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IMA Imaging Gallery

Imaging (September 1, 2005 - June 30, 2006)

In connection with the 2005-2006 program on Imaging at the Institute for Mathematics and its Applications, we have created this web gallery of contributed images. For this we solicited images for their visual rather than scientific interest. Each image can be viewed as a JPEG file and in the original contributed format. Rights to the images are retained by their owners. To contribute an image for inclusion, see the instructions.

Chaotic CT reconstruction.

Alex Zamyatin, Bio-Imaging Research

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3D cryo-static micro CT of some snow and some of the individual snow flakes extracted from that 3D image.

E. L. Ritman et al., Mayo Clinic College of Medicine

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Seismic reflection image of a vertical slice through the upper 3 km of the Earth's crust.

Kidane Araya

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Electromagnetic wave in the Fujisawa-Koshiba photonic crystal with a waveguide bend.

Igor Tsukerman

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Yellow lily reconstructed from hyperspectral data.

Foster, D. H., Nascimento, S. M. C. & Amano, K. (2004). Information limits on neural identification of colored surfaces in natural scenes. Visual Neuroscience 21, 331-336.

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The depth of brain sulci in axial, coronal and sagittal view

Chiu-Yen Kao, IMA

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High dynamic range volume rendering result for turbulent mixing of air and Sulfur Hexafluoride(SF6). Left: tone mapped image from high dynamic range volume rendering; right: images at different exposure levels from the same rendering.
Xiaoru Yuan, Minh X. Nguyen, Baoquan Chen and David H. Porter, Dept. of Computer Science and Engineering University of Minnesota,

High Dynamic Range Volume Visualization." In Proceedings of IEEE Visualization 2005, pages 327-334. Minneapolis, MN, USA. Oct 23 - 28, 2005.


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(a) is at a time when the turbulence is in the process of developing.



(b) is at a time when the turbulence is fully developed.
High dynamic range volume rendered Images depict magnitude of vorticity from a high-resolution simulation of homogenous decaying compressible uid turbulence.

Xiaoru Yuan, Minh X. Nguyen, Baoquan Chen and David H. Porter, Dept. of Computer Science and Engineering University of Minnesota,

High Dynamic Range Volume Visualization." In Proceedings of IEEE Visualization 2005, pages 327-334. Minneapolis, MN, USA. Oct 23 - 28, 2005.


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Illustrative rendering of a simulated Fullerene (C60) molecular model. more images see: http://www-users.cs.umn.edu/~xyuan/research/publication/isv.htm

Xiaoru Yuan and Baoquan Chen , Dept. of Computer Science and Engineering University of Minnesota,

"Illustrating Surfaces in Volume." In Proceedings of Joint IEEE/EG Symposium on Visualization (VisSym'04), pages 9-16. Konstanz, Germany, May 19-21, 2004.


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Finger position risk landscapes for lifting and touching a cylinder, respectively.

Erik J. Schlicht and Paul R. Schrater, Computational Perception and Action Laboratory, University of Minnesota

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Part 1 is the 3 dimensional view of the convergents.


Part 2 is the projection of the convergents onto the complex plane revealing the structure of the orbits.
scaled odd (blue/green/cyan) and even (red/yellow/orange/magenta) convergents of a continued fraction of Ramanujan with complex coefficients.

Russell Luke, Department of Mathematical Sciences, University of Delaware

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Reconstruction of the acoustic field in the plane from boundary measurements in the far field.

Russell Luke, Department of Mathematical Sciences, University of Delaware

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Figure 1: A comparison of classical transfer function based classification (left) and probabilistic classification (right) of brain data, showing cerebro-spinal fluid, white matter, and gray matter.


Figure 6: An illustration of Graph-based Data-space Reparameterization of fuzzy classified data. Both datasets, the engine (top) and Brainweb Phantom (bottom), were reparameterized from a 10 dimensional probability data-space to a 3D data-space. The slices on the left were colored by mapping the 3D reparameterized data directly to the RGB color space. The graphs on the right show how the individual classes' data values are arranged in the new 3D data-space.


