Visualizing Tensor Normal Distributions at Multiple Levels of Detail

In: IEEE Trans. on Visualization and Computer Graphics (2016), 22:1(975-984)
 

Abstract

Despite the widely recognized importance of symmetric second order tensor fields in medicine and engineering, the visualization of data uncertainty in tensor fields is still in its infancy. A recently proposed tensorial normal distribution, involving a fourth order covariance tensor, provides a mathematical description of how different aspects of the tensor field, such as trace, anisotropy, or orientation, vary and covary at each point. However, this wealth of information is far too rich for a human analyst to take in at a single glance, and no suitable visualization tools are available. We propose a novel approach that facilitates visual analysis of tensor covariance at multiple levels of detail. We start with a visual abstraction that uses slice views and direct volume rendering to indicate large-scale changes in the covariance structure, and locations with high overall variance. We then provide tools for interactive exploration, making it possible to drill down into different types of variability, such as in shape or orientation. Finally, we allow the analyst to focus on specific locations of the field, and provide tensor glyph animations and overlays that intuitively depict confidence intervals at those points. Our system is demonstrated by investigating the effects of measurement noise on diffusion tensor MRI, and by analyzing two ensembles of stress tensor fields from solid mechanics.

Keywords: direct volume rendering, glyph based visualization., interaction, tensor visualization, Uncertainty visualization

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Bibtex

@ARTICLE{abbasloo:VIS2015,
    author = {Abbasloo, Amin and Wiens, Vitalis and Hermann, Max and Schultz, Thomas},
     pages = {975--984},
     title = {Visualizing Tensor Normal Distributions at Multiple Levels of Detail},
   journal = {IEEE Trans. on Visualization and Computer Graphics},
    volume = {22},
    number = {1},
      year = {2016},
  keywords = {direct volume rendering, glyph based visualization., interaction, tensor visualization, Uncertainty
              visualization},
  abstract = {Despite the widely recognized importance of symmetric second order tensor fields in medicine and
              engineering, the visualization of data uncertainty in tensor fields is still in its infancy. A
              recently proposed tensorial normal distribution, involving a fourth order covariance tensor,
              provides a mathematical description of how different aspects of the tensor field, such as trace,
              anisotropy, or orientation, vary and covary at each point. However, this wealth of information is
              far too rich for a human analyst to take in at a single glance, and no suitable visualization tools
              are available. We propose a novel approach that facilitates visual analysis of tensor covariance at
              multiple levels of detail. We start with a visual abstraction that uses slice views and direct
              volume rendering to indicate large-scale changes in the covariance structure, and locations with
              high overall variance. We then provide tools for interactive exploration, making it possible to
              drill down into different types of variability, such as in shape or orientation. Finally, we allow
              the analyst to focus on specific locations of the field, and provide tensor glyph animations and
              overlays that intuitively depict confidence intervals at those points. Our system is demonstrated by
              investigating the effects of measurement noise on diffusion tensor MRI, and by analyzing two
              ensembles of stress tensor fields from solid mechanics.}
}