Shape Trajectory Analysis Using Procrustes Analysis and VARMA Models
-The Procrustes paradigm of morphometrics provides a four step work flow for shape analysis: 1) Collect landmark data, 2) Align shapes via Generalized Procrustes Analysis, 3) Analyze resulting data via multivariate statistics, 4) Visualize data (Adams et al. 2013)
-A shape trajectory is a time-ordered set of shapes that an organism assumes during some behavior or process. Since after alignment, shape trajectories are functions, rather than points, in shape space, the third step of the paradigm cannot be implemented with- out bias.
-Shape trajectory data is similar to outline data, in that the unit of interest is a con- tinuous function. To analyze outlines, morphometricians often approximate the outline using a combination of one or more basis functions and use the parameters of these functions as proxies for the outlines themselves. These parameters define a single point in parameter space, thus allowing for statistical analysis of the original outlines (Rohlf 1990).