Probabilistic Asymptotic Decider for Topological Ambiguity Resolution in Level-Set Extraction for Uncertain 2D Data

Area of Science:

• Computational geometry
• Data visualization
• Scientific computing

Background:

• Isocontour extraction is crucial for visualizing scalar fields.
• The marching squares algorithm can produce topological ambiguities due to saddle points in piecewise bilinear interpolation.
• Existing methods like the midpoint and asymptotic deciders struggle with data uncertainty.

Purpose of the Study:

• To develop a framework for analyzing and resolving uncertainty in isocontour extraction.
• To investigate the behavior of the asymptotic decider under uncertain grid vertex data.
• To introduce a probabilistic asymptotic decider for robust topological ambiguity resolution.

Main Methods:

• Derived closed-form distributions for saddle point variations in uncertain bilinear interpolants, assuming uniform and nonparametric noise models.
• Developed a probabilistic asymptotic decider utilizing these derived distributions for ambiguity resolution.
• Employed a colormapping technique to visualize confidence in probabilistic topological decisions.

Main Results:

• Characterized saddle point value variations for uncertain bilinear interpolants.
• The probabilistic asymptotic decider demonstrated higher accuracy and stability compared to existing methods.
• Successful isocontour visualization of synthetic and real datasets with uncertain data was achieved.

Conclusions:

• The probabilistic asymptotic decider effectively resolves topological ambiguities in isocontour extraction with uncertain data.
• This framework offers a more accurate and stable approach for analyzing uncertainty in this domain.
• The visualization technique provides valuable confidence measures for topological decisions.