Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userUncertainty Visualization of the Marching Squares and Marching Cubes Topology Cases
332
0
0.0
(
0
)
Added by
Tushar Athawale
Publication date
2021
fields
Informatics Engineering
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
Marching squares (MS) and marching cubes (MC) are widely used algorithms for level-set visualization of scientific data. In this paper, we address the challenge of uncertainty visualization of the topology cases of the MS and MC algorithms for uncertain scalar field data sampled on a uniform grid. The visualization of the MS and MC topology cases for uncertain data is challenging due to their exponential nature and the possibility of multiple topology cases per cell of a grid. We propose the topology case count and entropy-based techniques for quantifying uncertainty in the topology cases of the MS and MC algorithms when noise in data is modeled with probability distributions. We demonstrate the applicability of our techniques for independent and correlated uncertainty assumptions. We visualize the quantified topological uncertainty via color mapping proportional to uncertainty, as well as with interactive probability queries in the MS case and entropy isosurfaces in the MC case. We demonstrate the utility of our uncertainty quantification framework in identifying the isovalues exhibiting relatively high topological uncertainty. We illustrate the effectiveness of our techniques via results on synthetic, simulation, and hixel datasets.
rate research
Read More
Background: It is possible to find many different visual representations of data values in visualizations, it is less common to see visual representations that include uncertainty, especially in visualizations intended for non-technical audiences. Objective: our aim is to rigorously define and evaluate the novel use of visual entropy as a measure of shape that allows us to construct an ordered scale of glyphs for use in representing both uncertainty and value in 2D and 3D environments. Method: We use sample entropy as a numerical measure of visual entropy to construct a set of glyphs using R and Blender which vary in their complexity. Results: A Bradley-Terry analysis of a pairwise comparison of the glyphs shows participants (n=19) ordered the glyphs as predicted by the visual entropy score (linear regression R2 >0.97, p<0.001). We also evaluate whether the glyphs can effectively represent uncertainty using a signal detection method, participants (n=15) were able to search for glyphs representing uncertainty with high sensitivity and low error rates. Conclusion: visual entropy is a novel cue for representing ordered data and provides a channel that allows the uncertainty of a measure to be presented alongside its mean value.
As an important method of handling potential uncertainties in numerical simulations, ensemble simulation has been widely applied in many disciplines. Visualization is a promising and powerful ensemble simulation analysis method. However, conventional visualization methods mainly aim at data simplification and highlighting important information based on domain expertise instead of providing a flexible data exploration and intervention mechanism. Trial-and-error procedures have to be repeatedly conducted by such approaches. To resolve this issue, we propose a new perspective of ensemble data analysis using the attribute variable dimension as the primary analysis dimension. Particularly, we propose a variable uncertainty calculation method based on variable spatial spreading. Based on this method, we design an interactive ensemble analysis framework that provides a flexible interactive exploration of the ensemble data. Particularly, the proposed spreading curve view, the region stability heat map view, and the temporal analysis view, together with the commonly used 2D map view, jointly support uncertainty distribution perception, region selection, and temporal analysis, as well as other analysis requirements. We verify our approach by analyzing a real-world ensemble simulation dataset. Feedback collected from domain experts confirms the efficacy of our framework.
3D visualization is an important data analysis and knowledge discovery tool, however, interactive visualization of large 3D astronomical datasets poses a challenge for many existing data visualization packages. We present a solution to interactively visualize larger-than-memory 3D astronomical data cubes by utilizing a heterogeneous cluster of CPUs and GPUs. The system partitions the data volume into smaller sub-volumes that are distributed over the rendering workstations. A GPU-based ray casting volume rendering is performed to generate images for each sub-volume, which are composited to generate the whole volume output, and returned to the user. Datasets including the HI Parkes All Sky Survey (HIPASS - 12 GB) southern sky and the Galactic All Sky Survey (GASS - 26 GB) data cubes were used to demonstrate our frameworks performance. The framework can render the GASS data cube with a maximum render time < 0.3 second with 1024 x 1024 pixels output resolution using 3 rendering workstations and 8 GPUs. Our framework will scale to visualize larger datasets, even of Terabyte order, if proper hardware infrastructure is available.
We present a method for computing exact reachable sets for deep neural networks with rectified linear unit (ReLU) activation. Our method is well-suited for use in rigorous safety analysis of robotic perception and control systems with deep neural network components. Our algorithm can compute both forward and backward reachable sets for a ReLU network iterated over multiple time steps, as would be found in a perception-action loop in a robotic system. Our algorithm is unique in that it builds the reachable sets by incrementally enumerating polyhedral cells in the input space, rather than iterating layer-by-layer through the network as in other methods. If an unsafe cell is found, our algorithm can return this result without completing the full reachability computation, thus giving an anytime property that accelerates safety verification. In addition, our method requires less memory during execution compared to existing methods where memory can be a limiting factor. We demonstrate our algorithm on safety verification of the ACAS Xu aircraft advisory system. We find unsafe actions many times faster than the fastest existing method and certify no unsafe actions exist in about twice the time of the existing method. We also compute forward and backward reachable sets for a learned model of pendulum dynamics over a 50 time step horizon in 87s on a laptop computer. Algorithm source code: https://github.com/StanfordMSL/Neural-Network-Reach.
We present a novel privacy preservation strategy for decentralized visualization. The key idea is to imitate the flowchart of the federated learning framework, and reformulate the visualization process within a federated infrastructure. The federation of visualization is fulfilled by leveraging a shared global module that composes the encrypted externalizations of transformed visual features of data pieces in local modules. We design two implementations of federated visualization: a prediction-based scheme, and a query-based scheme. We demonstrate the effectiveness of our approach with a set of visual forms, and verify its robustness with evaluations. We report the value of federated visualization in real scenarios with an expert review.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