Figures 1 and 6 combined, using only the brain data from Figure 6

Top: A comparison of classical transfer function based classification (left) and probabilistic classification (right) of brain data, showing cerebro-spinal fluid, white matter, and gray matter.

Bottom: An illustration of Graph-based Data-space Reparameterization of fuzzy classified data. The Brainweb Phantom data was reparameterized from a 10 dimensional probability data-space to a 3D data-space. The slice on the left was colored by mapping the 3D reparameterized data directly to the RGB color space. The graph on the right show how the individual classes' data values are arranged in the new 3D data-space.


Joe Michael Kniss, School of Computing, Scientific Computing and Imaging Institute, University of Utah

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Tensorlines and superquadric glyphs

Gordon Kindlmann, Dr. David Weinstein, Scientific Computing and Imaging Institute, University of Utah


Some tensor-line fiber tracts and superquadric tensor glyphs used to depict some of the white matter structure in a DT-MRI scan. The tensorlines have been highlighted for emphasis. Determining the extent to which the the computed fiber tracts actually correspond to white matter pathways is a subject of ongoing work.

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Interactive Level-Set Segmentation and Volume Rendering of a Brain Tumor from MRI Data

Aaron E. Lefohn, Joe M. Kniss, Charles D. Hansen, Ross T. Whitaker, Scientific Computing and Imaging Institute, University of Utah

A slice through a segmented brain tumor from an MRI volume. The brown surface is the level-set segmented surface and the yellow is the intersection of this surface with the clipping plane. The blue volume rendering gives the segmentation context within the patient's head. The level-set surface is defined with an interactive segmentation tool. The level-set and volume rendering computations are both interactively computed entirely on the graphics processing unit (GPU).

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Interactive Level-Set Segmentation and Volume Rendering of the Cerebral Cortex from MRI Data

Aaron E. Lefohn, Joe M. Kniss, Charles D. Hansen, Ross T. Whitaker, Scientific Computing and Imaging Institute, University of Utah

A slice through a segmented cerebral cortex from an MRI volume. The brown surface is the level-set segmented surface and the yellow is the intersection of this surface with the clipping plane. The blue volume rendering gives the segmentation context within the patient's head. The level-set surface is defined with an interactive segmentation tool. The level-set and volume rendering computations are both interactively computed entirely on the graphics processing unit (GPU).

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Dragon distance field sampled with a particle system

Miriah Meyer, Pierre Georgel, Ross Whitaker, Scientific Computing and Imaging Institute, University of Utah

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Anisotropic smoothing

Tolga Tasdizen, Ross Whitaker, Scientific Computing and Imaging Institute, University of Utah

Mean curvature computed after anisotropic smoothing of surface. Noise is smoothed and details are preserved.

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Image Based Phenotyping using the Mouse Hox Genes as a Prototype System

R. Whitaker, M.R. Capecchi, L. McAninch-Healy, Z.B. Warnock, A. Zharkikh, A.M. Boulet, Scientific Computing and Imaging Institute, University of Utah

Segmentations of assorted mouse metacarpals and phlanges. Segmentations were done using the Insight ToolKit (ITK) (National Library of Medicine). The segmentation algorithms within ITK were engineering by the SCI Institute.

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Visualization of Spiny Dendrite Using Level-Set Surface Models

Vidya Elangovan, Ross Whitaker, Scientific Computing and Imaging Institute, University of Utah

Microscopic electron tomography produces noisy 3D data, which can be visualized using level-set surface model, which fits the data while preserving some level of continuity and smoothness. Electron tomography data courtesy of Mark Ellisman, National Center for Microscopy and Imaging Research.

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Fourier basis functions of Japan (lowest 25 "frequencies")

Naoki Saito, Department of Mathematics, University of California, Davis

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Image visualizing vertical movement of data points during constrained terrain regularization

Michael Hofer, Guillermo Sapiro, Department of Electrical and Computer Engineering, University of Minnesota and Johannes Wallner, Institute of Discrete Mathematics and Geometry, Vienna University of Technology, Austria

Fair polyline networks for constrained smoothing of digital terrain elevation data. IMA Preprint 2058, University of Minnesota, August 2005.

