Differential topology, and specifically Morse theory, provide a suitable setting for formalizing
and solving several problems related to shape analysis. The fundamental idea behind …

In topological data analysis and visualization, topological descriptors such as persistence
diagrams, merge trees, contour trees, Reeb graphs, and Morse–Smale complexes play an …

Reeb graphs are compact shape descriptors which convey topological information related to
the level sets of a function defined on the shape. Their definition dates back to 1946, and …

This paper presents the state of the art in the area of topology‐based visualization. It
describes the process and results of an extensive annotation for generating a definition and …

Large-scale simulations are increasingly being used to study complex scientific and
engineering phenomena. As a result, advanced visualization and data analysis are also …

When a heavy fluid is placed above a light fluid, tiny vertical perturbations in the interface
create a characteristic structure of rising bubbles and falling spikes known as Rayleigh …

This paper presents topology-based methods to robustly extract, analyze, and track features
defined as subsets of isosurfaces. First, we demonstrate how features identified by …

This paper presents a robust and efficient method for tracking topological features in time-
varying scalar data. Structures are tracked based on the optimal matching between …

This paper presents a novel approach for fast and efficient partial shape retrieval on a
collection of 3D shapes. Each shape is represented by a Reeb graph associated with …

Generalizing the concept of a Reeb graph, the Reeb space of a multivariate continuous
mapping identifies points of the domain that belong to a common component of the …