Searching similarity between a pair of shapes or data is an important problem in data analysis and visualization. The problem of computing similarity measures using scalar topology has been studied extensively and proven useful in the shape and data matching. Even though multi-field or multivariate (consists of multiple scalar fields) topology reveals richer topological features, research on building tools for computing similarity measures using multi-field topology is still in its infancy. In the current paper, we propose a novel similarity measure between two piecewise-linear multi-fields based on their multi-resolution Reeb spaces - a newly developed data-structure that captures the topology of a multi-field. Overall, our method consists of two steps: (i) building a multi-resolution Reeb space corresponding to each of the multi-fields and (ii) proposing a similarity measure between two multi-resolution Reeb spaces by computing a list of topologically consistent matching pairs (of nodes) and the similarity between them. We demonstrate the effectiveness of the proposed similarity measure in detecting topological features from real time-varying multi-field data in two application domains - one from computational physics and one from computational chemistry.

A wide range of data that appear in scientific experiments and simulations are multivariate or multifield in nature, consisting of multiple scalar fields. Topological feature search of such data aims to reveal important properties useful to the domain scientists. It has been shown in recent works that a single scalar field is insufficient to capture many important topological features in the data, instead one needs to consider topological relationships between multiple scalar fields. In the current paper, we propose a novel method of finding similarity between two multifield data by comparing their respective fiber component distributions. Given a time-varying multifield data, the method computes a metric plot for each pair of histograms at consecutive time stamps to understand the topological changes in the data over time. We validate the method using real and synthetic data. The effectiveness of the proposed method is shown by its ability to capture important topological features that are not always possible to detect using the individual component scalar fields.