Procrustes analysis for diffusion tensor image processing
journal contributionposted on 12.03.2015 by Diwei Zhou, Ian L. Dryden, Alexey Koloydenko, Li Bai
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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.
The work was supported by the European Commission FP6 Marie Curie program through the CMIAG Research Training Network. The diffusion MR image data used in this paper is provided by the Division of Academic Radiology, University of Nottingham and Queen’s Medical Centre, UK.
- Mathematical Sciences