Assessment of the Characteristics of Orientation Distribution Functions in HARDI Using Morphological Metrics

Orientation distribution functions (ODFs) are widely used to resolve fiber crossing problems in high angular resolution diffusion imaging (HARDI). The characteristics of the ODFs are often assessed using a visual criterion, although the use of objective criteria is also reported, which are directly borrowed from classic signal and image processing theory because they are intuitive and simple to compute. However, they are not always pertinent for the characterization of ODFs. We propose a more general paradigm for assessing the characteristics of ODFs. The idea consists in regarding an ODF as a three-dimensional (3D) point cloud, projecting the 3D point cloud onto an angle-distance map, constructing an angle-distance matrix, and calculating metrics such as length ratio, separability, and uncertainty. The results from both simulated and real data show that the proposed metrics allow for the assessment of the characteristics of ODFs in a quantitative and relatively complete manner.