Registration: Aligning Features for Samples of Curves

Abstract

This chapter presents two methods for separating phase variation from amplitude variation in functional data: landmark and continuous registration. We mentioned this problem in Section 1.1.1. We saw in the height acceleration curves in Figure 1.2 that the age of the pubertal growth spurt varies from girl to girl; this is phase variation. In addition, the intensity of the pubertal growth spurt also varies; this is amplitude variation. Landmark registration aligns features that are visible in all curves by estimating a strictly increasing nonlinear transformation of time that takes all the times of a given feature into a common value. Continuous registration uses the entire curve rather than specified features and can provide a more complete curve alignment. The chapter also describes a decomposition technique that permits the expression of the amount of phase variation in a sample of functional variation as a proportion of total variation.