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
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.
- 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.