Uncertainty-Aware Jacobi Set Computation

2026-08-14

AI Summary

This study addresses the absence of uncertainty quantification in Jacobi set computation for multi-scalar fields by proposing an uncertainty-aware computational framework. Leveraging multivariate normal distribution modeling and analytical propagation mechanisms, this work achieves precise uncertainty quantification within Jacobi set analysis for the first time, complemented by a visualization overlay scheme integrating multidimensional information. Validated through Monte Carlo simulations on fluid dynamics and meteorological ensemble datasets, the proposed method accurately reveals topological structures alongside their associated uncertainties. Consequently, this approach significantly enhances the reliability and interpretability of multi-field visualization, providing novel theoretical support for complex data analysis in scientific domains requiring rigorous uncertainty characterization.

Abstract

We present an uncertainty-aware Jacobi set computation method. In general, Jacobi sets are topological descriptors that capture the gradient alignments of two scalar fields, as, e.g., used for multi-field visualization. We adopt and reformulate an existing computational approach that relies on an edge-based identification of Jacobi set edges on a given triangulation. Our extension to uncertainty visualization builds upon a versatile, spatially coherent uncertainty model for pairs of scalar fields based on multivariate normal distributions. We propagate the uncertainty analytically, thereby lifting the original Jacobi set computation to uncertain inputs. Furthermore, we present an overlay of visual mappings specifically designed to show the Jacobi sets along with different facets of uncertainty information. Both the uncertainty model and uncertainty-aware method are validated against a Monte Carlo approach on an analytic dataset and applied to two use cases from fluid dynamics and weather ensembles.

Problem

• Jacobi set
• uncertainty visualization
• scalar fields
• topological descriptors

Innovation

• Uncertainty-Aware Jacobi Set
• Multivariate Normal Distribution
• Analytical Uncertainty Propagation
• Uncertainty Visualization