Percolation Analysis for Sampled Scalar Fields

Time: Thu 2019-06-13 11.15 - 12.15

Lecturer: Wiebke Köpp, CST/EECS/KTH

Location: Room 4423, Lindstedtsvägen 5, KTH, Stockholm

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Percolation theory traditionally studies the change in connectivity of infinite graphs when randomly adding more edges. For finite scalar fields, percolation analysis is based on a set of graphs given by the field's underlying connectivity and the super-level sets for selected thresholds. A percolation function captures the relative volume of the largest connected component of these graphs. Prior work has shown that random scalar fields with little spatial correlation yield a sharp transition in this function. However, little is known about its behavior on real data.
In this talk, we discuss a novel memory-distributed parallel algorithm to finely sample the percolation function enabling percolation analysis for large data sets. We further explore how different characteristics of a scalar field - such as its histogram or degree of structure - influence the analysis result and suggest adaptations to facilitate the comparison to known results on infinite graphs. Three application examples are presented: Large turbulent flow data, Gaussian random fields and uniformly random sampled data of varying dimension.

References

  • A. Friederici*, W. Köpp*, M. Atzori, R. Vinuesa, P. Schlatter, and T. Weinkauf. Distributed Percolation Analysis for Turbulent Flows. Currently under review
  • W. Köpp*, A. Friederici*, M. Atzori, R. Vinuesa, P. Schlatter, and T. Weinkauf. Notes on Percolation Analysis of Sampled Scalar Fields. Accepted for presentation at TopoInVis 2019

* Both authors contributed equally to these works.

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