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8th workshop on topological methods in data analysis and visualization, TopoInVis 2019

作者： Sakurai, Daisuke Yamamoto, Takahiro Kyushu University 6-1 Kasugakoen Kasuga Fukuoka Japan Tokyo Gakugei University 4-1-1 Nukuikita-machi Koganei-shi Tokyo Japan

ISBN: (纸本)9783030834999

We apply visualization to evaluating a new topological equivalence relation, which we call the topological B+ -equivalence. It has been used in our separate, yet ongoing, study in mathematics. The equivalence is a building block for the topological study of maps of bounded manifolds into the plane (aka bounded bivariate fields). In that study, we have introduced a few invariants that approximate the equivalence, which is hard to treat directly. In this chapter dedicated to the visualization community, we show that visualizing the Reeb space gives us a near-instant way of evaluating the invariants. The process has traditionally required an unpredictable amount of time due to manual analysis of high-order polynomials, which was necessary to obtain the invariant values. Our Reeb space visualization reveals the topological information necessary for evaluating the invariants, and, in doing so, the topological B+ -equivalence itself. Previously, the visualization was found to serve as an introductory learning tool for studying examples of singular fibers. The present article goes further to demonstrate professional use cases. © 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： visualization

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Mergemaps: Treemaps for Scientific data 8th

Mergemaps: Treemaps for Scientific Data

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8th workshop on topological methods in data analysis and visualization, TopoInVis 2019

作者： Kamakshidasan, Adhitya Natarajan, Vijay Inria Saclay – Île-de-France Palaiseau France Indian Institute of Science Bangalore India

ISBN: (纸本)9783030834999

Topology driven methods for analysis of scalar fields often begin with an exploration of an abstract topological structure such as the merge tree. Such abstractions are hard to interpret and time-consuming, particularly for feature-rich data. Current visualization schemes often place less emphasis on enriching user experience, human perception, or interaction. In this work, we aim to bridge that gap by utilizing treemaps towards effective topological analysis. We present mergemaps, a treemap based interactive design, to better understand merge trees. To aid the perceptual understanding of large merge trees, we provide fusing and diffusing operations to reduce its hierarchical size while preserving topological features. We show multiple examples where our design leads to easy interpretations. © 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： Topology

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Using Contour Trees in the analysis and visualization of Radio Astronomy data Cubes 8th

Using Contour Trees in the Analysis and Visualization of Rad...

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8th workshop on topological methods in data analysis and visualization, TopoInVis 2019

作者： Rosen, Paul Seth, Anil Mills, Elisabeth Ginsburg, Adam Kamenetzky, Julia Kern, Jeff Johnson, Chris R. Wang, Bei University of South Florida Tampa United States University of Utah Salt Lake City United States Brandeis University Waltham United States National Radio Astronomy Observatory Charlottesville United States Westminster College Salt Lake City United States

ISBN: (纸本)9783030834999

The current generation of radio and millimeter telescopes, particularly the Atacama Large Millimeter Array (ALMA), offers enormous advances in observing capabilities. While these advances represent an unprecedented opportunity to facilitate scientific understanding, the increased complexity in the spatial and spectral structure of these ALMA data cubes lead to challenges in their interpretation. In this paper, we perform a feasibility study for applying topological data analysis and visualization techniques never before tested by the ALMA community. Using techniques based on contour trees, we seek to improve upon existing analysis and visualization workflows of ALMA data cubes, in terms of accuracy and speed in feature extraction. We review our development process in building effective analysis and visualization capabilities for the astrophysicists. We also summarize effective design practices by identifying domain-specific needs of simplicity, integrability, and reproducibility, in order to best target and service the large astrophysics community. © 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： visualization

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Automatically recognize and segment morphological features of the 3D vertebra based on topological data analysis

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COMPUTERS IN BIOLOGY AND MEDICINE 2022年 149卷 106031-106031页

作者： Cheng, Pengfei Cao, Xiaohan Yang, Yusheng Zhang, Guoqi He, Yongyi Shanghai Univ Shanghai Key Lab Intelligent Mfg & Robot Shanghai Peoples R China Hong Kong Polytech Univ Hong Kong Peoples R China

