  Three dimensional Polarized Light Imaging (3D-PLI) is an optical technique
which allows mapping the spatial fiber architecture of fibrous postmortem
tissues, at sub-millimeter resolutions. Here, we propose an analytical and fast
approach to compute the fiber orientation distribution (FOD) from
high-resolution vector data provided by 3D-PLI. The FOD is modeled as a sum of
K orientations/Diracs on the unit sphere, described on a spherical harmonics
basis and analytically computed using the spherical Fourier transform.
Experiments are performed on rich synthetic data which simulate the geometry of
the neuronal fibers and on human brain data. Results indicate the analytical
FOD is computationally efficient and very fast, and has high angular precision
and angular resolution. Furthermore, investigations on the right occipital lobe
illustrate that our strategy of FOD computation enables the bridging of spatial
scales from microscopic 3D-PLI information to macro- or mesoscopic dimensions
of diffusion Magnetic Resonance Imaging (MRI), while being a means to evaluate
prospective resolution limits for diffusion MRI to reconstruct region-specific
white matter tracts. These results demonstrate the interest and great potential
of our analytical approach.
