Robust on-line computation of Reeb graphs

Pascucci, Valerio; Scorzelli, Giorgio; Bremer, Peer-Timo; Mascarenhas, Ajith

doi:10.1145/1275808.1276449

Cited by 99 publications

(98 citation statements)

References 19 publications

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“…However, the Reeb graph [28], a generalisation of the contour tree, can be used to compute the topology of scalar data in such situations [29]. As with the contour tree, the Reeb graph can be applied to models of any dimension provided it is represented on a simplicial mesh [30]. The Reeb graph has also been used to assist in the design of transfer functions in volume visualisation [31], by assigning opacity based upon how many objects were obscured by nested surfaces and their proximity to the edge of a scalar field.…”

Section: The Reeb Graphmentioning

confidence: 99%

“…The first use of the Reeb graph for encoding topological features for visualisation purposes was by Shinagawa and Kunii [32] where the structure was used as a way of representing objects obtained from computerised-tomography (CT) sources [33]. An online algorithm is given by Pascucci et al [30] that allowed the Reeb graph of a function to be computed using a streaming approach with the output continually updated as additional data points are added. Efficiency of the algorithm is optimal for two dimensional inputs and the streaming nature of the algorithm limits peak memory usage.…”

Section: The Reeb Graphmentioning

confidence: 99%

See 1 more Smart Citation

Topological Visualisation Techniques for Volume Multifield Data

Thomas¹,

Borgo²,

Laramee³

et al. 2019

Computer Graphics and Imaging

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This survey paper provides an overview of topological visualisation techniques for scalar data sets. Topological algorithms are used to reduce scalar fields to a skeleton by mapping critical changes in the topology to the vertices of graph structures. These can be visualised using graph drawing techniques or used as a method of seeding meshes of distinct objects existing in the data. Many techniques are discussed in detail, beginning with a review of algorithms working on scalar fields defined with a single variable, and then generalised to multivariate and temporal data. The survey is completed with a discussion of methods of presenting data in higher dimensions.

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Section: The Reeb Graphmentioning

confidence: 99%

Section: The Reeb Graphmentioning

confidence: 99%

Topological Visualisation Techniques for Volume Multifield Data

Thomas¹,

Borgo²,

Laramee³

et al. 2019

Computer Graphics and Imaging

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show abstract

“…In order to keep the final skeleton's centrality, we utilize an embedding method described in Document to make the skeleton embed in the original point cloud when it is in the calculating process of OG skeleton [11]. Every vertex in octree-graph has an initial weight of w, which represents the number of points in the vertex's corresponding subspace.…”

Section: Graph Embeddingmentioning

confidence: 99%

“…The third step of strategy, simultaneous performance with the second step, is to embed the OG graph into the original point sets. The centeredness is improved by an existing embedding strategy with respect to the original object [11]. The contribution of this algorithm contains a new OG graph construction and a new graph reduction method that automatically incorporates the approximate local structure skeleton by using suitable methods.…”

Section: Introductionmentioning

confidence: 99%

Fast Point Cloud Skeleton Extraction via Octree-graph

Jia¹

2015

Proceedings of the 5th International Conference on Computer Engineering and Networks — PoS(CENet2015)

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We present a fast algorithm to implement curve-skeleton extraction from imperfect point sets. The algorithm works directly on the point clouds data without transforming the point cloud object into a volumetric or mesh form, which can be readily extracted qualified skeletons by plenty of mature methods. Specially, we first extract a novel graph called octree-graph from the original point cloud data, then reduce it into a linear skeleton, and simultaneously embed it into the original point cloud. The final skeleton can possess excellent centeredness and topological correctness on a variety of three-dimensional models.

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“…As scientific data sets become more intricate and larger in size, advanced data analysis algorithms are needed for their efficient visualization and interactive exploration. For scalar field visualization, topological data analysis techniques [16,27,39] have shown to be practical solutions in various contexts by enabling the concise and complete capture of the structure of the input data into high-level topological abstractions such as merge trees [6,35,46], contour trees [5,7,13,49], Reeb graphs [3,38,40,44,52], or Morse-Smale complexes [14,24,41,56]. Such topological abstractions are fundamental data-structures that enable the development of advanced data analysis, exploration and visualization techniques, including for instance: small seed set extraction for fast isosurface traversal [8,53], feature tracking [47], data-summarization [37,55], transfer function design for volume rendering [54], similarity estimation [28,50].…”

Section: Introductionmentioning

confidence: 99%

Task-based augmented merge trees with Fibonacci heaps

Gueunet

Fortin

Jomier

et al. 2017

2017 IEEE 7th Symposium on Large Data Analysis and Visualization (LDAV)

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This paper presents a new algorithm for the fast, shared memory multi-core computation of augmented merge trees on triangulations. In contrast to most existing parallel algorithms, our technique computes augmented trees. This augmentation is required to enable the full extent of merge tree based applications, including data segmentation. Our approach completely revisits the traditional, sequential merge tree algorithm to re-formulate the computation as a set of independent local tasks based on Fibonacci heaps. This results in superior time performance in practice, in sequential as well as in parallel thanks to the OpenMP task runtime. In the context of augmented contour tree computation, we show that a direct usage of our merge tree procedure also results in superior time performance overall, both in sequential and parallel. 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 runtime efficiency of our approach as well as its scalability on common workstations. We demonstrate the utility of our approach in data segmentation applications. We also provide a lightweight VTK-based C++ implementation of our approach for reproduction purposes.

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Robust on-line computation of Reeb graphs

Cited by 99 publications

References 19 publications

Topological Visualisation Techniques for Volume Multifield Data

Topological Visualisation Techniques for Volume Multifield Data

Fast Point Cloud Skeleton Extraction via Octree-graph

Task-based augmented merge trees with Fibonacci heaps

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