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.