A Polynomial Based Approach to Extract Fiber Directions from the ODF and its Experimental Validation

Aurobrata Ghosh 1 Elias P. Tsigaridas 2, 3 Maxime Descoteaux 4 Rachid Deriche 1
1 ODYSSEE - Computer and biological vision
DI-ENS - Département d'informatique de l'École normale supérieure, CRISAM - Inria Sophia Antipolis - Méditerranée , ENS Paris - École normale supérieure - Paris, Inria Paris-Rocquencourt, ENPC - École des Ponts ParisTech
3 GALAAD - Geometry, algebra, algorithms
CRISAM - Inria Sophia Antipolis - Méditerranée , UNS - Université Nice Sophia Antipolis, CNRS - Centre National de la Recherche Scientifique : UMR6621
Abstract : In Diffusion MRI, spherical functions are commonly employed to represent the diffusion information. The ODF is an intuitive spherical function since its maxima are aligned with the dominant fiber directions. Therefore, it is important to correctly determine these maximal directions, as they are the key to tracing fiber tracts. A tractography algorithm will suffer from cumulative error when the maximal directions are incorrectly estimated locally. The goal of this work is to present a polynomial based approach for estimating the maximal directions correctly. The paper will also present a measure of the correctness of the estimation. This approach will be tested on synthetic, phantom, and real data, and will be compared to an existing discrete “mesh-search” approach [2]. It will be shown how this approach naturally overcomes the inherent shortcomings of the discrete search. Finally, although, the approach is demonstrated on the ODF, it can be equally applied to any spherical function.
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Aurobrata Ghosh, Elias P. Tsigaridas, Maxime Descoteaux, Rachid Deriche. A Polynomial Based Approach to Extract Fiber Directions from the ODF and its Experimental Validation. Proceedings ISMRM, Apr 2009, Honolulu, United States. 2009. 〈inria-00496876〉

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