Merge Tree Geodesics and Barycenters with Path Mappings.

Area of Science:

• Computer Science
• Data Visualization
• Scientific Computing

Background:

• Comparative visualization of scalar fields relies on similarity measures like edit distances.
• Existing methods, such as Wasserstein distance, can be sensitive to data perturbations.

Purpose of the Study:

• To develop a novel approach for scalar field similarity analysis.
• To combine Wasserstein geodesics/barycenters with path mappings for improved robustness.

Main Methods:

• Integration of Wasserstein geodesics/barycenters with path mappings, a branch decomposition-independent edit distance.
• Leveraging the reduced susceptibility of path mappings to small data perturbations.

Main Results:

• Superior performance and quality in ensemble summarization, ensemble clustering, and temporal reduction of time series.
• Maintained practically feasible runtimes compared to traditional methods.
• Demonstrated advantages in both synthetic and real-world scenarios through case studies.

Conclusions:

• The novel approach offers enhanced similarity analysis for scalar fields.
• The method provides practical benefits for comparative visualization tasks.
• A C++ implementation is available for reproducing results and further research.