Background: For spinal surgery, exact knowledge about the shape of individual vertebra is of great impor-tance. However, due to the complex morphological features of human vertebrae and spine, it is challenging to locate, segment automatically, and recognize the morphological features in vertebral images. Significantly, pedicle recognition is more challenging because of the particular structure. methods: topological structures such as the Reeb graph could facilitate effective visualization and interactive exploration of feature-rich data. In this paper, we conducted topological data analysis on the 3D vertebra, whereby some principal morphological features of the 3D vertebra are recognized and segmented. First, a scalar field of the 3D vertebra is created in a vertebra coordinate system (VCS). Then, the Reeb graph is adopted for topological data analysis on the scalar field. Morphological features of the 3D vertebra are separated using a cycle-detect-based algorithm in the Reeb graph, and the valid pedicle region is finally generated. Pedicle morphometry is measured for surgical ***: Experiments on the dataset from the CSI 2014 workshop with our method show that the spinous process and vertebral body are 100% (255/255) recognized, the pedicle is 99.8% (509/510) recognized, the transverse process is 94.1% (240/255) recognized. The parameters incl. chord length and diameter of pedicle morphometry are measured and verify the efficiency of the valid pedicle region deduced from the recognized ***: topological data analysis is an effective and promising automatic tool for segmenting and recognizing morphological features on the 3D vertebra. The final extracted valid pedicle region and its pedicle morphometry can provide good references for pedicle screw placement.

关键词： Morphological feature recognition topological data analysis Reeb graph Vertebra Pedicle recognition

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topological Feature Search in Time-Varying Multifield data 8th

Topological Feature Search in Time-Varying Multifield Data

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8th workshop on topological methods in data analysis and visualization, TopoInVis 2019

作者： Agarwal, Tripti Chattopadhyay, Amit Natarajan, Vijay International Institute of Information Technology Bangalore India Indian Institute of Science Bangalore India

ISBN: (纸本)9783030834999

A wide range of data that appear in scientific experiments and simulations are multivariate or multifield in nature, consisting of multiple scalar fields. topological feature search of such data aims to reveal important properties useful to the domain scientists. It has been shown in recent works that a single scalar field is insufficient to capture many important topological features in the data, instead one needs to consider topological relationships between multiple scalar fields. In the current paper, we propose a novel method of finding similarity between two multifield data by comparing their respective fiber component distributions. Given a time-varying multifield data, the method computes a metric plot for each pair of histograms at consecutive time stamps to understand the topological changes in the data over time. We validate the method using real and synthetic data. The effectiveness of the proposed method is shown by its ability to capture important topological features that are not always possible to detect using the individual component scalar fields. © 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： Topology

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Implicit visualization of 2D Vector Field Topology for Periodic Orbit Detection 8th

Implicit Visualization of 2D Vector Field Topology for Perio...

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8th workshop on topological methods in data analysis and visualization, TopoInVis 2019

作者： Straub, Alexander Karch, Grzegorz K. Sadlo, Filip Ertl, Thomas University of Stuttgart Stuttgart Germany Heidelberg University Heidelberg Germany

ISBN: (纸本)9783030834999

We present implicit visualization of 2D vector field topology, and show its utility for validating and guiding approaches for periodic orbit extraction. Instead of following the traditional approach by explicit extraction of the topological skeleton, we investigate its implicit visualization by approaches that label the regions that are separated by the skeleton. While such approaches perform well for gradient fields, they fail, in particular, to visualize periodic orbits. This motivates us to complement the label-based approach with a closely related distance-based metric. We show that our approach is able to reveal periodic orbits, also in configurations in which the state-of-the-art techniques for periodic orbit extraction fail, and demonstrate their utility for interactive extraction of all periodic orbits of a 2D vector field. © 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： visualization

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topologically Robust B-spline Reconstruction of Fibers from 3D Images 8th

Topologically Robust B-spline Reconstruction of Fibers from ...

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8th workshop on topological methods in data analysis and visualization, TopoInVis 2019

作者： Mosbach, Dennis Schladitz, Katja Hamann, Bernd Hagen, Hans Computer Graphics and HCI Group University of Kaiserslautern Kaiserslautern67663 Germany Image Processing Department Fraunhofer ITWM Kaiserslautern67663 Germany Department of Computer Science University of California DavisCA95616 United States

ISBN: (纸本)9783030834999

The micro-structure of wood-based insulation materials is analyzed to gain insight into how features on microscopic scales influence macroscopic thermal conductivity. Three-dimensional (3D) image data obtained by micro-computed tomography reveals a complex structure formed by cellulose fibers. To study the effect of geometry changes, simple B-spline representations of these fibers are highly desirable. A straightforward solution is to extract a triangulated isosurface from the 3D image and partition it into quadrilateral macro-cells with disk-like topology. For each cell, a B-spline surface is constructed by minimizing a least squares error term. However, the physical processing of the material affects the structure of the fibers. The resulting changes in surface topology cause difficulties for the quadrilateral partitioning. Image processing tools can solve these topological issues, but they also impact geometry. We present a novel approach that splits geometry and topology processing of the data. It allows for topological simplification while still preserving the geometry of a scanned object. Established B-spline approximation methods are used to create a model. The involved mathematical equations are described in detail with a focus on simple implementation. Our presented results demonstrate that smooth and accurate models can be created for challenging data. © 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： Fibers

