  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.
