Topological spines: a structure-preserving visual representation of scalar fields

Area of Science:

• Scientific visualization
• Data analysis
• Computational geometry

Background:

• Scalar fields are fundamental in scientific data.
• Existing topological representations like contour trees can obscure geometric details.
• Visualizing complex scalar fields often suffers from clutter and occlusion.

Purpose of the Study:

• To introduce topological spines, a new visual representation for scalar fields.
• To preserve both topological and geometric information of scalar fields.
• To overcome limitations of existing topological representations.

Main Methods:

• Developed a novel mechanism based on extremum graph extraction.
• Extremum graphs are sparse subsets of the Morse-Smale complex.
• Utilized a multiresolution structure for noise suppression and feature enhancement via persistence.

Main Results:

• Topological spines preserve local geometric structure, including structural cycles.
• The method avoids clutter and occlusion issues inherent in visualizing the full Morse-Smale complex.
• Demonstrated applications in 3D scalar field visualization and high-dimensional function analysis.

Conclusions:

• Topological spines offer a powerful new way to visualize scalar fields.
• This representation enhances the understanding of data symmetries and structures.
• The approach facilitates effective exploratory data analysis, particularly for complex datasets.