The Reeb graph is the quotient space X /~ endowed with the quotient topology. Generally, this quotient space does not have the structure of a finite graph. Even for a smooth function on a smooth manifold, the Reeb graph can be not one-dimensional and even non- Hausdorff space .

2008年2月28日 · 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 finds its root in Morse theory.

V.4 Reeb Graphs The structure of a continuous function can sometimes be made explicit by plotting the evolution of the components of the level set. This leads to the concept of the Reeb graph of the function. It has applications in medical imaging and other areas of science and engineering. Iso-surface extraction.

2012年9月26日 · In this paper, we initiate the study of two important aspects of the Reeb graph, which can facilitate its broader applications in shape and data analysis. The first one is the approximation of the Reeb graph of a function on a smooth compact manifold M without boundary. The approximation is computed from a set of points P sampled from M.

In this paper, we develop a framework to extract, as well as to sim- plify, a one-dimensional ”skeleton” from unorganized data using the Reeb graph. Our algorithm is very simple, does not require complex optimizations and can be easily applied to unorganized high-dimensional data such as point clouds or proximity graphs.

Reeb图则是另一种关键的工具，它可以用来抽象和概括3D形状的拓扑特性，通过分析点云的局部极值点来捕获其全局结构。 形状分析与理解是3维点云处理的重要部分，拓扑结构在这里起到关键的角色。

Reeb图是一种三维模型的拓扑信息描述子，一般基于函数 水平集来处理，表达模型上各部分之间的拓扑邻接关系， 在模型匹配、三维动画、拓扑分析等方面有重要应用。

We study the evolution of the Reeb graph of a time-varying con-tinuous function defined in three-dimensional space. While main-taining the Reeb graph, we compress the evolving sequence into a single, partially persistent data structure.

2009年8月1日 · The Reeb graph tracks topology changes in level sets of a scalar function and finds applications in scientific visualization and geometric modeling. We describe an algorithm that constructs the Reeb graph of a Morse function defined on a 3-manifold.

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 measure of similarity between these structures.