Topological volume skeletonization and its application to transfer function design

Takahashi, Shigeo; Takeshima, Yuriko; Fujishiro, Issei

doi:10.1016/j.gmod.2003.08.002

Cited by 111 publications

(80 citation statements)

References 22 publications

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“…In the case of simply connected domains, the Reeb graph has no cycles and is called a contour tree. Reeb graphs, contour trees, and their variants have been used successfully to guide the removal of topological features [7,4,13,27,28,30]. The MS complex decomposes the domain of a function into regions having uniform gradient flow behavior [24].…”

Section: Related Workmentioning

confidence: 99%

Topologically Clean Distance Fields

Gyulassy

Duchaineau

Natarajan

et al. 2007

IEEE Trans. Visual. Comput. Graphics

107

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Abstract-Analysis of the results obtained from material simulations is important in the physical sciences. Our research was motivated by the need to investigate the properties of a simulated porous solid as it is hit by a projectile. This paper describes two techniques for the generation of distance fields containing a minimal number of topological features, and we use them to identify features of the material. We focus on distance fields defined on a volumetric domain considering the distance to a given surface embedded within the domain. Topological features of the field are characterized by its critical points. Our first method begins with a distance field that is computed using a standard approach, and simplifies this field using ideas from Morse theory. We present a procedure for identifying and extracting a feature set through analysis of the MS complex, and apply it to find the invariants in the clean distance field. Our second method proceeds by advancing a front, beginning at the surface, and locally controlling the creation of new critical points. We demonstrate the value of topologically clean distance fields for the analysis of filament structures in porous solids. Our methods produce a curved skeleton representation of the filaments that helps material scientists to perform a detailed qualitative and quantitative analysis of pores, and hence infer important material properties. Furthermore, we provide a set of criteria for finding the "difference" between two skeletal structures, and use this to examine how the structure of the porous solid changes over several timesteps in the simulation of the particle impact.

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Section: Related Workmentioning

confidence: 99%

Topologically Clean Distance Fields

Gyulassy

Duchaineau

Natarajan

et al. 2007

IEEE Trans. Visual. Comput. Graphics

107

View full text Add to dashboard Cite

show abstract

“…Local geometric measures, like persistence (difference in function value) or volume, define an order in which arcs are pruned, i.e., what isosurface features are deemed less important and are removed first. Takahashi et al [20,19] use the related volume skeleton tree to simplify topology in a similar fashion. In subsequent work, they utilized the results, e.g., for the design of transfer functions that emphasize topology and take contour nesting properties into account [21].…”

Section: Contour Treesmentioning

confidence: 99%

“…While prior work uses, e.g., interval volumes [7], to derive measures such as area and volume for contours (i.e., connected isosurface components), our approach provides these measures as a function of isovalue that is associated with contour tree edges. This function representation makes it possible to compute an individual, contour-specific area or volume for any isovalue along an edge, as opposed to approximating a single volume for an entire edge like prior work on topology simplification [20,21].…”

Section: Computing Per-component Measuresmentioning

confidence: 99%

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Topological Cacti: Visualizing Contour-Based Statistics

Weber

Bremer

Pascucci

2011

Mathematics and Visualization

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Contours, the connected components of level sets, play an important role in understanding the global structure of a scalar field. In particular their nesting behavior and topology-often represented in form of a contour tree-have been used extensively for visualization and analysis. However, traditional contour trees only encode structural properties like number of contours or the nesting of contours, but little quantitative information such as volume or other statistics. Here we use the segmentation implied by a contour tree to compute a large number of per-contour (interval) based statistics of both the function defining the contour tree as well as other co-located functions. We introduce a new visual metaphor for contour trees, called topological cacti, that extends the traditional toporrery display of a contour tree to display additional quantitative information as width of the cactus trunk and length of its spikes. We apply the new technique to scalar fields of varying dimension and different measures to demonstrate the effectiveness of the approach.

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“…Visualizations of contour trees are often based on dot-and-line diagrams in two dimensions (Bajaj et al, 1997;Pascucci and Cole-McLaughlin, 2002;Carr et al, 2004) or three dimensions (Takahashi et al, 2004a;Takahashi et al, 2004b;Pascucci et al, 2004). Furthermore, the use of icons has been proposed by Shinagawa et al (Shinagawa et al, 1991).…”

Section: Related Workmentioning

confidence: 99%

Visualization of Uncertain Contour Trees

Kraus¹

2010

Proceedings of the International Conference on Imaging Theory and Applications and International Conference on Information Visu

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Abstract:Contour trees can represent the topology of large volume data sets in a relatively compact, discrete data structure. However, the resulting trees often contain many thousands of nodes; thus, many graph drawing techniques fail to produce satisfactory results. Therefore, several visualization methods were proposed recently for the visualization of contour trees. Unfortunately, none of these techniques is able to handle uncertain contour trees although any uncertainty of the volume data inevitably results in partially uncertain contour trees. In this work, we visualize uncertain contour trees by combining the contour trees of two morphologically filtered versions of a volume data set, which represent the range of uncertainty. These two contour trees are combined and visualized within a single image such that a range of potential contour trees is represented by the resulting visualization. Thus, potentially erroneous topological structures are visually distinguished from more certain structures. Moreover, topological structures can be revealed that are otherwise obscured by data errors. We present and discuss results obtained with a prototypical implementation using well-known volume data sets.

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Topological volume skeletonization and its application to transfer function design

Cited by 111 publications

References 22 publications

Topologically Clean Distance Fields

Topologically Clean Distance Fields

Topological Cacti: Visualizing Contour-Based Statistics

Visualization of Uncertain Contour Trees

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