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An Overview of the Topology ToolKit 8th

An Overview of the Topology ToolKit

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8th workshop on topological methods in data analysis and visualization, TopoInVis 2019

作者： Masood, Talha Bin Budin, Joseph Falk, Martin Favelier, Guillaume Garth, Christoph Gueunet, Charles Guillou, Pierre Hofmann, Lutz Hristov, Petar Kamakshidasan, Adhitya Kappe, Christopher Klacansky, Pavol Laurin, Patrick Levine, Joshua A. Lukasczyk, Jonas Sakurai, Daisuke Soler, Maxime Steneteg, Peter Tierny, Julien Usher, Will Vidal, Jules Wozniak, Michal Linköping University Norrköping Sweden Sorbonne Université Paris France INRIA Saclay - Île-de-France Palaiseau France TU Kaiserslautern Kaiserslautern Germany Kitware New York United States Heidelberg University Heidelberg Germany University of Leeds Leeds United Kingdom SCI Institute University of Utah Salt Lake City United States ShapeShift3D Montreal Canada University of Arizona Tucson United States Arizona State University Phoenix United States Kyushu University Fukuoka Japan Total / Sorbonne Université Paris France CNRS / Sorbonne Université Paris France

ISBN: (纸本)9783030834999

This software paper gives an overview of the features supported by the Topology ToolKit (TTK), which is an open-source library for topological data analysis (TDA). TTK implements, in a generic and efficient way, a substantial collection of reference algorithms in TDA. Since its initial public release in 2017, both its user and developer bases have grown, resulting in a significant increase in the number of supported features. In contrast to the original paper introducing TTK [40] (which detailed the core algorithms and data structures of TTK), the purpose of this software paper is to describe the list of features currently supported by TTK, ranging from image segmentation tools to advanced topological analysis of high-dimensional data, with concrete usage examples available on the TTK website [42]. © 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： Topology

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Tensor Fields for data Extraction from Chart Images: Bar Charts and Scatter Plots 8th

Tensor Fields for Data Extraction from Chart Images: Bar Cha...

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8th workshop on topological methods in data analysis and visualization, TopoInVis 2019

作者： Sreevalsan-Nair, Jaya Dadhich, Komal Daggubati, Siri Chandana Graphics-Visualization-Computing Lab International Institute of Information Technology Bangalore Karnataka India

ISBN: (纸本)9783030834999

Charts are an essential part of both graphicacy (graphical literacy), and statistical literacy. As chart understanding has become increasingly relevant in data science, automating chart analysis by processing raster images of the charts has become a significant problem. Automated chart reading involves data extraction and contextual understanding of the data from chart images. In this paper, we perform the first step of determining the computational model of chart images for data extraction for selected chart types, namely, bar charts, and scatter plots. We demonstrate the use of positive semidefinite second-order tensor fields as an effective model. We identify an appropriate tensor field as the model and propose a methodology for the use of its degenerate point extraction for data extraction from chart images. Our results show that tensor voting is effective for data extraction from bar charts and scatter plots, and histograms, as a special case of bar charts. © 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： Graphic methods

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Notes on Percolation analysis of Sampled Scalar Fields 8th

Notes on Percolation Analysis of Sampled Scalar Fields

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8th workshop on topological methods in data analysis and visualization, TopoInVis 2019

作者： Köpp, Wiebke Friederici, Anke Atzori, Marco Vinuesa, Ricardo Schlatter, Philipp Weinkauf, Tino Division of Computational Science and Technology KTH Royal Institute of Technology Stockholm Sweden Linné FLOW Centre KTH Mechanics Royal Institute of Technology Stockholm Sweden

ISBN: (纸本)9783030834999

Percolation analysis is used to explore the connectivity of randomly connected infinite graphs. In the finite case, a closely related percolation function captures the relative volume of the largest connected component in a scalar field’s superlevel set. While prior work has shown that random scalar fields with little spatial correlation yield a sharp transition in this function, little is known about its behavior on real data. In this work, we explore how different characteristics of a scalar field—such as its histogram or degree of structure—influence the shape of the percolation function. We estimate the critical value and transition width of the percolation function, and propose a corresponding normalization scheme that relates these values to known results on infinite graphs. In our experiments, we find that percolation analysis can be used to analyze the degree of structure in Gaussian random fields. On a simulated turbulent duct flow data set we observe that the critical values are stable and consistent across time. Our normalization scheme indeed aids comparison between data sets and relation to infinite graphs. © 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： Solvents

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