Abstract and Keywords
This article deals with curve registration, which refers to methods for aligning prominent features in a set of curves by transforming their abscissa variables. It first illustrates the concepts of amplitude and phase variation schematically and with real data before defining the time-warping functions and their functional inverse. It then describes the decomposition of total mean squared variation into separate amplitude and phase components, along with an R2 measure of the proportion of functional variation due to phase in a sample of curves. It also considers landmark registration, novel ways of defining curve features, continuous registration, and methods based on structured models for amplitude and phase variation combined with more statistically oriented fitting methods such as maximum likelihood or Bayesian estimation. The article concludes with a brief survey of software resources for registration.
Keywords: curve registration, amplitude variation, phase variation, time-warping functions, total mean squared variation, functional variation, landmark registration, continuous registration, maximum likelihood estimation, Bayesian estimation
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