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Towards Resolving Fiber Crossings with Higher Order Tensor Inpainting

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New Developments in the Visualization and Processing of Tensor Fields

Part of the book series: Mathematics and Visualization ((MATHVISUAL))

Abstract

The use of second-order tensors for the modeling of data from Diffusion Weighted Magnetic Resonance Imaging (DW-MRI) is limited by their inability to represent more than one dominant direction in cases of crossing fiber bundles or partial voluming. Higher-order tensors have been used in High Angular Resolution Diffusion Imaging (HARDI) to overcome these problems, but their larger number of parameters leads to longer measurement times for data acquisition. In this work, we demonstrate that higher-order tensors that indicate likely fiber directions can be estimated from a small number of diffusion-weighted measurements by taking into account information from local neighborhoods. To this end, we generalize tensor voting, a method from computer vision, to higher-order tensors. We demonstrate that the resulting even-order tensor fields facilitate fiber reconstruction at crossings both in synthetic and in real DW-MRI data, and that the odd-order fields differentiate crossings from junctions.

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Acknowledgements

I would like to thank Alfred Anwander (MPI CBS, Leipzig, Germany) for providing the DW-MRI dataset that was used to create Fig. 6. This work was supported by a fellowship within the Postdoc Program of the German Academic Exchange Service (DAAD).

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Authors and Affiliations

  1. Computation Institute, University of Chicago, 5735 S. Ellis Ave #209A, Chicago, IL, 60637, USA

    Thomas Schultz

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  1. Thomas Schultz
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Correspondence to Thomas Schultz .

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Editors and Affiliations

  1. Dept. Computer Science, Brown University, Providence, Rhode Island, USA

    David H. Laidlaw

  2. Department of Biomedical Engineering, Einhoven University of Technology, Eindhoven, 5600 MB, Netherlands

    Anna Vilanova

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Schultz, T. (2012). Towards Resolving Fiber Crossings with Higher Order Tensor Inpainting. In: Laidlaw, D., Vilanova, A. (eds) New Developments in the Visualization and Processing of Tensor Fields. Mathematics and Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27343-8_13

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