Uncertainty Visualization of 2D Morse Complex Ensembles Using Statistical Summary Maps.

Area of Science:

• Topological Data Analysis
• Scientific Visualization
• Uncertainty Quantification

Background:

• Morse complexes are crucial for understanding scalar field topology in scientific visualization.
• Data uncertainty inherent in scalar fields limits the structural interpretation of Morse complexes.
• Existing methods struggle to represent the impact of data uncertainty on topological structures.

Purpose of the Study:

• To develop methods for visualizing uncertainty in ensembles of 2D Morse complexes derived from uncertain scalar fields.
• To introduce novel statistical summary maps for quantifying structural variations and positional uncertainties.
• To enhance the understanding of Morse complexes as structural abstractions in the presence of data uncertainty.

Main Methods:

• Generating ensembles of 2D Morse complexes from uncertain scalar fields.
• Developing three types of statistical summary maps: probabilistic, significance, and survival maps.
• Applying these maps to quantify structural variations and positional uncertainties of Morse complex features.

Main Results:

• Demonstrated the ability of statistical summary maps to characterize uncertain behaviors of gradient flows.
• Quantified structural variations and positional uncertainties of Morse complexes in ensembles.
• Provided new visual entities for understanding topological structures under data uncertainty.

Conclusions:

• The proposed statistical summary maps effectively visualize uncertainty in 2D Morse complexes.
• This approach enhances the interpretability of topological structures in scalar fields with inherent data uncertainty.
• The methods are validated on diverse simulation datasets including wind, flow, and ocean eddy.