Scale-Space Approaches to FTLE Ridges

  • Raphael Fuchs
  • Benjamin Schindler
  • Ronald Peikert
Part of the Mathematics and Visualization book series (MATHVISUAL)


The finite-time Lyapunov Exponent (FTLE) is useful for the visualization of time-dependent velocity fields. The ridges of this derived scalar field have been shown to correspond well to attracting or repelling material structures, so-called Lagrangian coherent structures (LCS). There are two issues involved in the computation of FTLE for this purpose. Firstly, it is often not practically possible to refine the grid for sampling the flow map until convergence of FTLE is reached. Slow conversion is mostly caused by gradient underestimation. Secondly, there is a parameter, the integration time, which has to be chosen sensibly. Both of these problems call for an examination in scale-space. We show that a scale-space approach solves the problem of gradient underestimation. We test optimal-scale ridges for their usefulness with FTLE fields, obtaining a negative result. However, we propose an optimization of the time parameter for a given scale of observation. Finally, an incremental method for computing smoothed flow maps is presented.


Integration Time Lyapunov Exponent Lagrangian Coherent Structure Slide Time Window Neighbor Trajectory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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We thank Filip Sadlo for the simulation of the air convection. The project SemSeg acknowledges the financial support of the Future and Emerging Technologies (FET) program within the Seventh Framework Program for Research of the European Commission, under FET-Open grant number 226042.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Raphael Fuchs
    • 1
  • Benjamin Schindler
    • 1
  • Ronald Peikert
    • 1
  1. 1.ETH ZurichZurichSwitzerland

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