Coherent Structures of Characteristic Curves in Symmetric Second Order Tensor Fields

Abstract

This paper generalizes the concept of Lagrangian coherent structures, which is known for its potential to visualize coherent regions in vector fields and to distinguish them from each other. In particular, we extend the concept of the flow map to generic mappings of coordinates. As the major application of this generalization, we present a semiglobal method for visualizing coherent structures in symmetric second order tensor fields. We demonstrate the usefulness by examples from DT-MRI, uncovering anatomical structures in linearly anisotropic regions not amenable to local feature criteria. To further exemplify the suitability of our concept, we also present its application to stress tensor fields. Last, an accelerated implementation utilizing GPUs is presented.