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This collection of peer-reviewed workshop papers provides
comprehensive coverage of cutting-edge research into topological
approaches to data analysis and visualization. It encompasses the
full range of new algorithms and insights, including fast homology
computation, comparative analysis of simplification techniques, and
key applications in materials and medical science. The book also
addresses core research challenges such as the representation of
large and complex datasets, and integrating numerical methods with
robust combinatorial algorithms. In keeping with the focus of the
TopoInVis 2017 Workshop, the contributions reflect the latest
advances in finding experimental solutions to open problems in the
sector. They provide an essential snapshot of state-of-the-art
research, helping researchers to keep abreast of the latest
developments and providing a basis for future work. Gathering
papers by some of the world's leading experts on topological
techniques, the book represents a valuable contribution to a field
of growing importance, with applications in disciplines ranging
from engineering to medicine.
This collection of peer-reviewed workshop papers provides
comprehensive coverage of cutting-edge research into topological
approaches to data analysis and visualization. It encompasses the
full range of new algorithms and insights, including fast homology
computation, comparative analysis of simplification techniques, and
key applications in materials and medical science. The book also
addresses core research challenges such as the representation of
large and complex datasets, and integrating numerical methods with
robust combinatorial algorithms. In keeping with the focus of the
TopoInVis 2017 Workshop, the contributions reflect the latest
advances in finding experimental solutions to open problems in the
sector. They provide an essential snapshot of state-of-the-art
research, helping researchers to keep abreast of the latest
developments and providing a basis for future work. Gathering
papers by some of the world's leading experts on topological
techniques, the book represents a valuable contribution to a field
of growing importance, with applications in disciplines ranging
from engineering to medicine.
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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