3D Shape Analysis

4Global Shape Descriptors

4.1 Introduction

The main building block and core component of any 3D shape analysis task is a mechanism for measuring the similarity, or the dissimilarity, between 3D models. This is often achieved using:

• Descriptors, which characterize the geometry, topology, and semantics of 3D objects,
• Dissimilarity functions, which measure distances between descriptors, and
• Algorithms, which use the descriptors and the dissimilarity measures for the matching, classification, or retrieval of 3D models.

In short, a descriptor is a compact numerical representation of the shape of a 3D object. Distances in the descriptor space should reflect the dissimilarities between the objects that these descriptors represent. Such dissimilarities can be geometric, topological, or semantic. A good descriptor is the one that is

• Concise, compact, quick to compute, and efficient to compare. Ideally, a descriptor should be composed of a few numbers, which capture the essence of the shape so that it will be easy to store and to compare.
• Discriminative. Objects of different shapes should have different descriptors while objects of similar shapes should have similar descriptors.
• Insensitive to geometric and topological noise such as acquisition noise (see Chapter 2) and missing parts.
• Invariant to similarity transformations. A good shape descriptor should capture properties that characterize the shape of objects, by representing key shape features, while remaining invariant to transformations, ...