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Compute an elastic full Procrustes mean for a collection of curves

Source: R/compute_elastic_shape_mean.R
compute_elastic_shape_mean.Rd

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)