Notes on Percolation Analysis of Sampled Scalar Fields
Köpp W, Friederici A, Atzori M, Vinuesa R, Schlatter P, Weinkauf T (2021)
Publication Type: Conference contribution
Publication year: 2021
Publisher: Springer Science and Business Media Deutschland GmbH
Pages Range: 39-54
Conference Proceedings Title: Mathematics and Visualization
Event location: Nyköping, SWE
ISBN: 9783030834999
DOI: 10.1007/978-3-030-83500-2_3
Abstract
Percolation analysis is used to explore the connectivity of randomly connected infinite graphs. In the finite case, a closely related percolation function captures the relative volume of the largest connected component in a scalar field’s superlevel set. While prior work has shown that random scalar fields with little spatial correlation yield a sharp transition in this function, little is known about its behavior on real data. In this work, we explore how different characteristics of a scalar field—such as its histogram or degree of structure—influence the shape of the percolation function. We estimate the critical value and transition width of the percolation function, and propose a corresponding normalization scheme that relates these values to known results on infinite graphs. In our experiments, we find that percolation analysis can be used to analyze the degree of structure in Gaussian random fields. On a simulated turbulent duct flow data set we observe that the critical values are stable and consistent across time. Our normalization scheme indeed aids comparison between data sets and relation to infinite graphs.
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Sweden (SE)How to cite
APA:
Köpp, W., Friederici, A., Atzori, M., Vinuesa, R., Schlatter, P., & Weinkauf, T. (2021). Notes on Percolation Analysis of Sampled Scalar Fields. In Ingrid Hotz, Talha Bin Masood, Filip Sadlo, Julien Tierny (Eds.), Mathematics and Visualization (pp. 39-54). Nyköping, SWE: Springer Science and Business Media Deutschland GmbH.
MLA:
Köpp, Wiebke, et al. "Notes on Percolation Analysis of Sampled Scalar Fields." Proceedings of the 8th Workshop on Topological Methods in Data Analysis and Visualization, TopoInVis 2019, Nyköping, SWE Ed. Ingrid Hotz, Talha Bin Masood, Filip Sadlo, Julien Tierny, Springer Science and Business Media Deutschland GmbH, 2021. 39-54.
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