A common challenge for the statistical analysis of various spectra,
such as those common to proteomics, is time registration of curves. An
approach to data driven time warping for registration, based on the
Fisher Rao metric on square root velocity functions, is seen to give a
particularly attractive approach, with some important invariance
properties.  This forms the basis of an intuitve decomposition of the
variation into horizontal and vertical components.  Especially
impressive results are shown for aligning peaks in a Total Ion
Chromatography data set.