Related papers: Reeb Graph of Sample Thickenings
A Reeb graph is a graphical representation of a scalar function on a topological space that encodes the topology of the level sets. A Reeb space is a generalization of the Reeb graph to a multiparameter function. In this paper, we propose…
As graphical summaries for topological spaces and maps, Reeb graphs are common objects in the computer graphics or topological data analysis literature. Defining good metrics between these objects has become an important question for…
The Reeb space, which generalizes the notion of a Reeb graph, is one of the few tools in topological data analysis and visualization suitable for the study of multivariate scientific datasets. First introduced by Edelsbrunner et al., it…
We study the probabilistic convergence between the mapper graph and the Reeb graph of a topological space $\mathbb{X}$ equipped with a continuous function $f: \mathbb{X} \rightarrow \mathbb{R}$. We first give a categorification of the…
The Reeb graph is a construction that studies a topological space through the lens of a real valued function. It has widely been used in applications, however its use on real data means that it is desirable and increasingly necessary to…
The Reeb graph has been utilized in various applications including the analysis of scalar fields. Recently, research has been focused on using topological signatures such as the Reeb graph to compare multiple scalar fields by defining…
Reeb graphs are a fundamental structure for analyzing the topological and geometric properties of scalar fields. Comparing Reeb graphs is crucial for advancing research in this domain, yet existing metrics are often computationally…
Since its introduction as a computable approximation of the Reeb graph, the Mapper graph has become one of the most popular tools from topological data analysis for performing data visualization and inference. However, finding an…
The Reeb graph is a construction which originated in Morse theory to study a real valued function defined on a topological space. More recently, it has been used in various applications to study noisy data which creates a desire to define a…
Reeb graphs are widely used in a range of fields for the purposes of analyzing and comparing complex spaces via a simpler combinatorial object. Further, they are closely related to extended persistence diagrams, which largely but not…
The Reeb graph of a scalar function defined on a domain gives a topologically meaningful summary of that domain. Reeb graphs have been shown in the past decade to be of great importance in geometric processing, image processing, computer…
One of the prevailing ideas in geometric and topological data analysis is to provide descriptors that encode useful information about hidden objects from observed data. The Reeb graph is one such descriptor for a given scalar function. The…
Previously, we have investigated a natural smooth map onto the region surrounded by the graphs of two smooth real-valued functions in the plane converging to a same value or diverges to $+\infty$ or $-\infty$ simultaneously, at each…
To investigate the topological structure of planar polygon decomposition on trapezoids, which is formed by height functions. We use the oriented Reeb graph of the function with a marked vertex. We describe all possible optimal Reeb graphs…
The Reeb graph of a function on a smooth manifold is the graph obtained as the space of all connected components of level sets such that the set of all vertices coincides with the set of all connected components of level sets including…
The Reeb graph of a smooth function is a graph being a natural quotient space of the manifold of the domain and the space of all connected components of preimages. Such a combinatorial and topological object roughly and compactly represents…
The Reeb space of a smooth function is a topological and combinatoric object and fundamental and important in understanding topological and geometric properties of the manifold of the domain. It is the graph and a topological space endowed…
Reeb spaces of continuous real-valued functions on topological spaces are fundamental and strong tools in investigating the spaces. The Reeb space is the natural quotient space of the space of the domain represented by connected components…
Given a map $f:X \to M$ from a topological space $X$ to a metric space $M$, a decorated Reeb space consists of the Reeb space, together with an attribution function whose values recover geometric information lost during the construction of…
This is a note on the graphs of two smooth real-valued functions in the plane with no intersection and the natural map onto the region surrounded by them with the canonical projection to the line composed, yielding its Reeb space. The Reeb…