Visualizing Contour Trees within Histograms

Many of the topological features of the isosurfaces of a scalar volume field can be compactly represented by its contour tree. Unfortunately, the contour trees of most real-world volume data sets are too complex to be visualized by dot-and-line diagrams. Therefore, we propose a new visualization that is suitable for large contour trees and efficiently conveys the topological structure of the most important isosurface components. This visualization is integrated into a histogram of the volume data; thus, it offers strictly more information than a traditional histogram. We present algorithms to automatically compute the graph layout and to calculate appropriate approximations of the contour tree
and the surface area of the relevant isosurface components. The benefits of this new visualization are demonstrated with the help of several publicly available volume data sets.