Diffusion Maps Segmentation of Magnetic Resonance Q-Ball Imaging

We present a Diffusion Maps clustering method applied to diffusion MRI in order to segment complex white matter fiber bundles. It is well-known that diffusion tensor imaging (DTI) is restricted in complex fiber regions with crossings and this is why recent High Angular Resolution Diffusion Imaging (HARDI) such has Q-Ball Imaging (QBI) have been introduced to overcome these limitations. QBI reconstructs the diffusion orientation distribution function (ODF), a spherical function that has its maximum(a) agreeing with the underlying fiber population. In this paper, we use the ODF representation in a small set of spherical harmonic coefficients as input to the Diffusion Maps clustering method. We first show the advantage of using Diffusion Maps clustering over classical methods such as N-Cuts and Laplacian Eigenmaps. In particular, our ODF Diffusion Maps requires a smaller number of hypothesis from the input data, reduces the number of artifacts in the segmentation and automatically exhibits the number of clusters segmenting the Q-Ball image by using an adaptative scale-space parameter. We also show that our ODF Diffusion Maps clustering can reproduce published results using the diffusion tensor (DT) clustering with N-Cuts on simple synthetic images without crossings. On more complex data with crossings, we show that our method succeeds to separate fiber bundles and crossing regions whereas the DT- based methods generate artifacts and exhibit wrong number of clusters. Finally, we show results on a real brain dataset where we successfully segment the fiber bundles.