eng., vol. 5032, pp. 507-516, San Diego, February 2003.

Quality Issues of Hardware-Accelerated High-Quality Filtering on PC Graphics Hardware
Markus Hadwiger, Helwig Hauser, Torsten Möller
Proceedings of the 11th International Conference in Central Europe on Computer Graphics, Visualization and Computer Vision 2003, WSCG'2003, University of West Bohemia, Pilsen, Czech Republic, February 2003.

Interactive Spectral Volume Rendering
Steven Bergner, Torsten Möller, Mark S. Drew, Graham D. Finlayson
Proceedings of IEEE Visualization 2002, pp. 101-108, October 2002.

Shading For Fourier Volume Rendering
Alireza Entezari, Randy Scoggins, Torsten Möller, Raghu Machiraju
Proceedings of Symposium of Volume Visualization and Graphics 2002, pp. 131-138, October 2002.

Full search content independent block matching based on the fast Fourier transform
Steven L. Kilthau, Mark S. Drew, Torsten Möller
Proceedings of IEEE International Conference on Image Processing, pp. 669-672, September 2002.

Modified Marching Octahedra for Optimal Regular Meshes
Hamish Carr, Thomas Theußl, Torsten Möller
Conference Abstracts and Applications of SIGGRAPH 2002, pp. 219, San Antonio, US, July 2002.

4D Space-Time Techniques: A Medical Imaging Case Study
Melanie Tory, Niklas Röber, Torsten Möller, Anna Celler, M. Stella Atkins
Proceedings of IEEE Visualization 2001, pp. 473-476, October 2001.

Optimal Regular Volume Sampling
Melanie Tory, Niklas Röber, Torsten Möller, Anna Celler, M. Stella Atkins
Proceedings of IEEE Visualization 2001, pp. 91-98, October 2001. 

Simplicial subdivisions and sampling artifacts
Hamish Carr, Torsten Möller, Jack Snoeyink
Proceedings of IEEE Visualization 2001, pp. 99-108, October 2001.

Accelerated Splatting using a 3D Adjacency Data Structure
Jeff Orchard, Torsten Möller
Graphics Interface 2001, pp. 191--200, Ottawa, June 2001. 

Visualizing Time-Varying Data from MRI and Dynamic SPECT
Melanie Tory, Niklas Röber, Torsten Möller, Anna Celler
Graphics Interface 2001, June 2001.

Visualization of Time-Varying MRI Data for MS Lesion Analysis
Melanie Tory, Torsten Möller, M. Stella Atkins
Proceedings of SPIE International Symposium on Medical Imaging. Proc. SPIE Int. Soc. Opt. Eng., vol. 4319, pp. 590-598, San Diego, February 2001.

Splatting Without The Blur
Klaus Mueller, Torsten Möller, and Roger A. Crawfis
Proceedings of IEEE Conference on Visualization 1999, pp. 363-371, October 1999. 

Design Of Accurate And Smooth Filters For Function And Derivative Reconstruction
Torsten Möller, Klaus Mueller, Yair Kurzion, Raghu Machiraju, Roni Yagel
Proceedings of the 1998 Symposium on Volume Visualization, pp. 143-151, October 1998. 

Size Preserving Pattern Mapping
Yair Kurzion, Torsten Möller, Roni Yagel
Proceedings of IEEE Conference on Visualization 1998, pp. 197-204, October 1998. 

Splatting Errors and Antialiasing
Klaus Mueller, Torsten Möller, J. Ed Swan II, Roger A. Crawfis, Naeem Shareef, Roni Yagel
IEEE Transactions on Visualization and Computer Graphics, ITVCG 4(2): 178-191, June 1998.

Fast Volume Rendering of Curvilinear Data Sets Using a Splatting Approach
Torsten Möller, Roger A. Crawfis, Nelson Max
Technical Report, Department of Computer and Information Science, Ohio State University, (OSU-CISRC-11/97-TR52), November 1997. 

A Comparison Of Normal Estimation Schemes
Torsten Möller, Raghu Machiraju, Klaus Mueller, Roni Yagel
Proceedings of IEEE Conference on Visualization 1997, pp. 19-26, October 1997.

An Anti-Aliasing Technique for Splatting
J. Ed Swan II, Klaus Mueller, Torsten Möller, Naeem Shareef, Roger A. Crawfis, Roni Yagel
Proceedings of IEEE Conference on Visualization 1997, pp. 197-204, October 1997. 

Evaluation and Design of Filters Using a Taylor Series Expansion
Torsten Möller, Raghu Machiraju, Klaus Mueller, Roni Yagel
IEEE Transactions on Visualization and Computer Graphics, ITVCG 3(2): 184-199, June 1997. 

Classification and Local Error Estimation of Interpolation and Derivative Filters for Volume Rendering
Torsten Möller, Raghu Machiraju, Klaus Mueller, Roni Yagel
Proceedings of the 1996 Symposium on Volume Visualization, pp. 71-78, October 1996. 

Efficient Rasterization of Implicit Functions
Torsten Möller, Roni Yagel
Technical Report, Department of Computer and Information Science, Ohio State University, (OSU-CISRC-11/95-TR50), November 1995.