A Practical Solver for Scalar Data Topological Simplification

Area of Science:

• Scientific visualization
• Computational topology
• Data analysis

Background:

• Topological simplification is crucial for analyzing and visualizing scalar data.
• Existing methods are limited in the types of topological features they can preserve, especially saddle pairs in 3D data.
• Optimization of topological simplification is computationally intensive and not practical for real-world datasets.

Purpose of the Study:

• To develop a practical and efficient approach for optimizing topological simplification of scalar data.
• To extend existing persistence optimization frameworks for topological simplification.
• To enable the preservation of significant topological features, including saddle pairs, and the cancellation of non-signal features.

Main Methods:

• Leveraging generic persistence optimization frameworks.
• Developing tailored accelerations for topological simplification.
• Producing an output field close to the input field by optimizing the cancellation of non-signal persistence pairs and the preservation of signal persistence pairs.
• Extending the approach beyond extrema to include saddle pairs.

Main Results:

• Achieved substantial accelerations compared to existing frameworks, making optimization practical for real-life datasets.
• Enabled direct visualization and analysis of topologically simplified data, such as isosurfaces with fewer components and handles.
• Demonstrated practical improvements in extracting filament structures and removing filament loops from 3D data.
• Showcased the ability to repair genus defects in surface processing.

Conclusions:

• The proposed approach offers a practical and efficient solution for topological simplification optimization.
• It significantly enhances the analysis and visualization of scalar data by preserving essential topological features.
• The method has broad applicability in scientific data analysis, including feature extraction and surface processing.