Topology-based Feature Definition and Analysis

2004

The Contour Tree of a scalar field is the graph obtained by contracting all the connected components of the level sets of the field into points. This is a powerful abstraction for representing the structure of the field with explicit description of the topological changes of its level sets. It has proven effective as a data-structure for fast extraction of isosurfaces and its application has been advocated as a user interface component guiding interactive data exploration sessions. We propose a new metaphor for visualizing the Contour Tree borrowed from the classical design of a mechanical orrery-see Figure 1(a)-reproducing a hierarchy of orbits of the planets around the sun or moons around a planet. In the toporrery-see Figure 1(b)-the hierarchy of stars, planets and moons is replaced with a hierarchy of maxima, minima and saddles that can be interactively filtered, both uniformly and adaptively, by importance with respect to a given metric.

SC14: International Conference for High Performance Computing, Networking, Storage and Analysis, 2014

The ever increasing amount of data generated by scientific simulations coupled with system I/O constraints are fueling a need for in-situ analysis techniques. Of particular interest are approaches that produce reduced data representations while maintaining the ability to redefine, extract, and study features in a post-process to obtain scientific insights. This paper presents two variants of in-situ feature extraction techniques using segmented merge trees, which encode a wide range of threshold based features. The first approach is a fast, low communication cost technique that generates an exact solution but has limited scalability. The second is a scalable, local approximation that nevertheless is guaranteed to correctly extract all features up to a predefined size. We demonstrate both variants using some of the largest combustion simulations available on leadership class supercomputers. Our approach allows state-of-the-art, feature-based analysis to be performed in-situ at significantly higher frequency than currently possible and with negligible impact on the overal simulation runtime.

Journal of Physics: Conference Series, 2007

Scientific datasets obtained by measurement or produced by computational simulations must be analyzed to understand the phenomenon under study. The analysis typically requires a mathematically sound definition of the features of interest and robust algorithms to identify these features, compute statistics about them, and often track them over time. Because scientific datasets often capture phenomena with multi-scale behaviour, and almost always contain noise the definitions and algorithms must be designed with sufficient flexibility and care to allow multi-scale analysis and noise-removal. In this paper, we present some recent work on topological feature extraction and tracking with applications in molecular analysis, combustion simulation, and structural analysis of porous materials.

Feature-based conditional statistical methods are essential for the analysis of complex, large-scale data. We introduce two shape-based conditional analysis algorithms that can be deployed in complementary settings: local methods are required when the phenomena under study comprise many small intermittent features, while global shape methods are required to study large-scale structures. We present the algorithms in context with their motivating combustion science case studies, but we note that the methods are applicable to a broad class of physics-based phenomena.

Multi-Resolution computation and presentation of Contour Trees * PAPER 541 (a) (left) Orrery reproducing the hierarchical relationship between the orbits of the sun, the planets and their moons. Original design (1812) by A. Janvier reprinted recently by E. Tufte [25]. (center) Contour Tree drawn as an orrery where stars/planets/moons are replaced by critical points and the nested orbits represent the hierarchy of topological features. The scalar field of this particular example is the inverse air density distribution α of a fuel injection into a combustion chamber. (right) Semi-transparent level sets of α displayed together with the Contour Tree drawn with its critical points in their original position. (b) (left) Contour Tree at three levels of resolution for the electron density distribution (ρ) computed with an ab initio simulation for water molecules at high pressure. At the coarse scale (top) the tree has only one maximum (blue sphere) per water molecule. At medium scale (middle) the topology reconstructs one dipole per molecule with one maximum and one minimum (red sphere). At fine scale (bottom) only the noise is removed and three extrema per molecule reconstruct each atom in the simulation. (middle) Semi-transparent level sets of ρ together with the fine scale topology. Adaptive refinement in the area marked with a rectangle can be used to refine the topology for two particular molecules. This as shown on the right at coarse, medium and fine scale both for the Contour Tree and for the embedding (shown side by side).

IEEE Transactions on Visualization and Computer Graphics, 2000

This paper presents topology-based methods to robustly extract, analyze, and track features defined as subsets of isosurfaces. First, we demonstrate how features identified by thresholding isosurfaces can be defined in terms of the Morse complex. Second, we present a specialized hierarchy that encodes the feature segmentation independent of the threshold while still providing a flexible multi-resolution representation. Third, for a given parameter selection we create detailed tracking graphs representing the complete evolution of all features in a combustion simulation over several hundred time steps. Finally, we discuss a user interface that correlates the tracking information with interactive rendering of the segmented isosurfaces enabling an in-depth analysis of the temporal behavior. We demonstrate our approach by analyzing three numerical simulations of lean hydrogen flames subject to different levels of turbulence. Due to their unstable nature, lean flames burn in cells separated by locally extinguished regions. The number, area, and evolution over time of these cells provide important insights into the impact of turbulence on the combustion process. Utilizing the hierarchy we can perform an extensive parameter study without re-processing the data for each set of parameters. The resulting statistics enable scientist to select appropriate parameters and provide insight into the sensitivity of the results wrt. to the choice of parameters. Our method allows for the first time to quantitatively correlate the turbulence of the burning process with the distribution of burning regions, properly segmented and selected. In particular, our analysis shows that counter-intuitively stronger turbulence leads to larger cell structures, which burn more intensely than expected. This behavior suggests that flames could be stabilized under much leaner conditions than previously anticipated.

2011

Feature-based conditional statistical methods are essential for the analysis of complex, large-scale data. We introduce two shape-based conditional analysis algorithms that can be deployed in complementary settings: local methods are required when the phenomena under study comprises many small intermittent features, while global shape methods are required to study large-scale structures. We present the algorithms in context with their motivating combustion science case studies, but note that the methods are applicable to a broad class of physics-based phenomena.

Mathematics and Visualization, 2011

Mathematics and Visualization, 2007

The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.

IEEE Transactions on Visualization and Computer Graphics, 2019

With the rapid adoption of machine learning techniques for large-scale applications in science and engineering comes the convergence of two grand challenges in visualization. First, the utilization of black box models (e.g., deep neural networks) calls for advanced techniques in exploring and interpreting model behaviors. Second, the rapid growth in computing has produced enormous datasets that require techniques that can handle millions or more samples. Although some solutions to these interpretability challenges have been proposed, they typically do not scale beyond thousands of samples, nor do they provide the high-level intuition scientists are looking for. Here, we present the first scalable solution to explore and analyze high-dimensional functions often encountered in the scientific data analysis pipeline. By combining a new streaming neighborhood graph construction, the corresponding topology computation, and a novel data aggregation scheme, namely topology aware datacubes, we enable interactive exploration of both the topological and the geometric aspect of high-dimensional data. Following two use cases from high-energy-density (HED) physics and computational biology, we demonstrate how these capabilities have led to crucial new insights in both applications.