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 …

Terrestrial laser scanning (TLS) is a ground-based approach to rapidly acquire 3D point
clouds via Light Detection and Ranging (LiDAR) technologies. Quantifying tree-scale …

Morse theory offers a natural and mathematically‐sound tool for shape analysis and
understanding. It allows studying the behavior of a scalar function defined on a manifold …

This article presents a well-scaling parallel algorithm for the computation of Morse-Smale
(MS) segmentations, including the region separators and region boundaries. The …

Digital terrain models (DTMs) are pivotal in remote sensing cartography and landscape
management requiring accurate surface representation and topological information …

Persistent homology allows for tracking topological features, like loops, holes and their
higher-dimensional analogues, along a single-parameter family of nested shapes …

In this work we present the first algorithm for reconstructing multi-labeled material interfaces
the allows for explicit topology control. Our algorithm takes in a set of 2D cross-sectional …

We propose a family of spatial data structures for the representation and processing of
Triangulated Irregular Networks (TINs). We call such data structures Terrain trees. A Terrain …

We introduce the Stellar decomposition, a model for efficient topological data structures over
a broad range of simplicial and cell complexes. A Stellar decomposition of a complex is a …

We consider the problem of analyzing the topology of scalar fields defined on a triangulated
shape by using a multi-scale approach, which allows reducing storage costs and …