The tasks of identifying separation structures and clusters in flow data are fundamental to flow visualization. Significant work has been devoted to these tasks in flow represented by vector fields, but there are unique challenges in addressing these tasks for time-varying particle data. The unstructured nature of particle data, nonuniform and sparse sampling, and the inability to access arbitrary particles in space-time make it difficult to define separation and clustering for particle data. We observe that weaker notions of separation and clustering through continuous measures of these structures are meaningful when coupled with user exploration. We achieve this goal by defining a measure of particle similarity between pairs of particles. More specifically, separation occurs when spatially-localized particles are dissimilar, while clustering is characterized by sets of particles that are similar to one another. To be robust to imperfections in sampling we use diffusion geometry to compute particle similarity. Diffusion geometry is parameterized by a scale that allows a user to explore separation and clustering in a continuous manner. We illustrate the benefits of our technique on a variety of 2D and 3D flow datasets, from particles integrated in fluid simulations based on time-varying vector fields, to particle-based simulations in astrophysics.
A basic problem when deriving information from measured data, such as images, originates from the fact that objects in the world, and hence image structures, exist as meaningful entities only over ...  Scale-space techniques have become popular in computer vision for their capability to access the multiscale information inherently contained in images. We show that the field of flow visualization can benefit from these techniques, too, yielding more coherent features and sorting out numerical artifacts as well as irrelevant large-scale features. We describe an implementation of scale-space computation using finite elements and show that performance is sufficient for computing a scale-space of time-dependent CFD data. Feature tracking, if available, allows to process the information provided by scale-space not just visually but also algorithmically. We present a technique for extending a class of feature extraction schemes by an additional dimension, resulting in an efficient solution of the tracking problem.