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Computer generated painterly image rendered from a 3D laser-scanned dataset of the Stone Arch Bridge, Minneapolis

Hui Xu, Nathan Gossett and Baoquan Chen, Department of Computer Science and Engineering, University of Minnesota

PointWorks: Abstraction and Rendering of Sparsely Scanned Outdoor Environments, In Proceedings of the 2004 Eurographics Symposium on Rendering (EGSR'04). Norrköping, Sweden, Jun 21-23, 2004

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a. Computer generated stippling rendering of the Mount Rushmore


b. Demonstrates a novel viwing angle of the Mount Rushmore from the captured data set.

Capturing and Stylized Rendering of Mount Rushmore

Hui Xu and Baoquan Chen, Department of Computer Science and Engineering, University of Minnesota

Stylized Rendering of 3D Scanned Real World Environments, In Proceedings of the 3rd International Symposium on Non-Photorealistic Animation and Rendering (NPAR'04). Annecy, France, Jun 7-9, 2004

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Edges in Schlieren data of reacting turbulent flow via mean-curvature dependent filtering

Walter Richardson, Department of Mathematical Sciences, The University of Texas at San Antonio

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Cross-sections of random samples from a family of 3D binary Markov random fields

Hstau Liao, The Graduate Center, City University of New York

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Beamformer image of tumors based on UWB microwave backscatter from a numerical breast phantom

Shakti Davis, Susan Hagness, and Barry Van Veen,

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Figure 1: Boy surface with triple point

The Boy surface is a model of the real projective plane. Each immersion of the projective plane must have self-intersection and at least one triple point where three parts of the surface meet. The self-intersection is emphasized by the thicker red line which also highlights the triple point. This model is colored by Gauss curvature.



Figure 2: Tessellation of the hyperbolic plane

Tessellation of the hyperbolic plane with a triangle (2,3,7). The numbers determine how many (twice as much) triangles fit around each vertex.



Figure 3: Geodesic curves on a pretzel

Geodesic curves are the shortest and straightest lines on a curved surfaces. Physically geodesics can be produced by letting a rubber band vary on a surface with both end points been fixed. The pretzel world shows that there may be more than one geodesic connecting two locations, each of them is a local minimum for the length functional.

From video "Geodesics and Waves" http://www.zib.de/polthier/video/
Geodesics/index.html



Figure 4: The ideal Platonic solids of hyperbolic 3-space

The four ideal Platonic solids in hyperbolic space shown in an arrangement over a hyperbolic plane. Each solid is enclosed in an own glass ball.



Figure 5: Klein Bottle with Moebius Band

The Klein bottle is a non-orientable surface found by Felix Klein in 1882 while working on a topological classification of surfaces.

There exists two Moebius bands on a Klein bottle. The second band is symmetric to the shown Moebius band.

Article "Imaging maths - Inside the Klein bottle" at http://plus.maths.org/
issue26/index.html

Konrad Polthier, Zuse Institute Berlin (ZIB)

http://www.zib.de/polthier/images

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Figure 1: Height map for a textile texture from a flatbed scanner


Figure 2: Height + colour map for a textile texture from a flatbed scanner

Andy Spence and Mike Chantler, Texture Lab, Heriot-Watt University, Edinburgh, UK

We present results from the application of our algorithm for producing 3D texture data from a small number of images acquired using an ordinary flatbed scanner. The corresponding height, bump and colour maps may be utilised to render mixed reality scenes with photorealistic textures.

For more textures, check http://www.macs.hw.ac.uk/texturelab/scan/texturescan.html

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SURFACE INACCURACIES. Intersection of gray-matter (GM) and white-matter (WM) CLASP surfaces: the GM surface is rendered in red, the corresponding WM surface in green. White circles indicate an intersection of the GM and WM surfaces (cutaway view). In the right lower panel BRAINVISA surfaces-- WM (blue) and GM (red)--are embedded in an axial brain slice; visible flaws include a midline crossing (A), an inaccurate WM-GM boundary (B), failure to penetrate a sulcus (C), and an inaccurate GM-CSF boundary (D).

