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Geometric and Topological Mesh Feature Extraction for 3D Shape Analysis

Geometric and Topological Mesh Feature Extraction for 3D Shape Analysis

Jean-Luc Mari, Franck Hetroy-Wheeler, Gérard Subsol

ISBN: 978-1-786-30041-6

Apr 2020

Select type: Hardcover


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Shapes, either from the natural world or man-made, are more and more digitized for visualization or measurement purposes, among others. This process results in general in 3D surface meshes, composed of collections of planar polygons. Such meshes nowadays are the most common discrete representation of the surface of a virtual shape. These 3D surface meshes are automatically, or sometimes interactively, examined, in order their overall structure or some details to be understood or evaluated. This can be done by extracting relevant geometric or topological features. Such shape characteristics can simplify the way the object is looked at, can help recognition, and can describe and categorize it according to specific criteria.

This book deals with feature definition and computation on a 3D surface mesh, and their use for shape analysis. Recent methods are described to extract feature lines having a meaning related not only to geometry but to topology as well. Differential estimators like discrete principal curvatures are detailed as they play a critical role for the computation of salient structures. Several applications are developed, and each of them needs specific adjustments to generic approaches. These applications are related to geology, planetary science, paleo-anthropology, astrophysics, medicine, and forestry.

1 - Introduction

2 - Overview of what is called a "feature"

3 - Geometric features based on curvatures

Some reminders of differential geometry of surfaces

Feature lines detection approaches

Region-based approaches

Point-based approaches

4 - Topological features

Mathematical background

Global topological features computation

Combining geometrical and topological features

Topological persistence

5 - Applications

6 - Conclusion