Uncertainty Visualization for Approximated Barycenter of Contour Trees Based on Partial Optimal Transport
Authors
Mingzhe Li (University of Notre Dame), Fangfei Lan (University of Lausanne), Gunther H Weber (Lawrence Berkeley National Laboratory), Bei Wang (University of Utah)
Presentation
- Session
- Can We Trust This Chart? (Asking for a Friend)
- Time
- Wednesday, Nov 11, 08:18 – 08:27 (US/Eastern) · session 08:00 – 09:30
- Location
- Hall America south
Keywords
Optimal transport, contour tree, uncertainty visualization, topological data analysis
Abstract
Analyzing ensembles of contour trees is challenging due to variability in both topology and node attributes across instances. We present a framework for summarizing and visualizing such ensembles via approximate barycenter contour trees computed using the Fused Partial Gromov-Wasserstein (FPGW) distance. These barycenters provide representative summaries that capture shared structural patterns while supporting partial correspondences for unmatched or transient features. Our approach first estimates a representative barycenter matrix under the FPGW formulation and then reconstructs an approximate contour tree from this matrix. We further introduce a visualization that integrates the structural summary with transport-induced uncertainty. Specifically, we encode variability in function values, spatial embedding, and node correspondences, and propose a MetroSets-inspired view to expose structural differences among ensemble members. We demonstrate the effectiveness of our method on flow simulation ensembles, where barycenter contour trees yield interpretable summaries of topological variability and highlight regions of structural and scalar uncertainty grounded in the underlying data.
For Practitioners
This work is relevant to practitioners who analyze ensembles or time-varying scientific simulation data, including computational scientists, flow visualization researchers, and domain experts in engineering and climate science who use topological analysis to study complex scalar fields. Our framework provides an interpretable visual summary of topological variability and uncertainty across multiple datasets, enabling practitioners to identify stable structures, detect localized variations, and better understand ensemble behavior without inspecting individual contour trees separately.