Diffusion MRI (dMRI) provides rich information on the white matter of the human brain, enabling insight into neurological disease, normal aging, and neuroplasticity. We present BundleMAP, an approach to extracting features from dMRI data that can be used for supervised classification, regression, and hypothesis testing. Our features are based on aggregating measurements along nerve fiber bundles, enabling visualization and anatomical interpretation. The main idea behind BundleMAP is to use the ISOMAP manifold learning technique to jointly parametrize nerve fiber bundles. We combine this idea with mechanisms for outlier removal and feature selection to obtain a practical machine learning pipeline. We demonstrate that it increases accuracy of disease detection and estimation of disease activity, and that it improves the power of statistical tests.

Despite the widely recognized importance of symmetric second order tensor fields in medicine and engineering, the visualization of data uncertainty in tensor fields is still in its infancy. A recently proposed tensorial normal distribution, involving a fourth order covariance tensor, provides a mathematical description of how different aspects of the tensor field, such as trace, anisotropy, or orientation, vary and covary at each point. However, this wealth of information is far too rich for a human analyst to take in at a single glance, and no suitable visualization tools are available. We propose a novel approach that facilitates visual analysis of tensor covariance at multiple levels of detail. We start with a visual abstraction that uses slice views and direct volume rendering to indicate large-scale changes in the covariance structure, and locations with high overall variance. We then provide tools for interactive exploration, making it possible to drill down into different types of variability, such as in shape or orientation. Finally, we allow the analyst to focus on specific locations of the field, and provide tensor glyph animations and overlays that intuitively depict confidence intervals at those points. Our system is demonstrated by investigating the effects of measurement noise on diffusion tensor MRI, and by analyzing two ensembles of stress tensor fields from solid mechanics.