3D Shape Analysis

7Nonrigid Registration

7.1 Introduction

In the previous chapter, we discussed techniques for rigid registration, i.e. finding correspondences between and aligning to each other 3D objects or partial 3D scans that are equivalent up to a rigid transform. In this chapter, we shift our focus to the more complex problem where the objects under consideration undergo elastic deformations, which involve bending and stretching. Such 3D objects appear in many applications. For instance, anatomical organs deform in an elastic way during their growth and during their alteration as a result of disease progression. Similarly, human body shapes, as shown in Figure 7.1a–c, significantly bend and stretch during their motion and their growth. 3D reconstruction, growth and motion analysis, motion interpolation, and deformation transfer are examples of applications that require matching features across such 3D objects.

Figure 7.1Examples of (a) 3D models that undergo nonrigid deformations, (b) correspondences when the 3D models undergo only stretching, and (c) correspondences when the 3D models stretch and bend at the same time.

Source: Reproduced with permission of Morgan & Claypool Publishers.

This chapter describes a set of techniques for finding correspondences and computing registrations between 3D objects, which deform in a nonrigid way. While the literature is very rich, see for example 183 ...