compute_elastic_shape_mean: Compute an elastic full Procrustes mean for a collection of...

In elastes: Elastic Full Procrustes Means for Sparse and Irregular Planar Curves

Compute an elastic full Procrustes mean for a collection of curves

Description

Computes an elastic full Procrustes mean for curves stored in data_curves. Constructor function for class elastic_shape_mean.

Usage

compute_elastic_shape_mean(
  data_curves,
  knots = seq(0, 1, len = 13),
  type = c("smooth", "polygon"),
  penalty = 2,
  var_type = c("smooth", "constant", "zero"),
  pfit_method = c("smooth", "polygon"),
  smooth_warp = function(i) 0,
  eps = 0.05,
  max_iter = 50,
  verbose = FALSE,
  cluster = NULL
)

Arguments

data_curves	list of data.frames with observed points in each row. Each variable is one coordinate direction. If there is a variable t, it is treated as the time parametrization, not as an additional coordinate.
knots	set of knots for the mean spline curve
type	if "smooth" linear srv-splines are used which results in a differentiable mean curve if "polygon" the mean will be piecewise linear.
penalty	the penalty to use in the covariance smoothing step. use '-1' for no penalty.
var_type	(experimental) assume "smooth", "constant" or "zero" measurement-error variance along t
pfit_method	(experimental) "smooth" or "polygon"
smooth_warp	(experimental) controls the weighting of original and smoothed observations over the iterations, if pfit_method == "smooth".
eps	the algorithm stops if L2 norm of coefficients changes by less than eps
max_iter	maximal number of iterations
verbose	print iterations
cluster	(experimental) use the parallel package for faster computation

Value

an object of class elastic_shape_mean, which is a list with entries

type	"smooth" if mean was modeled using linear srv-splines, "polygon" if constant srv-splines
coefs	spline coefficients
knots	spline knots
variance	sample elastic shape variance
data_curves	list of data.frames with observed points in each row. First variable t gives the initial parametrization, second variable t_optim the optimal parametrization when the curve is aligned to the mean. Has the attributes 'rotation', 'scaling', 'translation' and 'dist_to_mean'. Use get_procrustes_fit to get the elastic full Procrustes fit.
fit	see fit_mean

Examples

curve <- function(t){
  rbind(t*cos(13*t), t*sin(13*t))
}
set.seed(18)
data_curves <- lapply(1:4, function(i){
  m <- sample(10:15, 1)
  delta <- abs(rnorm(m, mean = 1, sd = 0.05))
  t <- cumsum(delta)/sum(delta)
  data.frame(t(curve(t)) + 0.07*t*matrix(cumsum(rnorm(2*length(delta))),
             ncol = 2))
})

#randomly rotate and scale curves
rand_scale <- function(curve){ ( 0.5 + runif(1) ) * curve }
rand_rotate <- function(curve){
  names <- colnames(curve)
  theta <- 2*pi*runif(1)
  mat <- matrix(c(cos(theta), sin(theta), -sin(theta), cos(theta)), nrow = 2, ncol = 2)
  curve.rot <- as.matrix(curve) %*% t(mat)
  curve.rot <- as.data.frame(curve.rot)
  colnames(curve.rot) <- names
  return(curve.rot)
}
data_curves <- lapply(data_curves, rand_scale)
data_curves <- lapply(data_curves, rand_rotate)

#compute smooth procrustes mean with 2 order penalty
knots <- seq(0,1, length = 11)
elastic_shape_mean <- compute_elastic_shape_mean(
    data_curves,
    knots = knots,
    type = "smooth",
    penalty = 2
    )
plot(elastic_shape_mean)

elastes documentation built on Aug. 21, 2023, 5:12 p.m.