 Best Paper Award

Objective Observer-Relative Flow Visualization in Curved Spaces for Unsteady 2D Geophysical Flows

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Peter Rautek, Matej Mlejnek, Johanna Beyer, Jakob Troidl, Hanspeter Pfister, Thomas Theussl, Markus Hadwiger

 View presentation: 2020-10-27T15:35:00Z GMT-0600 Change your timezone on the schedule page
2020-10-27T15:35:00Z

Exemplar figure — We illustrate the automatic computation of observer motion relative to the time evolution of features in flow fields, such as the time-dependent global wind data set shown here, with hurricane Isabel (2003) as the feature in the center. Feature-relative visualization is enabled by an observer field that is automatically computed via global optimization, minimizing the observed time derivative to make the observed field as steady as possible. Relative to the observer field, the hurricane appears to be static, with the Earth moving inversely underneath. This enables the direct analysis of the time evolution of features in place.

Keywords

Flow visualization, observer fields, frames of reference, objectivity, symmetry groups, intrinsic covariant derivatives

Abstract

Computing and visualizing features in fluid flow often depends on the observer, or reference frame, relative to which the input velocity field is given. A desired property of feature detectors is therefore that they are objective, meaning independent of the input reference frame. However, the standard definition of objectivity is only given for Euclidean domains, and cannot be applied in curved spaces. We build on methods from mathematical physics and Riemannian geometry to generalize objectivity to curved spaces, using the powerful notion of symmetry groups as the basis for defining objectivity. From this, we develop a general mathematical framework for computing objective observer fields for curved surfaces, relative to which other computed measures become objective. An important property of our framework is that it works intrinsically in 2D, instead of in the 3D ambient space. This enables a direct generalization of the 2D computation of observer fields via optimization from flat domains to curved domains, without having to perform optimization in 3D. We specifically develop the case of unsteady 2D geophysical flows given on spheres, such as the Earth. Observer fields on curved surfaces enable objective feature computation as well as the visualization of the time evolution of scalar and vector fields, such that the automatically computed reference frames follow moving structures like vortices in a way that makes them appear to be steady.