A Progressive Approach to Scalar Field Topology

Area of Science:

• Computer Science
• Data Analysis
• Scientific Visualization

Background:

• Topological analysis of scalar data is crucial for understanding complex datasets.
• Existing algorithms can be computationally intensive and lack interactivity.

Purpose of the Study:

• To introduce progressive algorithms for efficient topological analysis of scalar data.
• To enable interactive exploration and control over topological computations.

Main Methods:

• Hierarchical data representation for fast identification of topologically invariant vertices.
• Coarse-to-fine topological algorithms with efficient update mechanisms.
• Progressive refinement of topological features like critical points and persistence diagrams.

Main Results:

• Algorithms provide interpretable outputs upon interruption and progressively refine them.
• Progressive strategy improves run time performance compared to non-progressive methods.
• Shared-memory parallelism further accelerates computations.

Conclusions:

• The proposed progressive approach enhances efficiency and interactivity in topological data analysis.
• Continuous visual feedback and controlled execution times are key benefits.
• This method is valuable for both batch-mode and interactive analysis scenarios.