Robust Extraction and Simplification of 2D Symmetric Tensor Field Topology

Jankowai, Jochen; Wang, Bei; Hotz, Ingrid

doi:10.1111/cgf.13693

Cited by 8 publications

(6 citation statements)

References 21 publications

(50 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…By extending this concept to two-dimensional symmetric second-order tensor fields, a basis for hierarchical-based tensor field topology simplification was created. Jankowai et al [JWH19] extended this work by presenting a computational pipeline for generating a hierarchical set of degenerate points, indicating their likelihood to cancel at field perturbation.…”

Section: Topology Simplificationmentioning

confidence: 91%

Visualization of Tensor Fields in Mechanics

Hergl

Blecha

Kretzschmar

et al. 2021

Computer Graphics Forum

Self Cite

View full text Add to dashboard Cite

Tensors are used to describe complex physical processes in many applications. Examples include the distribution of stresses in technical materials, acting forces during seismic events, or remodeling of biological tissues. While tensors encode such complex information mathematically precisely, the semantic interpretation of a tensor is challenging. Visualization can be beneficial here and is frequently used by domain experts. Typical strategies include the use of glyphs, color plots, lines, and isosurfaces. However, data complexity is nowadays accompanied by the sheer amount of data produced by large-scale simulations and adds another level of obstruction between user and data. Given the limitations of traditional methods, and the extra cognitive effort of simple methods, more advanced tensor field visualization approaches have been the focus of this work. This survey aims to provide an overview of recent research results with a strong application-oriented focus, targeting applications based on continuum mechanics, namely the fields of structural, bio-, and geomechanics. As such, the survey is complementing and extending previously published surveys. Its utility is twofold: (i) It serves as basis for the visualization community to get an overview of recent visualization techniques. (ii) It emphasizes and explains the necessity for further research for visualizations in this context.

show abstract

Section: Topology Simplificationmentioning

confidence: 91%

Visualization of Tensor Fields in Mechanics

Hergl

Blecha

Kretzschmar

et al. 2021

Computer Graphics Forum

Self Cite

View full text Add to dashboard Cite

show abstract

“…Lately, Wang et al [WBR*17] further extended the classic definition of robustness to a Galilean invariant robustness framework that quantifies the stability of critical points across different frames of reference. The notion of robustness was further extended to study the stability of degenerate points in tensor fields [WH17,JWH19]. The concept of robustness, first introduced by Edelsbrunner et al [EMP11b,EMP11a], is closely related to the notion of persistence [ELZ02] -a common tool used to quantify feature importance.…”

Section: Related Workmentioning

confidence: 99%

Multilevel Robustness for 2D Vector Field Feature Tracking, Selection and Comparison

Yan

Ullrich

Roekel³

et al. 2023

Computer Graphics Forum

Self Cite

View full text Add to dashboard Cite

Critical point tracking is a core topic in scientific visualization for understanding the dynamic behaviour of time‐varying vector field data. The topological notion of robustness has been introduced recently to quantify the structural stability of critical points, that is, the robustness of a critical point is the minimum amount of perturbation to the vector field necessary to cancel it. A theoretical basis has been established previously that relates critical point tracking with the notion of robustness, in particular, critical points could be tracked based on their closeness in stability, measured by robustness, instead of just distance proximity within the domain. However, in practice, the computation of classic robustness may produce artifacts when a critical point is close to the boundary of the domain; thus, we do not have a complete picture of the vector field behaviour within its local neighbourhood. To alleviate these issues, we introduce a multilevel robustness framework for the study of 2D time‐varying vector fields. We compute the robustness of critical points across varying neighbourhoods to capture the multiscale nature of the data and to mitigate the boundary effect suffered by the classic robustness computation. We demonstrate via experiments that such a new notion of robustness can be combined seamlessly with existing feature tracking algorithms to improve the visual interpretability of vector fields in terms of feature tracking, selection and comparison for large‐scale scientific simulations. We observe, for the first time, that the minimum multilevel robustness is highly correlated with physical quantities used by domain scientists in studying a real‐world tropical cyclone dataset. Such an observation helps to increase the physical interpretability of robustness.

show abstract

“…. It has been shown that this value is also related to the stability of degenerate points in tensor field topology [11] and is the measure we are mostly interested in. In the following, we will however consider the squared value of α(T ), which has the same topological characteristics but simplifies the computations a lot.…”

Section: Second Order Symmetric Tensors and Anisotropymentioning

confidence: 99%

“…Further, it is frequently used in mechanical engineering applications to analyze the failure of materials. The join tree, a subset of the contour tree, of this anisotropy can be used for a topology-preserving simplification of 2d tensor fields [11].…”

Section: Introductionmentioning

confidence: 99%

Continuous Histograms for Anisotropy of 2D Symmetric Piece-Wise Linear Tensor Fields

Masood

Hotz

2021

Mathematics and Visualization

Self Cite

View full text Add to dashboard Cite

In this chapter we present an accurate derivation of the distribution of scalar invariants with quadratic behavior represented as continuous histograms. The anisotropy field, computed from a two-dimensional piece-wise linear tensor field, is used as an example and is discussed in all details. Histograms visualizing an approximation of the distribution of scalar values play an important role in visualization. They are used as an interface for the design of transfer-functions for volume rendering or feature selection in interactive interfaces. While there are standard algorithms to compute continuous histograms for piece-wise linear scalar fields, they are not directly applicable to tensor invariants with non-linear, often even non-convex behavior in cells when applying linear tensor interpolation. Our derivation is based on a sub-division of the mesh in triangles that exhibit a monotonic behavior. We compare the results to a naïve approach based on linear interpolation on the original mesh or the subdivision.

show abstract

Robust Extraction and Simplification of 2D Symmetric Tensor Field Topology

Cited by 8 publications

References 21 publications

Visualization of Tensor Fields in Mechanics

Visualization of Tensor Fields in Mechanics

Multilevel Robustness for 2D Vector Field Feature Tracking, Selection and Comparison

Continuous Histograms for Anisotropy of 2D Symmetric Piece-Wise Linear Tensor Fields

Contact Info

Product

Resources

About