Tensor splats

  title={Tensor splats},
  author={Werner Benger and Hans-Christian Hege},
  booktitle={IS\&T/SPIE Electronic Imaging},
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 directional information content of a tensor. The result is an information-rich image that allows to read off the preferred directions in a tensor field. It is useful for analyzing slices or volumes of a three-dimensional… 

Superquadric Glyphs for Symmetric Second-Order Tensors

This work generalizes a previous method of superquadric glyphs for positive-definite tensors by drawing upon a larger portion of the superquadrics shape space, supplemented with a coloring that indicates the tensor's quadratic form.

Diffusion Tensor Visualization with Glyph Packing

This work adapt particle systems originally developed for surface modeling and anisotropic mesh generation to enhance the utility of glyph-based tensor visualizations, by carefully distributing glyphs throughout the field into a dense packing.

Asymmetric Tensor Field Visualization for Surfaces

  • D. PalkeZ. Lin E. Zhang
  • Computer Science
    IEEE Transactions on Visualization and Computer Graphics
  • 2011
A hybrid visualization technique in which hyperstreamlines and elliptical glyphs are used in real and complex domains, respectively, which enables a more faithful representation of flow behaviors inside complex domains and leads to an efficient tensor field visualization system for domain scientists.

An Evaluation of Glyph Perception for Real Symmetric Traceless Tensor Properties

A perceptual study of four tensor glyphs for symmetric, real, traceless tensors was performed to evaluate the effectiveness of visually communicating the properties and discusses the significant differences found between the methods as guidance to the use of these Glyphs for trACeless tensor visualization.

HOT-lines: tracking lines in higher order tensor fields

This paper unites the definition of streamlines and tensor lines and generalizes Tensor lines to those applications where second order tensor representations fail and points out similarities of symmetric higher order tensors and spherical harmonics.

Visualization and Analysis of Second‐Order Tensors: Moving Beyond the Symmetric Positive‐Definite Case

This review focuses on second‐order tensors that are not diffusion tensors, and discusses the strengths and limitations of existing methods when dealing with such tensors as well as challenges introduced by them.

Hybrid visualization of asymmetric tensor fields : glyphs and hyperstreamlines

A hybrid visualization approach in which hyperstreamlines are used to illustrate the tensors in the real domains and glyphs are employed in complex domains and this enables an effective visualization of the physical patterns everywhere and also provides a more intuitive illustration of elliptical patterns in the complex domains.

Fast and Memory Efficient GPU-Based Rendering of Tensor Data

A method to display a large amount of superquadric glyphs is presented and its use for visualization of measured secondorder tensor data in diffusion tensor imaging (DTI) and to stress and strain tensors of computational fluid dynamic and material simulations is demonstrated.

Asymmetric tensor visualization with glyph and hyperstreamline placement on 2D manifolds

A hybrid visualization approach is presented in which hyperstreamlines are used to illustrate the tensors in the real domains while glyphs are employed for complex domains, which enables an effective visualization of the flow patterns everywhere and also provides a more intuitive illustration of elliptical flow patterns in the complex domains.


A new visualization technique for visualizing three-dimensional symmetric positivedefinite tensor fields of rank two is described. It supports studying the spatialprojection of a spacetime metric. The



Hue-balls and lit-tensors for direct volume rendering of diffusion tensor fields

Direct volume rendering is proposed, with novel approaches for the tensors' coloring, lighting, and opacity assignment based on a novel two-dimensional barycentric space of anisotropy, to produce informative renderings of measured diffusion tensor data from the human brain.

Volume deformation for tensor visualization

Two new methods are presented, based on volume deformation, to show the effects of the tensor field upon its underlying media, and focus on providing a continuous representation of the nature of the Tensor fields.

Tensor field visualisation using adaptive filtering of noise fields combined with glyph rendering

A method for visualising second order tensors in three dimensions using a hybrid between direct volume rendering and glyph rendering, giving both an overview of the tensor field as well as detailed information on individual tensors.

Strategies for Direct Volume Rendering of Diffusion Tensor Fields

This paper describes and demonstrates further means of generating opacity, color, and shading from the tensor information in diffusion tensor MRI data, and proposes anisotropic reaction-diffusion volume textures as an additional tool for visualizing the structure of diffusion data.

Oriented tensor reconstruction: tracing neural pathways from diffusion tensor MRI

A new technique for tracing anatomical fibers from 3D tensor fields is developed using a local regularization technique that allows the algorithm to cross noisy regions and bridge gaps in the data.

Interactive deformations from tensor fields

  • Ed BoringA. Pang
  • Engineering
    Proceedings Visualization '98 (Cat. No.98CB36276)
  • 1998
Techniques for interactively visualizing tensor fields using deformations are presented and the effectiveness of the Deviator-Isotropic tensor decomposition in deformation visualizations of CFD strain rate is illustrated.

Interaction of Light and Tensor Fields

Three new ways of looking at tensor volumes are presented that can work directly with non-symmetric tensor fields without first decomposing them into components and use the concept of treating the tensor volume as a special lens that distorts an image.

A geometric analysis of diffusion tensor measurements of the human brain

A new method for representing the diffusion tensor shape, called the three‐phase (3P) plot, is described, which is a graphical technique based upon a barycentric coordinate system, which weights the Tensor shape by a combination of linear, cylindrical, and spherical shape factors.

Tensorlines: advection-diffusion based propagation through diffusion tensor fields

A novel feature extraction method which is based on incorporating information about the nearby orientation of the feature, as well as the anisotropic classification of the local tensor, which has the effect of stabilizing the tracking.

Elucidating Neural Structure in Diffusion Tensor MRI Volumes using Streamtubes and Streamsurfaces

diffusion tensor MRI images. We distinguish between linear anisotropy and planar anisotropy and represent values within the two regimes using streamtubes and streamsurfaces, respectively. Streamtubes