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.

Abstract We propose a novel vortex core line extraction method based on the λ2vortex region criterion in order to improve the detection of vortex features for 3D flow visualization. The core line is defined as a curve that connects λ2minima restricted to planes that are perpendicular to the core line. The basic algorithm consists of the following stages: (1) λ2field construction and isosurface extraction; (2) computation of the curve skeleton of the λ2isosurface to build an initial prediction for the core line; (3) correction of the locations of the prediction by searching for λ2minima on planes perpendicular to the core line. In particular, we consider the topology of the vortex core lines, guaranteeing the same topology as the initial curve skeleton. Furthermore, we propose a geometry‐guided definition of vortex bifurcation, which represents the split of one core line into two parts. Finally, we introduce a user‐guided approach in order to narrow down vortical regions taking into account the graph of λ2along the computed vortex core line. We demonstrate the effectiveness of our method by comparing our results to previous core line detection methods with both simulated and experimental data; in particular, we show robustness of our method for noise‐affected data.