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Elastic (SRVF) alignment of two curves

Source: R/align-elastic.R
elasticAlign.Rd

Aligns curve y to curve x by an optimal time warping computed in the Square-Root Velocity Function representation, separating phase (the warping) from amplitude (the residual shape difference). A pure-R dynamic-programming solver is used by default; if the fdasrvf package is available it is used for higher accuracy.

Usage

elasticAlign(
  x,
  y,
  t = NULL,
  lambda = 0,
  method = c("srvf"),
  max_step = 6L,
  smooth = FALSE,
  use_fdasrvf = NA
)

Arguments

x, y

Numeric curves of the same length.

t

Optional grid (defaults to an evenly spaced grid on 0..1).

lambda

Non-negative warping-roughness penalty (passed to fdasrvf when used; the pure-R solver ignores it beyond boundary/monotonicity).

method

Currently "srvf".

max_step

Maximum DP step (bounds the local warping slope) for the pure-R solver (default: 6).

smooth

Smooth the pure-R warping with a monotone spline (default: FALSE).

use_fdasrvf

NA (default) uses fdasrvf if installed; TRUE requires it; FALSE forces the pure-R solver.

Value

A list with gamma (the warping), aligned (y warped to x), amplitude_distance, phase_distance, the SRVFs, and the solver used.

References

Srivastava, A., Wu, W., Kurtek, S., Klassen, E., & Marron, J. S. (2011). Registration of functional data using Fisher-Rao metric. arXiv:1103.3817.

See also

srvfMean(), warpApply()

Examples

t <- seq(0, 1, length.out = 80)
x <- exp(-((t - 0.5)^2) / (2 * 0.08^2))
y <- exp(-((t - 0.65)^2) / (2 * 0.08^2))
al <- elasticAlign(x, y)
al$amplitude_distance
#> [1] 0.06749576