Criteria for representations of shape

Uncertainty and its representation have an important role to play in any situation where the goal is to infer useful information from noisy data. In diffusion-weighted MRI (DW-MRI) scientists attempt to infer information about, for example, diffusion anisotropy or underlying fiber tract direction, by fitting models of the diffusion and measurement processes to DW-MRI data (e.g., Refs. 1, 2). In this scheme there is uncertainty caused both by the noise and artifacts present in any MR scan, but also by the incomplete modeling of the diffusion signal. That is, the true diffusion signal is more complicated than we choose to model. This additional complexity in the diffusion signal appears as residuals when we fit a simple model to the data, causing additional uncertainty in the model parameters.