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Efficient Computation of Combinatorial Feature Flow Fields
Sept. 2012 (vol. 18 no. 9)
pp. 1563-1573
J. Kasten, Konrad-Zuse-Zentrum fuer Informationstechnik, Zuse Inst., Berlin, Germany
J. Reininghaus, Konrad-Zuse-Zentrum fuer Informationstechnik, Zuse Inst., Berlin, Germany
T. Weinkauf, Dept. 4: Comput. Graphics, Max Planck Inst. for Inf., Saarbrucken, Germany
I. Hotz, Konrad-Zuse-Zentrum fuer Informationstechnik, Zuse Inst., Berlin, Germany
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. Furthermore, we propose an importance measure that combines the spatial persistence of a critical point with its temporal evolution. This leads to a time-aware feature hierarchy, which allows us to discriminate important from spurious features. Our method requires only a single, easy-to-tune computational parameter and is naturally formulated in an out-of-core fashion, which enables the analysis of large data sets. We apply our method to synthetic data and data sets from computational fluid dynamics and compare it to the stabilized continuous Feature Flow Field tracking algorithm.

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Index Terms:
numerical analysis,combinatorial mathematics,computational fluid dynamics,flow visualisation,flow visualization,combinatorial feature flow field computation,combinatorial algorithm,critical points tracking,2D time-dependent scalar fields,tracking algorithms,numerical schemes,computational parameters,noise robustness,importance measure,spatial persistence,temporal evolution,time-aware feature hierarchy,computational fluid dynamics,Feature extraction,Algorithm design and analysis,Joining processes,Manifolds,Noise measurement,Jacobian matrices,Noise,graph algorithms.,Flow visualization
Citation:
J. Kasten, J. Reininghaus, T. Weinkauf, I. Hotz, "Efficient Computation of Combinatorial Feature Flow Fields," IEEE Transactions on Visualization and Computer Graphics, vol. 18, no. 9, pp. 1563-1573, Sept. 2012, doi:10.1109/TVCG.2011.269
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