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Topology-based methods are of increasing importance in the analysis
and visualization of datasets from a wide variety of scientific
domains such as biology, physics, engineering, and medicine.
Current challenges of topology-based techniques include the
management of time-dependent data, the representation of large and
complex datasets, the characterization of noise and uncertainty,
the effective integration of numerical methods with robust
combinatorial algorithms, etc. . The editors have brought together
the most prominent and best recognized researchers in the field of
topology-based data analysis and visualization for a joint
discussion and scientific exchange of the latest results in the
field. This book contains the best 20 peer-reviewed papers
resulting from the discussions and presentations at the third
workshop on "Topological Methods in Data Analysis and
Visualization", held 2009 in Snowbird, Utah, US. The 2009
"TopoInVis" workshop follows the two successful workshops in 2005
(Slovakia) and 2007 (Germany).
Topology-based methods are of increasing importance in the analysis
and visualization of dataset from a wide variety of scientific
domains such as biology, physics, engineering, and medicine.
Current challenges of topology-based techniques include the
management of time-dependent data, the representation large and
complex datasets, the characterization of noise and uncertainty,
the effective integration of numerical methods with robust
combinatorial algorithms, etc. (see also below for a list of
selected issues). While there is an increasing number of
high-quality publications in this field, many fundamental questions
remain unsolved. New focused efforts are needed in a variety of
techniques ranging from the theoretical foundations of topological
models, algorithmic issues related to the representation power of
computer-based implementations as well as their computational
efficiency, user interfaces for presentation of quantitative
topological information, and the development of new techniques for
systematic mapping of science problems in topological constructs
that can be solved computationally. In this forum the editors have
brought together the most prominent and best recognized researchers
in the field of topology-based data analysis and visualization for
a joint discussion and scientific exchange of the latest results in
the field. The 2009 workshop in Snowbird, Utah, follows the two
successful workshops in 2005 (Budmerice, Slovakia) and 2007
(Leipzig, Germany).
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