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This paper describes approaches to topologically segmenting 2D time-dependent vector fields. For this class of vector fields, two important classes of lines exist: stream lines and path lines. Because of this, two segmentations are possible: either concerning the behavior of stream lines or of path lines. While topological features based on stream lines are well established, we introduce path line oriented topology as a new visualization approach in this paper. As a contribution to stream line oriented topology, we introduce new methods to detect global bifurcations like saddle connections and cyclic fold bifurcations as well as a method of tracking all isolated closed stream lines. To get the path line oriented topology, we segment the vector field into areas of attracting, repelling, and saddle-like behavior of the path lines. We compare both kinds of topologies and apply them to a number of test data sets.
Index Terms- Flow visualization, vector field topology, bifurcations, stream lines, path lines.

T. Weinkauf, H. Hege, H. Seidel and H. Theisel, "Topological Methods for 2D Time-Dependent Vector Fields Based on Stream Lines and Path Lines," in IEEE Transactions on Visualization & Computer Graphics, vol. 11, no. , pp. 383-394, 2005.
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