Two-dimensional time-dependent vortex regions based on the acceleration magnitude.

Acceleration is a fundamental quantity of flow fields that captures Galilean invariant properties of particle motion. Considering the magnitude of this field, minima represent characteristic structures of the flow that can be classified as saddle- or vortex-like. We made the interesting observation that vortex-like minima are enclosed by particularly pronounced ridges.

A scale space based persistence measure for critical points in 2D scalar fields.

This paper introduces a novel importance measure for critical points in 2D scalar fields. This measure is based on a combination of the deep structure of the scale space with the well-known concept of homological persistence. We enhance the noise robust persistence measure by implicitly taking the hill-, ridge- and outlier-like spatial extent of maxima and minima into account.

Efficient Computation of Combinatorial Feature Flow Fields.

We propose a combinatorial algorithm to track critical points of 2D time-dependent scalar fields. Existing tracking algorithms such as Feature Flow Fields apply numerical schemes utilizing derivatives of the data, which makes them prone to noise and involve a large number of computational parameters. In contrast, our method is robust against noise since it does not require derivatives, interpolation, and numerical integration.