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As it provides the only method for mapping white matter fibers in vivo, diffusion MRI tractography is gaining importance in clinical and neuroscience research. However, despite the increasing availability of different diffusion models and tractography algorithms, it remains unclear how to select the optimal fiber reconstruction method, given certain imaging parameters. Consequently, it is of utmost importance to have a quantitative comparison of these models and algorithms and a deeper understanding of the corresponding strengths and weaknesses. In this work, we use a common dataset with known ground truth and a reproducible methodology to quantitatively evaluate the performance of various diffusion models and tractography algorithms. To examine a wide range of methods, the dataset, but not the ground truth, was released to the public for evaluation in a contest, the "Fiber Cup". 10 fiber reconstruction methods were evaluated. The results provide evidence that: 1. For high SNR datasets, diffusion models such as (fiber) orientation distribution functions correctly model the underlying fiber distribution and can be used in conjunction with streamline tractography, and 2. For medium or low SNR datasets, a prior on the spatial smoothness of either the diffusion model or the fibers is recommended for correct modelling of the fiber distribution and proper tractography results. The phantom dataset, the ground truth fibers, the evaluation methodology and the results obtained so far will remain publicly available on: http://www.lnao.fr/spip.php?rubrique79 to serve as a comparison basis for existing or new tractography methods. New results can be submitted to fibercup09@gmail.com and updates will be published on the webpage.

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We propose a novel algorithm for clustering data sampled from multiple submanifolds of a Riemannian manifold. First, we learn a representation of the data using generalizations of local nonlinear dimensionality reduction algorithms from Euclidean to Riemannian spaces. Such generalizations exploit geometric properties of the Riemannian space, particularly its Riemannian metric. Then, assuming that the data points from different groups are separated, we show that the null space of a matrix built from the local representation gives the segmentation of the data. Our method is computationally simple and performs automatic segmentation without requiring user initialization. We present results on 2-D motion segmentation and diffusion tensor imaging segmentation.

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Abstract. High angular resolution diffusion imaging (HARDI) has become an important magnetic resonance technique for in vivo imaging. Current techniques for estimating the diffusion orientation distribution function (ODF), i.e., the probability density function of water diffusion along any direction, do not enforce the estimated ODF to be nonnegative or to sum up to one. Very often this leads to an estimated ODF which is not a proper probability density function. In addition, current methods do not enforce any spatial regularity of the data. In this paper, we propose an estimation method that naturally constrains the estimated ODF to be a proper probability density function and regularizes this estimate using spatial information. By making use of the spherical harmonic representation, we pose the ODF estimation problem as a convex optimization problem and propose a coordinate descent method that converges to the minimizer of the proposed cost function. We illustrate our approach with experiments on synthetic and real data.