" In this chapter, we introduce some of the very basics that are used throughout the book.
First, we give the definition of a topological space and related notions of open and closed …

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

Combining concepts from topology and algorithms, this book delivers what its title promises:
an introduction to the field of computational topology. Starting with motivating problems in …

In this paper, we focus on the retrospective topology correction of surfaces. We propose a
technique to accurately correct the spherical topology of cortical surfaces. Specifically, we …

This handbook provides an up-to-date compendium of fundamental computer science
topics, techniques, and applications. Along with updating and revising many of the existing …

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 …

Reeb graphs are a fundamental data structure for understanding and representing the
topology of shapes. They are used in computer graphics, solid modeling, and visualization …

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 …

Scalar functions defined on manifold triangle meshes is a starting point for many geometry
processing algorithms such as mesh parametrization, skeletonization, and segmentation. In …

To fully exploit the valuable knowledge embedded in repositories of digital models, it is
crucial to devise search engines capable of expressing high-level and advanced queries …