David Rottenberg, University of Minnesota

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Diffraction tomography sinograms for isotropic and anisotropic cylinder/cube, and their difference

Matthew Lewis, Advanced Radiological Sciences, UT Southwestern Medical Center at Dallas

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fMRI in a cat at 9.4 Tesla. The color is high resolution (.15x.15x2 mm) BOLD activation patterns in response to visual stimulation across the LAYERS in primary visual cortex, overlayed on a high resolution T1 image.

Steen Moeller and Noam Harel, Center for Magnetic Resonance Research, University of Minnesota
Noam Harel, Joseph Lin, Steen Moeller, Kamil Ugurbil, and Essa Yacoub "Combined imaging.histological study of cortical laminar specificity of fMRI signals" To appear in NeuroImage 2005.

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Figure 1: Mean Diameter and Standard Deviation of Nanoparticle Sizes

This image represents nanoparticle formation in a TiCl4 combustion simulation. Spot sizes and color on the heated-object scale represent the mean diameter of particles at a given point in space, while the diversity of sizes of these spots in a given area relates to the standard deviation of spot sizes. For example, in an area with large particles of low deviation, we would expect mostly large spots. In an area with medium size particles and high deviation we would expect to see a wider range of spots, some large and some small, whose average size is medium.


Figure 2: Nanoparticle Count Information

Here we see a representation of nanoparticle quantities at a point for six different sizes of nanoparticles, each represented by a concentric ring in a target glyph. I've used six perceptually-equiluminant colorscales to show counts of particles of sizes 1,2,4,8,16,and 32 nanometers, each count linked sequentially to rings of the target glyphs from center outward. Brighter rings contain more particles of a given size.

Patrick Coleman Saunders, S.C. Garrick, and Victoria Interrante, Computer Graphics Group, Department of Computer Science and Engineering, University of Minnesota

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A composite 'color woven' image of an experimentally acquired particle image velocimetry dataset in which we simultaneously highlight areas of significant positive vorticity (red), negative vorticity (blue), strongely negative Reynolds shear stress (green), and high swirl strength (orange or magenta, depending on the direction of the swirl).

Tim Urness and Victoria Interrante, Computer Graphics Group, Department of Computer Science and Engineering, University of Minnesota

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Figure 1: Metal microstructure colorized with computer software and duplicated (by accident) by the computer and displayed as a background pixelated image.



Figure 2: Crystals being precipitated from solution (with a droplet in the center).

Richard H. Lee, Argonne National Laboratory, retired

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Abstract image synthesis from geometric principles

These examples illustrate how a small number of geometrical principles enables the creation of a wide range of abstract images, ranging from Mondrian-like juxtaposition of simple figures to complicated textures. Most of these principles, such as exclusion, occlusion or transparency, are at work in natural images formation.

Contributors: Luis Alvarez, Universidad de Las Palmas de Gran Canaria, Spain. Yann Gousseau, Ecole Nationale Superieure des telecommunications, Paris, France. Jean-Michel Morel, Ecole Normale Superieure de Cachan, France.

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The following links lead to more examples : http://serdis.dis.ulpgc.es/ami/demos/algomo/algomo.html and http://www.tsi.enst.fr/~gousseau/Algomo/

Antonello da Messina artworks depicted by Opus Vermiculatum Mosaic Rendering

Sebastiano Battiato, Università di Catania - Dipartimento di Matematica ed Informatica

The underlying details are available here:
S. Battiato, G. Di Blasi, G. M. Farinella, G. Gallo, A Novel Technique for Opus Vermiculatum Mosaic Rendering In Proceedings of 14-th International Conference in Central Europe on Computer Graphics, Visualization and Computer Vision, WSCG 2006 Plzen, Czech Republic, February 2006;

Visit http://svg.dmi.unict.it/iplab/ for more info.

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Lyapunov exponent of the logistic map with periodic forcing

Paul Jackway, CSIRO Australia

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Möbius transformed square and its inverse image under stereographic projection

This is a frame from the video Möbius Transformations Revealed

Douglas N. Arnold and Jonathan Rogness, University of Minnesota

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