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Computational Topology in Graphics & Visualization (Special Seminar in IMI)

Hold Date
2013-02-22 15:00〜2013-02-22 17:30
Seminar Room 1, Faculty of Mathematics building, Ito Campus
Object person
Hamish Carr (University of Leeds)

Computational Topology in Graphics & Visualization (Special Seminar in IMI)

Speaker: Hamish Carr (University of Leeds)
Event Date: February 22 (Fri), 15:00--16:00, 16:30--17:30

(1) 15:00~16:00
Title: Joint Contour Nets: Theory & Applications
(Joint work with David Duke, Aaron Knoll, Nicolas Schunck,
Hai-Ah Nam & Andrzej Staszczak)

As scientific data sets increase in size and complexity, scientific visualization increasingly depends on formal analysis of the data. One of the most successful forms of analysis uses computational topology to analyse properties such as minima, maxima, thresholds, ridges and flow. To date, however, these methods have been applied to univariate (scalar) fields and to vector fields, but not to the more general case of multivariate fields.

In particular, Contour Trees and Reeb Graphs are often used for analysing univariate (scalar) fields.  We generalize this analysis to multivariate fields with a data structure called the Joint Contour Net that quantizes the variation of multiple variables simultaneously. We report the first algorithm for constructing the Joint Contour Net, and demonstrate some of its fundamental properties. Based on this, we also show some preliminary results on its use for visualization by applying it to a problem from nuclear fission analysis, in which the topological insight provided aided scientists in understanding a physical phenomenon.

(2) 16:30~17:30
Title: Making Topology Computational

Disciplines such as computer graphics and scientific visualisation have pioneered applications exploiting topological structures such as the Reeb Graph, Contour Tree, Morse-Smale Complex and Joint Contour Net. However, in each case, there are substantial differences between the existing formal mathematics (particularly Morse Theory), and what can practically be computed.  Constructing useful algorithms often requires relaxing some of the formal assumptions, and sometimes adopting alternate formulations of the same topological ideas.  Since the process of shifting from a mathematically well-founded abstraction to a computational algorithm has identifiable stages, this talk will outline the process by which a mathematical abstraction can be implemented in practice.

Organizer: Osamu Saeki (IMI)