Critical Points of Gaussian‐Distributed Scalar Fields on Simplicial Grids

TitleCritical Points of Gaussian‐Distributed Scalar Fields on Simplicial Grids
Publication TypeConference Paper
Year of Publication2016
AuthorsTom Liebmann, and Gerik Scheuermann
Conference NameEuroVis 2016, 18th EG/VGTC Conference on Visualization
PublisherComputer Graphics Forum
AbstractSimulations and measurements often result in scalar fields with uncertainty due to errors or output sensitivity estimates. Methods for analyzing topological features of such fields usually are not capable of handling all aspects of the data. They either are not deterministic due to using Monte Carlo approaches, approximate the data with confidence intervals, or miss out on incorporating important properties, such as correlation. In this paper, we focus on the analysis of critical points of Gaussian-distributed scalar fields. We introduce methods to deterministically extract critical points, approximate their probability with high precision, and even capture relations between them resulting in an abstract graph representation. Unlike many other methods, we incorporate all information contained in the data including global correlation. Our work therefore is a first step towards a reliable and complete description of topological features of Gaussian-distributed scalar fields.