Feature Tracking Using Reeb Graphs

Weber, Gunther H.; Bremer, Peer-Timo; Day, Marc; Bell, John B.; Pascucci, Valerio

doi:10.1007/978-3-642-15014-2_20

Cited by 39 publications

(23 citation statements)

References 16 publications

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“…Once an appropriate fuel consumption threshold is identified, they use the Reeb graph of a 4-D space-time isosurface to track these regions over time [4,28]. In later work, Bremer et al [5] use the merge tree to compute statistics about burning regions in combustion simulations within a single time step.…”

Section: Related Workmentioning

confidence: 99%

Computing and Visualizing Time-Varying Merge Trees for High-Dimensional Data

Oesterling¹,

Heine

Weber

et al. 2017

Mathematics and Visualization

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We introduce a new method that identifies and tracks features in arbitrary dimensions using the merge tree-a structure for identifying topological features based on thresholding in scalar fields. This method analyzes the evolution of features of the function by tracking changes in the merge tree and relates features by matching subtrees between consecutive time steps. Using the time-varying merge tree, we present a structural visualization of the changing function that illustrates both features and their temporal evolution. We demonstrate the utility of our approach by applying it to temporal cluster analysis of high-dimensional point clouds.

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Section: Related Workmentioning

confidence: 99%

Computing and Visualizing Time-Varying Merge Trees for High-Dimensional Data

Oesterling¹,

Heine

Weber

et al. 2017

Mathematics and Visualization

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“…Gyulassy [3] characterized the range of features and extracted them from a Morse-Smale complex. The contour tree [4] and Reeb graph [5] are also used to define the features of interest, etc.…”

Section: Introductionmentioning

confidence: 99%

Statistical Property Guided Feature Extraction for Volume Data

Wang

Tang

Zhang

et al. 2018

IEICE Trans. Inf. & Syst.

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SUMMARYFeature visualization is of great significances in volume visualization, and feature extraction has been becoming extremely popular in feature visualization. While precise definition of features is usually absent which makes the extraction difficult. This paper employs probability density function (PDF) as statistical property, and proposes a statistical property guided approach to extract features for volume data. Basing on feature matching, it combines simple liner iterative cluster (SLIC) with Gaussian mixture model (GMM), and could do extraction without accurate feature definition. Further, GMM is paired with a normality test to reduce time cost and storage requirement. We demonstrate its applicability and superiority by successfully applying it on homogeneous and nonhomogeneous features. key words: feature extraction, probability density function (PDF), statistical property, simple liner iterative clustering (SLIC), Gaussian Mixture Model (GMM)

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“…This capability allows us to perform extensive parameter studies to determine and verify the choice of parameters as well as to study the sensitivity of the results to changes in these parameters. Once an appropriate choice of parameters has been determined we track the corresponding cells over time using the Reeb graph based tracking algorithm developed in [36]. The resulting graph not only encodes the evolution of cells over time but correlates each burning cell with a particular arc in the graph using a unique identifier.…”

Section: Introductionmentioning

confidence: 99%

Analyzing and Tracking Burning Structures in Lean Premixed Hydrogen Flames

Bremer

Weber

Pascucci

et al. 2010

IEEE Trans. Visual. Comput. Graphics

101

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Abstract-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.

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Feature Tracking Using Reeb Graphs

Cited by 39 publications

References 16 publications

Computing and Visualizing Time-Varying Merge Trees for High-Dimensional Data

Computing and Visualizing Time-Varying Merge Trees for High-Dimensional Data

Statistical Property Guided Feature Extraction for Volume Data

Analyzing and Tracking Burning Structures in Lean Premixed Hydrogen Flames

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