Topological Methods in Data Analysis and Visualization II [electronic resource] : Theory, Algorithms, and Applications / edited by Ronald Peikert, Helwig Hauser, Hamish Carr, Raphael Fuchs.

Contributor(s): Peikert, Ronald [editor.] | Hauser, Helwig [editor.] | Carr, Hamish [editor.] | Fuchs, Raphael [editor.] | SpringerLink (Online service)
Material type: TextTextSeries: Mathematics and Visualization: Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2012Description: XI, 299 p. 200 illus., 106 illus. in color. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783642231759Subject(s): Mathematics | Computers | Computer graphics | Algorithms | Visualization | Mathematics | Visualization | Algorithms | Computing Methodologies | Computer GraphicsAdditional physical formats: Printed edition:: No titleDDC classification: 004 LOC classification: QA76.9.I52Online resources: Click here to access online
Contents:
Part I: Discrete Morse Theory.- Part II: Hierarchical Methods for Extracting and Visualizing Topological Structures -- Part III: Visualization of Dynamical Systems, Vector and Tensor Fields -- Part IV: Topological Visualization of Unsteady Flow.
In: Springer eBooksSummary: When scientists analyze datasets in a search for underlying phenomena, patterns or causal factors, their first step is often an automatic or semi-automatic search for structures in the data. Of these feature-extraction methods, topological ones stand out due to their solid mathematical foundation. Topologically defined structures—as found in scalar, vector and tensor fields—have proven their merit in a wide range of scientific domains, and scientists have found them to be revealing in subjects such as physics, engineering, and medicine.   Full of state-of-the-art research and contemporary hot topics in the subject, this volume is a selection of peer-reviewed papers originally presented at the fourth Workshop on Topology-Based Methods in Data Analysis and Visualization, TopoInVis 2011, held in Zurich, Switzerland. The workshop brought together many of the leading lights in the field for a mixture of formal presentations and discussion. One topic currently generating a great deal of interest, and explored in several chapters here, is the search for topological structures in time-dependent flows, and their relationship with Lagrangian coherent structures. Contributors also focus on discrete topologies of scalar and vector fields, and on persistence-based simplification, among other issues of note. The new research results included in this volume relate to all three key areas in data analysis—theory, algorithms and applications.
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Part I: Discrete Morse Theory.- Part II: Hierarchical Methods for Extracting and Visualizing Topological Structures -- Part III: Visualization of Dynamical Systems, Vector and Tensor Fields -- Part IV: Topological Visualization of Unsteady Flow.

When scientists analyze datasets in a search for underlying phenomena, patterns or causal factors, their first step is often an automatic or semi-automatic search for structures in the data. Of these feature-extraction methods, topological ones stand out due to their solid mathematical foundation. Topologically defined structures—as found in scalar, vector and tensor fields—have proven their merit in a wide range of scientific domains, and scientists have found them to be revealing in subjects such as physics, engineering, and medicine.   Full of state-of-the-art research and contemporary hot topics in the subject, this volume is a selection of peer-reviewed papers originally presented at the fourth Workshop on Topology-Based Methods in Data Analysis and Visualization, TopoInVis 2011, held in Zurich, Switzerland. The workshop brought together many of the leading lights in the field for a mixture of formal presentations and discussion. One topic currently generating a great deal of interest, and explored in several chapters here, is the search for topological structures in time-dependent flows, and their relationship with Lagrangian coherent structures. Contributors also focus on discrete topologies of scalar and vector fields, and on persistence-based simplification, among other issues of note. The new research results included in this volume relate to all three key areas in data analysis—theory, algorithms and applications.

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