237 research outputs found
Task-based Augmented Contour Trees with Fibonacci Heaps
This paper presents a new algorithm for the fast, shared memory, multi-core
computation of augmented contour trees on triangulations. In contrast to most
existing parallel algorithms our technique computes augmented trees, enabling
the full extent of contour tree based applications including data segmentation.
Our approach completely revisits the traditional, sequential contour tree
algorithm to re-formulate all the steps of the computation as a set of
independent local tasks. This includes a new computation procedure based on
Fibonacci heaps for the join and split trees, two intermediate data structures
used to compute the contour tree, whose constructions are efficiently carried
out concurrently thanks to the dynamic scheduling of task parallelism. We also
introduce a new parallel algorithm for the combination of these two trees into
the output global contour tree. Overall, this results in superior time
performance in practice, both in sequential and in parallel thanks to the
OpenMP task runtime. We report performance numbers that compare our approach to
reference sequential and multi-threaded implementations for the computation of
augmented merge and contour trees. These experiments demonstrate the run-time
efficiency of our approach and its scalability on common workstations. We
demonstrate the utility of our approach in data segmentation applications
A Comparative Study of the Perceptual Sensitivity of Topological Visualizations to Feature Variations
Color maps are a commonly used visualization technique in which data are
mapped to optical properties, e.g., color or opacity. Color maps, however, do
not explicitly convey structures (e.g., positions and scale of features) within
data. Topology-based visualizations reveal and explicitly communicate
structures underlying data. Although we have a good understanding of what types
of features are captured by topological visualizations, our understanding of
people's perception of those features is not. This paper evaluates the
sensitivity of topology-based isocontour, Reeb graph, and persistence diagram
visualizations compared to a reference color map visualization for
synthetically generated scalar fields on 2-manifold triangular meshes embedded
in 3D. In particular, we built and ran a human-subject study that evaluated the
perception of data features characterized by Gaussian signals and measured how
effectively each visualization technique portrays variations of data features
arising from the position and amplitude variation of a mixture of Gaussians.
For positional feature variations, the results showed that only the Reeb graph
visualization had high sensitivity. For amplitude feature variations,
persistence diagrams and color maps demonstrated the highest sensitivity,
whereas isocontours showed only weak sensitivity. These results take an
important step toward understanding which topology-based tools are best for
various data and task scenarios and their effectiveness in conveying
topological variations as compared to conventional color mapping
Surface networks
© Copyright CASA, UCL. The desire to understand and exploit the structure of continuous surfaces is common to researchers in a range of disciplines. Few examples of the varied surfaces forming an integral part of modern subjects include terrain, population density, surface atmospheric pressure, physico-chemical surfaces, computer graphics, and metrological surfaces. The focus of the work here is a group of data structures called Surface Networks, which abstract 2-dimensional surfaces by storing only the most important (also called fundamental, critical or surface-specific) points and lines in the surfaces. Surface networks are intelligent and ânatural â data structures because they store a surface as a framework of âsurface â elements unlike the DEM or TIN data structures. This report presents an overview of the previous works and the ideas being developed by the authors of this report. The research on surface networks has fou
Task-based Augmented Reeb Graphs with Dynamic ST-Trees
International audienceThis paper presents, to the best of our knowledge, the first parallel algorithm for the computation of the augmented Reeb graph of piecewise linear scalar data. Such augmented Reeb graphs have a wide range of applications , including contour seeding and feature based segmentation. Our approach targets shared-memory multi-core workstations. For this, it completely revisits the optimal, but sequential, Reeb graph algorithm, which is capable of handing data in arbitrary dimension and with optimal time complexity. We take advantage of Fibonacci heaps to exploit the ST-Tree data structure through independent local propagations, while maintaining the optimal, linearithmic time complexity of the sequential reference algorithm. These independent propagations can be expressed using OpenMP tasks, hence benefiting in parallel from the dynamic load balancing of the task runtime while enabling us to increase the parallelism degree thanks to a dual sweep. We present performance results on triangulated surfaces and tetrahedral meshes. We provide comparisons to related work and show that our new algorithm results in superior time performance in practice, both in sequential and in parallel. An open-source C++ implementation is provided for reproducibility
Lifted Wasserstein Matcher for Fast and Robust Topology Tracking
This paper presents a robust and efficient method for tracking topological
features in time-varying scalar data. Structures are tracked based on the
optimal matching between persistence diagrams with respect to the Wasserstein
metric. This fundamentally relies on solving the assignment problem, a special
case of optimal transport, for all consecutive timesteps. Our approach relies
on two main contributions. First, we revisit the seminal assignment algorithm
by Kuhn and Munkres which we specifically adapt to the problem of matching
persistence diagrams in an efficient way. Second, we propose an extension of
the Wasserstein metric that significantly improves the geometrical stability of
the matching of domain-embedded persistence pairs. We show that this
geometrical lifting has the additional positive side-effect of improving the
assignment matrix sparsity and therefore computing time. The global framework
implements a coarse-grained parallelism by computing persistence diagrams and
finding optimal matchings in parallel for every couple of consecutive
timesteps. Critical trajectories are constructed by associating successively
matched persistence pairs over time. Merging and splitting events are detected
with a geometrical threshold in a post-processing stage. Extensive experiments
on real-life datasets show that our matching approach is an order of magnitude
faster than the seminal Munkres algorithm. Moreover, compared to a modern
approximation method, our method provides competitive runtimes while yielding
exact results. We demonstrate the utility of our global framework by extracting
critical point trajectories from various simulated time-varying datasets and
compare it to the existing methods based on associated overlaps of volumes.
Robustness to noise and temporal resolution downsampling is empirically
demonstrated
Ranking Viscous Finger Simulations to an Acquired Ground Truth with Topology-aware Matchings
International audienceThis application paper presents a novel framework based on topological data analysis for the automatic evaluation and ranking of viscous finger simulation runs in an ensemble with respect to a reference acquisition. Individual fingers in a given time-step are associated with critical point pairs in the distance field to the injection point, forming persistence diagrams. Different metrics, based on optimal transport, for comparing time-varying persistence diagrams in this specific applicative case are introduced. We evaluate the relevance of the rankings obtained with these metrics, both qualitatively thanks to a lightweight web visual interface, and quantitatively by studying the deviation from a reference ranking suggested by experts. Extensive experiments show the quantitative superiority of our approach compared to traditional alternatives. Our web interface allows experts to conveniently explore the produced rankings. We show a complete viscous fingering case study demonstrating the utility of our approach in the context of porous media fluid flow, where our framework can be used to automatically discard physically-irrelevant simulation runs from the ensemble and rank the most plausible ones. We document an in-situ implementation to lighten I/O and performance constraints arising in the context of parametric studies
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