# Uncertainty Visualization of 2D Morse Complex Ensembles Using Statistical Summary Maps

arXiv: https://arxiv.org/abs/1912.06341 · HTML: https://mlsanity.com/paper/1912.06341/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Dec 2019.

## Built on by (most cited first, 10 of 10)

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- [Wasserstein Dictionaries of Persistence Diagrams](https://mlsanity.com/paper/2304.14852/) (2023)
- [Wasserstein Auto-Encoders of Merge Trees (and Persistence Diagrams)](https://mlsanity.com/paper/2307.02509/) (2023)
- [BondMatcher: H-Bond Stability Analysis in Molecular Systems](https://mlsanity.com/paper/2504.03205/) (2025)
- [Robust Barycenters of Persistence Diagrams](https://mlsanity.com/paper/2509.14904/) (2025)
- [An Entropy-Based Test and Development Framework for Uncertainty Modeling in Level-Set Visualizations](https://mlsanity.com/paper/2409.08445/) (2024)
- [Efficient Probabilistic Visualization of Local Divergence of 2D Vector Fields with Independent Gaussian Uncertainty](https://mlsanity.com/paper/2510.01190/) (2025)

## Abstract (arXiv)

Morse complexes are gradient-based topological descriptors with close connections to Morse theory. They are widely applicable in scientific visualization as they serve as important abstractions for gaining insights into the topology of scalar fields. Noise inherent to scalar field data due to acquisitions and processing, however, limits our understanding of the Morse complexes as structural abstractions. We, therefore, explore uncertainty visualization of an ensemble of 2D Morse complexes that arise from scalar fields coupled with data uncertainty. We propose statistical summary maps as new entities for capturing structural variations and visualizing positional uncertainties of Morse complexes in ensembles. Specifically, we introduce two types of statistical summary maps -- the Probabilistic Map and the Survival Map -- to characterize the uncertain behaviors of local extrema and local gradient flows, respectively. We demonstrate the utility of our proposed approach using synthetic and real-world datasets.