Abstract—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.
Index Terms—Non-euclidean metric, diffusion tensor, procrustes analysis, anisotropic diffusion.
Diwei Zhou is with the School of Technology, University of Wolverhampton, Wolverhampton, WV1 1LY, UK (e-mail: firstname.lastname@example.org).
Ian L. Dryden is with the Department of Statistics, University of South Carolina, Columbia, SC 29208, USA.
Alexey A. Koloydenko is with the Department of Mathematics, Royal Holloway, University of London, Egham, TW20 0EX, UK.
Li Bai is with the School of Computer Science, University of Nottingham, Nottingham, NG8 1BB, UK
Cite: Diwei Zhou, Ian L. Dryden, Alexey A. Koloydenko, and Li Bai, "Procrustes Analysis for Diffusion Tensor Image Processing," International Journal of Computer Theory and Engineering vol. 5, no. 1, pp. 108-113, 2013.