Application of Uncertainty Modeling Frameworks to Uncertain Isosurface Extraction

Abstract. Proper characterization of uncertainty is a challenging task. Depend-ing on the sources of uncertainty, various uncertainty modeling frameworks have been proposed and studied in the uncertainty quantification literature. This pa-per applies various uncertainty modeling frameworks, namely possibility theory, Dempster-Shafer theory and probability theory to isosurface extraction from un-certain scalar fields. It proposes an uncertainty-based marching cubes template as an abstraction of the conventional marching cubes algorithm with a flexible uncertainty measure. The applicability of the template is demonstrated using 2D simulation data in weather forecasting and computational fluid dynamics and a synthetic 3D dataset

Uncertainty Propagation in DT-MRI Anisotropy Isosurface Extraction

Abstract. Scalar anisotropy indices are important means for the analysis and visualization of diffusion tensor fields. While the propagation of uncertainty and errors has been studied for a variety measures, this chapter additionally considers the extraction of isosurfaces from anisotropy fields. We use the numerical condition to estimate the uncertainty propagation from the DT’s eigenvalues via fractional (FA) and relative anisotropy (RA) to the position and shape of isosurfaces. Using level crossing probabilities we quantify and visualize the spatial distribution of uncertain isosurfaces. The superiority of FA to RA in terms of uncertainty propagation that was shown for anisotropy images in the literature does not hold for isosurfaces extracted from these images. Instead, our results indicate that for the purpose of isosurface extraction both measures perform approximately equally well.

From Quantification to Visualization: A Taxonomy of Uncertainty Visualization Approaches

Part 4: UQ PracticeInternational audienceQuantifying uncertainty is an increasingly important topic across many domains. The uncertainties present in data come with many diverse representations having originated from a wide variety of disciplines. Communicating these uncertainties is a task often left to visualization without clear connection between the quantification and visualization. In this paper, we first identify frequently occurring types of uncertainty. Second, we connect those uncertainty representations to ones commonly used in visualization. We then look at various approaches to visualizing this uncertainty by partitioning the work based on the dimensionality of the data and the dimensionality of the uncertainty. We also discuss noteworthy exceptions to our taxonomy along with future research directions for the uncertainty visualization community

Operation of HTS dc-SQUID sensors in high magnetic fields

Most visualization techniques have been designed on the assumption that the data to be represented are free from uncertainty. Yet this is rarely the case. Recently the visualization community has risen to the challenge of incorporating an indication of uncertainty into visual representations, and in this article we review their work. We place the work in the context of a reference model for data visualization, that sees data pass through a pipeline of processes. This allows us to distinguish the visualization of uncertainty - which considers how we depict uncertainty specified with the data - and the uncertainty of visualization - which considers how much inaccuracy occurs as we process data through the pipeline. It has taken some time for uncertain visualization methods to be developed, and we explore why uncertainty visualization is hard - one explanation is that we typically need to find another display dimension and we may have used these up already! To organise the material we return to a typology developed by one of us in the early days of visualization, and make use of this to present a catalogue of visualization techniques describing the research that has been done to extend each method to handle uncertainty. Finally we note the responsibility on us all to incorporate any known uncertainty into a visualization, so that integrity of the discipline is maintained

Overview and State-of-the-Art of Uncertainty Visualization

International audienceThe goal of visualization is to effectively and accurately communicate data. Visualization research has often overlooked the errors and uncertainty which accompany the scientific process and describe key characteristics used to fully understand the data. The lack of these representations can be attributed, in part, to the inherent difficulty in defining, characterizing, and controlling this uncertainty, and in part, to the difficulty in including additional visual metaphors in a well designed, potent display. However, the exclusion of this information cripples the use of visualization as a decision making tool due to the fact that the display is no longer a true representation of the data. This systematic omission of uncertainty commands fundamental research within the visualization community to address, integrate, and expect uncertainty information. In this chapter, we outline sources and models of uncertainty, give an overview of the state-of-the-art, provide general guidelines, outline small exemplary applications, and finally, discuss open problems in uncertainty visualization