HiFiVE: A Hilbert Space Embedding of Fiber Variability Estimates for Uncertainty Modeling and Visualization

Thomas Schultz, Lara Schlaffke, Bernhard Schölkopf, and Tobias Schmidt-Wilcke
In: Computer Graphics Forum (2013), 32:3(121-130)
 

Abstract

Obtaining reproducible fiber direction estimates from diffusion MRI is crucial for successful fiber tracking. Modeling and visualizing the probability distribution of the inferred fiber directions is an important step in evaluating and comparing different acquisition schemes and fiber models. However, this distribution is usually strongly dominated by its main direction, which makes it difficult to examine when plotted naively.

In this work, we propose a new visualization of the fiber probability distribution. It is based on embedding the probability measure into a particular reproducing kernel Hilbert space. This permits a decomposition into an embedded delta peak, representing the main direction, and a non-negative residual. They are then combined into a new glyph representation which visually enhances the residual, in order to highlight even subtle differences. Moreover, the magnitude of the delta peak component quantifies precision of the main fiber direction.

We demonstrate that our new glyph provides a more detailed impression of the uncertainty than the current standard method, cones that contain 95% of the estimated directions. We use our new method to contribute to the validation of different ways of resampling the data (bootstrapping), and to visualize the differences between alternative acquisition schemes and models for inferring fiber directions (DTI vs. HARDI).

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Bibtex

@ARTICLE{SchultzEuroVis2013,
    author = {Schultz, Thomas and Schlaffke, Lara and Sch{\"o}lkopf, Bernhard and Schmidt-Wilcke, Tobias},
     pages = {121--130},
     title = {HiFiVE: A Hilbert Space Embedding of Fiber Variability Estimates for Uncertainty Modeling and
              Visualization},
   journal = {Computer Graphics Forum},
    volume = {32},
    number = {3},
      year = {2013},
  abstract = {Obtaining reproducible fiber direction estimates from diffusion MRI is crucial for successful fiber
              tracking. Modeling and visualizing the probability distribution of the inferred fiber directions is
              an important step in evaluating and comparing different acquisition schemes and fiber models.
              However, this distribution is usually strongly dominated by its main direction, which makes it
              difficult to examine when plotted naively.
              
              In this work, we propose a new visualization of the fiber probability distribution. It is based on
              embedding the probability measure into a particular reproducing kernel Hilbert space. This permits a
              decomposition into an embedded delta peak, representing the main direction, and a non-negative
              residual. They are then combined into a new glyph representation which visually enhances the
              residual, in order to highlight even subtle differences. Moreover, the magnitude of the delta peak
              component quantifies precision of the main fiber direction.
              
              We demonstrate that our new glyph provides a more detailed impression of the uncertainty than the
              current standard method, cones that contain 95% of the estimated directions. We use our new method
              to contribute to the validation of different ways of resampling the data (bootstrapping), and to
              visualize the differences between alternative acquisition schemes and models for inferring fiber
              directions (DTI vs. HARDI).}
}