Probabilistic Inclusion Depth for Fuzzy Contour Ensemble Visualization

Area of Science:

• Scientific Visualization
• Data Analysis

Background:

• Scalar field ensembles are crucial in various scientific domains.
• Visualizing uncertainties and variations within these ensembles remains challenging.
• Existing methods struggle with fuzzy data and large-scale 3D ensembles.

Purpose of the Study:

• To develop a novel data depth model for ensemble visualization of scalar fields.
• To support both fuzzy and binary contour ensembles.
• To enable efficient computation and visualization of complex ensemble data.

Main Methods:

• Introduction of Probabilistic Inclusion Depth (PID) using a probabilistic inclusion operator (\subset_{p}).
• Extension of contour extraction to a fuzzy decision based on isovalue probabilistic distribution.
• Development of an efficient approximation using the mean probabilistic contour.
• Implementation of a parallel GPU algorithm for significant computational speedup.

Main Results:

• PID supports general data depth models for fuzzy and binary contour ensembles.
• The method effectively encodes sensitivity information through probabilistic contour extraction.
• An efficient approximation reduces computational complexity.
• GPU parallelization achieves an order-of-magnitude reduction in computation time.
• Enables computation of contour boxplots for probabilistic masks and large 3D ensembles.

Conclusions:

• Probabilistic Inclusion Depth (PID) offers a robust and efficient solution for scalar field ensemble visualization.
• The method advances the analysis of uncertain data by supporting fuzzy contours and providing sensitivity information.
• PID extends visualization capabilities to previously intractable large-scale and complex ensemble datasets.