Tensor splats

A new general-purpose technique for the visualization of time-dependent symmetric positive definite tensor fields of rank two is described. It is based on a splatting technique that is built from tiny transparent glyph primitives which are capable of incorporating the full orientational information content of a tensor. The result is an information-rich image that allows to read off the preferred orientations in a tensor field. It is useful for analyzing slices or volumes of a three-dimensional tensor field and can be overlaid with standard volume rendering or color mapping. The application of the rendering technique is demonstrated on numerically simulated general relativistic data and a measured diffusion tensor field of a human brain.

[1]  Alex Pang,et al.  Interactive deformations from tensor fields , 1998 .

[2]  John Moore,et al.  Methods of Classical Mechanics Applied to Turbulence Stresses in a Tip Leakage Vortex , 1995 .

[3]  Hanns Ruder,et al.  Visualization in Curved Spacetimes , 1996 .

[4]  Leonid Zhukov,et al.  Oriented tensor reconstruction: tracing neural pathways from diffusion tensor MRI , 2002, IEEE Visualization, 2002. VIS 2002..

[5]  D. Parker,et al.  A geometric analysis of diffusion tensor measurements of the human brain , 2000, Magnetic resonance in medicine.

[6]  Ingrid Hotz Isometric embedding by surface reconstruction from distances , 2002, IEEE Visualization, 2002. VIS 2002..

[7]  Richard H. Price,et al.  Embedding initial data for black-hole collisions , 1994, gr-qc/9409047.

[8]  D. Weiskopf Four-dimensional non-linear ray tracing as a visualization tool for gravitational physics , 2000 .

[9]  Carl-Fredrik Westin,et al.  Image Processing for Diffusion Tensor Magnetic Resonance Imaging , 1999, MICCAI.

[10]  Einar Heiberg,et al.  Tensor field visualisation using adaptive filtering of noise fields combined with glyph rendering , 2002, IEEE Visualization, 2002. VIS 2002..

[11]  B. Schutz Gravity from the ground up , 2003 .

[12]  J. Haueisen,et al.  The Influence of Brain Tissue Anisotropy on Human EEG and MEG , 2002, NeuroImage.

[13]  Alex T. Pang,et al.  Interaction of Light and Tensor Fields , 2003, VisSym.

[14]  Detlev Stalling,et al.  Fast texture based algorithms for vector field visualization , 1999 .

[15]  David E. Breen,et al.  Level Set Segmentation and Modeling of DT-MRI human brain data , 2003 .

[16]  Nelson L. Max,et al.  Texture Splats for 3D Scalar and Field Visualization , 1993, IEEE Visualization.

[17]  John Shalf,et al.  Solving Einstein's Equations on Supercomputers , 1999, Computer.

[18]  David H. Laidlaw,et al.  Visualizing diffusion tensor images of the mouse spinal cord , 1998 .

[19]  David H. Laidlaw,et al.  Visualizing the Differences between Diffusion Tensor Volume Images , 2000 .

[20]  Edward Seidel,et al.  Isometric embeddings of black-hole horizons in three-dimensional flat space , 2002 .

[21]  Steve Bryson Virtual spacetime: an environment for the visualization of curved spacetimes via geodesic flows , 1992, Proceedings Visualization '92.

[22]  Robert B. Haber,et al.  Visualization techniques for engineering mechanics , 1990 .

[23]  N. Makris,et al.  High angular resolution diffusion imaging reveals intravoxel white matter fiber heterogeneity , 2002, Magnetic resonance in medicine.

[24]  Gordon L. Kindlmann,et al.  Hue-balls and lit-tensors for direct volume rendering of diffusion tensor fields , 1999, Proceedings Visualization '99 (Cat. No.99CB37067).

[25]  Victoria Interrante,et al.  Strategies for effectively visualizing 3D flow with volume LIC , 1997 .

[26]  Lambertus Hesselink,et al.  Visualizing second-order tensor fields with hyperstreamlines , 1993, IEEE Computer Graphics and Applications.

[27]  E. Boring,et al.  Visualization of Tensor Fields , 1998 .

[28]  David H. Laidlaw,et al.  Elucidating Neural Structure in Diffusion Tensor MRI Volumes using Streamtubes and Streamsurfaces , 2001 .

[29]  Gordon L. Kindlmann,et al.  Strategies for Direct Volume Rendering of Diffusion Tensor Fields , 2000, IEEE Trans. Vis. Comput. Graph..

[30]  Gordon L. Kindlmann,et al.  Tensorlines: advection-diffusion based propagation through diffusion tensor fields , 1999, Proceedings Visualization '99 (Cat. No.99CB37067).

[31]  Alex T. Pang,et al.  Volume deformation for tensor visualization , 2002, IEEE Visualization, 2002. VIS 2002..