Probabilistic Inclusion Depth for Fuzzy Contour Ensemble Visualization

TL;DR

This paper introduces Probabilistic Inclusion Depth, a novel data depth model for ensemble visualization of scalar fields that efficiently handles fuzzy contours and probabilistic masks, enabling advanced visualization techniques like contour boxplots.

Contribution

The paper presents a new probabilistic data depth model supporting fuzzy contours, with an efficient GPU-based approximation for large and complex ensembles.

Findings

Enables visualization of probabilistic masks and fuzzy contours.

Achieves significant reduction in computational time.

Demonstrates effectiveness on synthetic and real-world datasets.

Abstract

We propose Probabilistic Inclusion Depth (PID) for the ensemble visualization of scalar fields. By introducing a probabilistic inclusion operator $\subset_{\!p}$, our method is a general data depth model supporting ensembles of fuzzy contours, such as soft masks from modern segmentation methods, and conventional ensembles of binary contours. We also advocate to extend contour extraction in scalar field ensembles to become a fuzzy decision by considering the probabilistic distribution of an isovalue to encode the sensitivity information. To reduce the complexity of the data depth computation, an efficient approximation using the mean probabilistic contour is devised. Furthermore, an order of magnitude reduction in computational time is achieved with an efficient parallel algorithm on the GPU. Our new method enables the computation of contour boxplots for ensembles of probabilistic masks, ensembles defined on various types of grids, and large 3D ensembles that are not studied by existing methods. The effectiveness of our method is evaluated with numerical comparisons to existing techniques on synthetic datasets, through examples of real-world ensemble datasets, and expert feedback.