Functional Convex Averaging and Synchronization for Time-Warped Random Curves

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Statistical analysis of trajectories on Riemannian manifolds: Bird migration, hurricane tracking and video surveillance (2014, background): “In case M = R, that is, if one is interested in registration and modeling of real-valued functions under random time-warpings, the problem has been studied by many authors, including Srivastava et al. (2011a), Liu and Müller (2004), Kneip and Ramsay (2008) and Tucker, Wu and Srivastava (2013).”
Functional Modelling and Classification of Longitudinal Data * (2005, background): “…1997), maximum likelihood based alignment (Rønn, 2001) and other forms of curve registration (Wang & Gasser, 1997, 1998, 1999; Kneip et al., 2000), and recently timesynchronization of random processes (Liu & Müller, 2004) have been proposed, and this subfield is still in rapid development.”
Functional Data Analysis (2016, background): “…to the deﬁnition of the mean curve as the function that corresponds to the bivariate Fr´echet mean of both time warping and amplitude processes (Liu & M¨uller 2004), which can be exempliﬁed with relative area-under-the curve warping, where the latter has been shown to be particularly well…”