Premium
Critical Points of Gaussian‐Distributed Scalar Fields on Simplicial Grids
Author(s) -
Liebmann T.,
Scheuermann G.
Publication year - 2016
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/cgf.12912
Subject(s) - gaussian , scalar (mathematics) , computer science , scalar field , topological data analysis , algorithm , monte carlo method , gaussian process , theoretical computer science , graph , focus (optics) , representation (politics) , statistical physics , topology (electrical circuits) , mathematics , geometry , statistics , physics , quantum mechanics , politics , law , political science , optics , mathematical physics , combinatorics
Simulations 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.