Towards Resolving Fiber Crossings with Higher Order Tensor Inpainting

  • Thomas Schultz
Conference paper
Part of the Mathematics and Visualization book series (MATHVISUAL)


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.


Fiber Bundle Diffusion Weight Magnetic Resonance Image Texture Synthesis Fiber Tracking Image Inpainting 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



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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Copyright information

© Springer Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Computation InstituteUniversity of ChicagoChicagoUSA

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