Visualization of tensor fields using superquadric glyphs

Daniel B. Ennis, Gordon Kindlman, Ignacio Rodriguez, Patrick A. Helm, Elliot R. McVeigh

Research output: Contribution to journalArticlepeer-review

40 Scopus citations


The spatially varying tensor fields that arise in magnetic resonance imaging are difficult to visualize due to the multivariate nature of the data. To improve the understanding of myocardial structure and function a family of objects called glyphs, derived from superquadric parametric functions, are used to create informative and intuitive visualizations of the tensor fields. The superquadric glyphs are used to visualize both diffusion and strain tensors obtained in canine myocardium. The eigensystem of each tensor defines the glyph shape and orientation. Superquadric functions provide a continuum of shapes across four distinct eigensystems (λi, sorted eigenvalues), λ1 = λ2 = λ3 (spherical), λ12 = λ3 (oblate), λ1 > λ2 = λ3 (prolate), and λ1 > λ2 > λ3 (cuboid). The superquadric glyphs are especially useful for identifying regions of anisotropic structure and function. Diffusion tensor renderings exhibit fiber angle trends and orthotropy (three distinct eigenvalues). Visualization of strain tensors with superquadric glyphs compactly exhibits radial thickening gradients, circumferential and longitudinal shortening, and torsion combined. The orthotropic nature of many biologic tissues and their DTMRI and strain data require visualization strategies that clearly exhibit the anisotropy of the data if it is to be interpreted properly. Superquadric glyphs improve the ability to distinguish fiber orientation and tissue orthotropy compared to ellipsoids.

Original languageEnglish (US)
Pages (from-to)169-176
Number of pages8
JournalMagnetic Resonance in Medicine
Issue number1
StatePublished - Jan 2005


  • Diffusion
  • Fiber angle
  • Myocardium
  • Tensor

ASJC Scopus subject areas

  • Radiology Nuclear Medicine and imaging
  • Radiological and Ultrasound Technology


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