Degeneracy-aware interpolation of 3D diffusion tensor fields

Visual analysis of 3D diffusion tensor fields has become an important topic especially in medical imaging for understanding microscopic structures and physical properties of biological tissues. However, it is still difficult to continuously track the underlying features from discrete tensor samples, due to the absence of appropriate interpolation schemes in the sense that we are able to handle possible degeneracy while fully respecting the smooth transition of tensor anisotropic features. This is because the degeneracy may cause rotational inconsistency of tensor anisotropy. This paper presents such an approach to interpolating 3D diffusion tensor fields. The primary idea behind our approach is to resolve the possible degeneracy through optimizing the rotational transformation between a pair of neighboring tensors by analyzing their associated eigenstructure, while the degeneracy can be identified by applying a minimum spanning tree-based clustering algorithm to the original tensor samples. Comparisons with existing interpolation schemes will be provided to demonstrate the advantages of our scheme, together with several results of tracking white matter fiber bundles in a human brain.