Metric Selection and Diffusion Tensor Swelling

  • Ofer Pasternak
  • Nir Sochen
  • Peter J. Basser
Conference paper
Part of the Mathematics and Visualization book series (MATHVISUAL)


The measurement of the distance between diffusion tensors is the foundation on which any subsequent analysis or processing of these quantities, such as registration, regularization, interpolation, or statistical inference is based. Euclidean metrics were first used in the context of diffusion tensors; then geometric metrics, having the practical advantage of reducing the “swelling effect,” were proposed instead. In this chapter we explore the physical roots of the swelling effect and relate it to acquisition noise. We find that Johnson noise causes shrinking of tensors, and suggest that in order to account for this shrinking, a metric should support swelling of tensors while averaging or interpolating. This interpretation of the swelling effect leads us to favor the Euclidean metric for diffusion tensor analysis. This is a surprising result considering the recent increase of interest in the geometric metrics.


Fractional Anisotropy Diffusion Tensor Imaging Diffusion Tensor Riemannian Metrics Anisotropic Tensor 
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.



We thank Liz Salak for reviewing the manuscript. OP wishes to acknowledge with thanks that part of the research on which this publication is based was supported by a Fulbright Post-doctoral Scholar Fellowship, awarded by the Fulbright commission for Israel, the United States-Israel Educational Foundation. PJB was supported by the Intramural Research Program of the Eunice Kennedy Shriver National Institute of Child Health and Human Development.


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Copyright information

© Springer Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Brigham and Women’s HospitalHarvard Medical SchoolBostonUSA
  2. 2.Department of Applied MathematicsTel Aviv UniversityTel AvivIsrael
  3. 3.The Eunice Kennedy Shriver National Institute of Child Health and Human Development (NICHD)National Institutes of HealthBethesdaUSA

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