Uncertain topology of 3D vector fields

Abstract

We present a technique to visualize global uncertainty in stationary 3D vector fields by a topological approach. We start from an existing approach for 2D uncertain vector field topology and extend this into 3D space. For this a number of conceptional and technical challenges in performance and visual representation arise. In order to solve them, we develop an acceleration for finding sink and source distributions. Having these distributions we use overlaps of their corresponding volumes to find separating structures and saddles. As part of the approach, we introduce uncertain saddle and boundary switch connectors and provide algorithms to extract them. For the visual representation, we use multiple direct volume renderings. We test our method on a number of synthetic and real data sets.

Closed stream lines in uncertain vector fields

“…It is an integration based approach that results in particle density distributions, which represent the probability distributions of sinks and sources. An extension of this approach for uncertain 3D vector fields is presented in [Otto et al 2011]. The main contribution of this paper is the application of the saddle and boundary switch connectors approaches [Theisel et al 2003;Weinkauf et al 2004] to uncertain 3D vector fields.…”

“…Our approach considers only closed stream lines with a sink and source like character. The concepts of the extraction of sinks and sources are directly applicable for 3D uncertain vector fields [Otto et al 2011].…”

“…In [Otto et al 2010] a topological analysis of 2D uncertain vector fields is presented that describes the computation and visualization of sink, source and saddle distributions. In [Otto et al 2011] this concept was extended for uncertain 3D vector fields. In this work we consider closed stream lines.…”

“…For this we extend the approaches presented in [Otto et al 2010] and [Otto et al 2011] for the detection of closed stream lines. This results in scalar fields, which represent the probability distributions of sinks and sources, respectively.…”

Flow Visualization with Quantified Spatial and Temporal Errors Using Edge Maps

“…The earlier work on vector field uncertainty visualization concentrated on visualizing extended glyphs for vector samples to represent uncertainty [29], [43] and comparisons of streamlines using different integration schemes, step sizes and data resolutions [40]. Recently, Otto et al described a method to obtain uncertain topological segmentations by sampling in a random 2D vector field [27], and later extending it to 3D vector fields [28]. While their method tries to simulate the uncertainty in data probabilistically, disregarding the uncertainty due to the computation and visualization itself, the edge maps assume the given data as certain, and enable visualization of uncertainty introduced during computation and visualization only.…”