Procrustes analysis of diffusion tensor image processing

Diwei Zhou, Ian L. Dryden, Alexey A. Koloydenko, Li Bai

Research output: Contribution to journalArticlepeer-review


There is an increasing need to develop processing tools for diffusion tensor image data with the consideration of the non-Euclidean nature of the tensor space. In this paper Procrustes analysis, a non-Euclidean shape analysis tool under similarity transformations (rotation, scaling and translation), is proposed to redefine sample statistics of diffusion tensors. A new anisotropy measure Procrustes Anisotropy (PA) is defined with the full ordinary Procrustes analysis. Comparisons are made with other anisotropy measures including Fractional Anisotropy and Geodesic Anisotropy. The partial generalized Procrustes analysis is extended to a weighted generalized Procrustes framework for averaging sample tensors with different fractions of contributions to the mean tensor. Applications of Procrustes methods to diffusion tensor interpolation and smoothing are compared with Euclidean, Log-Euclidean and Riemannian methods.
Original languageEnglish
Pages (from-to)108-113
Number of pages6
JournalInternational Journal of Computer Theory and Engineering
Issue number1
Publication statusPublished - 1 Feb 2013


  • Non-euclidean metric
  • diffusion tensor
  • procrustes analysis
  • anisotropic diffusion


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