Elastic Curve Alignment — elastic.align • fdars

Align a set of functional curves using the elastic (Fisher-Rao) framework. When no target is specified, the Karcher mean is used as the alignment target.

Usage

elastic.align(
  fdataobj,
  target = NULL,
  periodic = FALSE,
  rotate.method = "peak",
  rotate.args = list()
)

Arguments

fdataobj: An object of class 'fdata'.
target: Optional target curve (numeric vector). If NULL, uses the cross-sectional mean as the alignment target.
periodic: Logical; if TRUE, circularly rotate each curve to a canonical position before elastic alignment. This two-stage approach handles periodic functional data (e.g., data on \([0, 2\pi]\) where \(f(0) = f(2\pi)\)) that would otherwise be poorly aligned due to fixed boundary constraints \(\gamma(0)=0, \gamma(1)=1\). Default is FALSE.
rotate.method: Rotation method when periodic = TRUE: one of "peak" (default), "xcorr", "landmark", or "iterative". See periodic.rotate for details.
rotate.args: A named list of additional arguments passed to periodic.rotate (e.g., reference, landmark.func, max.iter).

Value

An object of class 'elastic.align' with components:

aligned: fdata of aligned curves
gammas: fdata of warping functions
distances: numeric vector of elastic distances
target: the target curve used for alignment
fdataobj: the original fdata input
rotations: integer vector of circular rotation shifts applied (NULL when periodic = FALSE)
rotate_method: the rotation method used (NULL when periodic = FALSE)

References

Srivastava, A., Klassen, E., Joshi, S.H., and Jermyn, I.H. (2011). Shape analysis of elastic curves in Euclidean spaces. IEEE Transactions on Pattern Analysis and Machine Intelligence, 33(7):1415–1428.

Tucker, J.D., Wu, W., and Srivastava, A. (2013). Generative models for functional data using phase and amplitude separation. Computational Statistics & Data Analysis, 61:50–66.

Examples

# \donttest{
fd <- fdata(matrix(rnorm(200), 20, 10), argvals = seq(0, 1, length.out = 10))
res <- elastic.align(fd)
# }