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Computational and Mathematical Methods in Medicine
Volume 2014, Article ID 476837, 18 pages
Research Article

Crossing Fibers Detection with an Analytical High Order Tensor Decomposition

1USTHB, FEI, LRPE, ParIMéd, Algiers, Algeria
2Equipe-Projet Athena, Inria Sophia Antipolis-Méditerranée, France

Received 21 March 2014; Revised 1 June 2014; Accepted 2 June 2014; Published 27 August 2014

Academic Editor: Xiaobo Qu

Copyright © 2014 T. Megherbi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Diffusion magnetic resonance imaging (dMRI) is the only technique to probe in vivo and noninvasively the fiber structure of human brain white matter. Detecting the crossing of neuronal fibers remains an exciting challenge with an important impact in tractography. In this work, we tackle this challenging problem and propose an original and efficient technique to extract all crossing fibers from diffusion signals. To this end, we start by estimating, from the dMRI signal, the so-called Cartesian tensor fiber orientation distribution (CT-FOD) function, whose maxima correspond exactly to the orientations of the fibers. The fourth order symmetric positive definite tensor that represents the CT-FOD is then analytically decomposed via the application of a new theoretical approach and this decomposition is used to accurately extract all the fibers orientations. Our proposed high order tensor decomposition based approach is minimal and allows recovering the whole crossing fibers without any a priori information on the total number of fibers. Various experiments performed on noisy synthetic data, on phantom diffusion, data and on human brain data validate our approach and clearly demonstrate that it is efficient, robust to noise and performs favorably in terms of angular resolution and accuracy when compared to some classical and state-of-the-art approaches.