Subdomain Aware Contour Trees and Contour Evolution in Time-Dependent Scalar Fields

Abstract

For time-dependent scalar fields, one is often interested in topology changes of contours in time. In this paper, we focus on describing how contours split and merge over a certain time interval. Rather than attempting to describe all individual contour splitting and merging events, we focus on the simpler and therefore more tractable in practice problem: describing and querying the cumulative effect of the splitting and merging events over a user-specified time interval. Using our system one can, for example, find all contours at time tº that continue to two contours at time t¹ without hitting the boundary of the domain. For any such contour, there has to be a bifurcation happening to it somewhere between the two times, but, in addition to that, many other events may possibly happen without changing the cumulative outcome (e.g. merging with several contours born after tº or splitting off several contours that disappear before t¹).

Our approach is flexible enough to enable other types of queries, if they can be cast as counting queries for numbers of connected components of intersections of contours with certain simply connected domains. Examples of such queries include finding contours with large life spans, contours avoiding certain subset of the domain over a given time interval or contours that continue to two at a later time and then merge back to one some time later.

Experimental results show that our method can handle large 3D (2 space dimensions plus time) and 4D (3D+time) datasets. Both preprocessing and query algorithms can easily be parallelized.