Robust Algorithms for Vector Field Topology

Monday, February 10, 2014 - 2:00pm - 2:50pm
Keller 3-180
Andrzej Szymczak (Colorado School of Mines)
Vector fields naturally arise in numerous areas of science and engineering,
such as fluid dynamics, aerodynamics, electromagnetism, computer vision and
biology. A popular approach to vector field analysis is vector field topology,
whose goal has traditionally been to describe vector field data in terms of
features such as stationary points, periodic orbits and separatrices.
Designing robust algorithms for finding such features and estimating their
importance is one of the important fundamental problems in scientific
visualization. Classical approaches to this problem are built upon the foundation
provided by classical dynamical systems theory. Roughly speaking, numerical
methods are used to approximate trajectories of the vector field and features
are a result of analysis of the structure of these approximations.
While these approaches have been used to obtain beautiful visualizations,
they have been hindered by high complexity of the output, sensitivity to
numerical error, high computational cost and consistency issues.
This talk will provide an overview of an alternative, purely computational
geometric framework based on discontinuous (piecewise constant) vector fields.
Our approach guarantees consistency of the output, can be used to estimate
stability of features with respect to perturbation of the input and supports
multi-scale analysis of vector field topology.
MSC Code: