Flexible and Probabilistic Topology Tracking With Partial Optimal Transport

Area of Science:

• Computational Science
• Data Analysis
• Scientific Visualization

Background:

• Topological features in scalar fields are crucial for understanding complex data.
• Existing methods for tracking these features can be rigid and lack probabilistic interpretations.
• Merge trees are effective topological descriptors but require robust comparison methods.

Purpose of the Study:

• To develop a flexible and probabilistic framework for tracking topological features in time-varying scalar fields.
• To introduce a new method for modeling and comparing merge trees using partial optimal transport.
• To enable more robust and interpretable feature tracking in scientific simulations.

Main Methods:

• Modeling merge trees as measure networks with probability distributions.
• Defining a novel distance metric on the space of merge trees inspired by partial optimal transport.
• Utilizing partial optimal transport for probabilistic coupling and feature matching across time steps.

Main Results:

• A new distance metric for comparing merge trees, offering flexibility in encoding feature information.
• A probabilistic framework for tracking topological features, leading to probabilistic tracking graphs.
• Demonstrated efficacy of the framework in extracting meaningful feature tracks through extensive experiments.

Conclusions:

• The proposed framework provides a flexible and probabilistic approach to topological feature tracking in time-varying scalar fields.
• The novel distance metric and partial matching enable robust comparison and tracking of complex data features.
• This work advances the analysis of scientific simulations by offering enhanced topological feature extraction and interpretation.