Distance between extremum graphs

Scientific phenomena are often studied through collections of related scalar fields generated from different observations of the same phenomenon. Exploration of such data requires a robust distance measure to compare scalar fields for tasks such as identifying key events and establishing correspondence between features in the data. Towards this goal, we propose a topological data structure called the complete extremum graph and define a distance measure on it for comparing scalar fields in a feature-aware manner. We design an algorithm for computing the distance and show its applications in analysing time varying data.