Figure 2

Illustration of merge trees and their relationships to isosurfaces. The top subfigure (a) illustrates the halo definition based on iso-density contours. Halos are regions above a density threshold \(t_{\text{boundary}}\) (light gray region) whose maximum density exceeds \(t_{\text{halo}}\) (dark gray regions). The bottom subfigure (b) shows the merge tree which corresponds to the level set parameters \(t_{{\text{boundary}}}\) and \(t_{{\text{halo}}}\) given in Figure 2(a). The black dots correspond to points on the same super-level set, with each representing a different connected component on that super-level set. The green dots indicate saddle points of the scalar function, while the red dots indicate local maxima.