Nonparametric registration to low-dimensional function spaces

Abstract

Registration aims to decompose amplitude and phase variation of samples of curves. Phase variation is captured by warping functions which monotonically transform the domains. Resulting registered curves should then only exhibit amplitude variation. Most existing methods assume that all sample functions exhibit a typical sequence of shape features like peaks or valleys, and registration focuses on aligning these features. A more general perspective is adopted which goes beyond feature alignment. A registration method is introduced where warping functions are defined in such a way that the resulting registered curves span a low dimensional linear function space. The approach may be used as a tool for analyzing any type of functional data satisfying a structural regularity condition called bounded shape variation. Problems of identifiability are discussed in detail, and connections to established registration procedures are analyzed. The method is applied to real and simulated data.