Generic objective vortices for flow visualization

In flow visualization, vortex extraction is a long-standing and unsolved problem. For decades, scientists developed numerous definitions that characterize vortex regions and their corelines in different ways, but none emerged as ultimate solution. One reason is that almost all techniques have a fundamental weakness: they are not invariant under changes of the reference frame, i.e., they are not objective. This has two severe implications: First, the result depends on the movement of the observer, and second, they cannot track vortices that are moving on arbitrary paths, which limits their reliability and usefulness in practice. Objective measures are rare, but recently gained more attention in the literature. Instead of only introducing a new objective measure, we show in this paper how all existing measures that are based on velocity and its derivatives can be made objective. We achieve this by observing the vector field in optimal local reference frames, in which the temporal derivative of the flow vanishes, i.e., reference frames in which the flow appears steady. The central contribution of our paper is to show that these optimal local reference frames can be found by a simple and elegant linear optimization. We prove that in the optimal frame, all local vortex extraction methods that are based on velocity and its derivatives become objective. We demonstrate our approach with objective counterparts to λ2, vorticity and Sujudi-Haimes.