3D Shape Analysis

8Semantic Correspondences

8.1 Introduction

The approaches presented so far for shape correspondence are geometry driven, focusing solely on the geometrical and topological similarities between shapes. However, in many situations, corresponding shape parts may significantly differ in geometry or even in topology. Take the 3D models shown in Figure 8.1. Any human can easily put in correspondence and match parts of the chairs of Figure 8.1a despite the fact that they differ significantly in geometry and topology. For instance, some chairs have one leg while others have four. In these examples, correspondence is simply beyond pure geometric analysis; it requires understanding the semantics of the shapes in order to reveal relations between geometrically dissimilar yet functionally or semantically equivalent shape parts.

Figure 8.1Partwise correspondences between 3D shapes in the presence of significant geometrical and topological variations. (a) Man‐made 3D shapes that differ in geometry and topology. The partwise correspondences are color coded. (b) A set of 3D models with significant shape differences, yet they share many semantic correspondences.

This fundamental problem of putting in correspondence 3D shapes that exhibit large geometrical and topological variations has been extensively studied in the literature, especially in the past five years 183, 203–205. Beyond standard applications, ...