Topological Cacti: Visualizing Contour-based Statistics

Contours, the connected components of level sets, play an important role in understanding the global structure of a scalar field. In particular their nesting behavior and topology—often represented in form of a contour tree—have been used extensively for visualization and analysis. However, traditional contour trees only encode structural properties like number of contours or the nesting of contours, but little quantitative information such as volume or other statistics. Here we use the segmentation implied by a contour tree to compute a large number of per-contour (interval) based statistics of both the function defining the contour tree as well as other co-located functions. We introduce a new visual metaphor for contour trees, called topological cacti, that extends the traditional toporrery display of a contour tree to display additional quantitative information as width of the cactus trunk and length of its spikes. We apply the new technique to scalar fields of varying dimension and different measures to demonstrate the effectiveness of the approach.