A multi-dimensional importance metric for contour tree simplification

Real-world data sets produce unmanageably large contour trees because of noise. Contour Tree Simplification (CTS) would remove small scale branches, and maintain essential structure of data. Despite multiple measures of importance (MOIs) available, conventional CTS approaches often use a single MOI, which is not enough in evaluating the importance of branches in the CTS. This paper proposes an importance-driven CTS approach. The proposed approach combines multiple MOIs through the introduction of various concepts to maximize advantages of each MOI. In the attribute space, various attributes of a branch are organized in a single space. The concept of the importance triangle is used to evaluate the importance of a branch by size of the importance triangle. It considers the whole attribute space and gives better evaluation of importance. Finally, new importance values of branches are compared in the importance space to make simplification decisions. Graphical Abstract