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Abstract #1389

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

Aurobrata Ghosh1, Elias Tsigaridas2, Maxime Descoteaux3, Rachid Deriche4

1Project Odysse, INRIA Sophia Antipolis Mditerrane, Sophia Antipolis, Alpes Maritimes, France; 2Project GALAAD, INRIA Sophia Antipolis Mditerrane, France; 3NMR Lab, Neurospin / CEA, Saclay, France; 4Project Odysse, INRIA Sophia Antipolis Mditerrane, France

This paper presents a polynomial based approach for extracting the maximal directions of a spherical function, for example the ODF. It rewrites the ODF in the homogeneous polynomial (HP) basis constrained to the sphere and solves a constrained optimization problem algebraically. This guarantees that all the maxima are computed at once and also provides a measure for the quality of the maxima estimation. Since it works with a continuous polynomial function, this approach is not dependent on a discrete mesh for the mesh-resolution and mesh-orientation. The approach is tested on synthetic, phantom and real datasets and compared to a discrete mesh search approach. It is shown how this HP method naturally overcomes the inherent limitations of the discrete search method.