Diffusion weighted magnetic resonance imaging (DW MRI) is a technique that measures the diffusion properties of water molecules to produce a tensor-valued volume dataset. Because water molecules can diffuse more easily along fiber tracts, for example in the brain, rather than across them, diffusion is anisotropic and can be used for segmentation. Segmentation requires the identification of regions with different diffusion properties. In this paper we propose a new set of rotationally invariant diffusion measures which may be used to map the tensor data into a scalar representation. Our invariants may be rapidly computed because they do not require the calculation of eigenvalues. We use these invariants to analyze a 3D DW MRI scan of a human head and build geometric models corresponding to isotropic and anisotropic regions. We then utilize the models to perform quantitative analysis of these regions, for example calculating their surface area and volume.