# R/image_median22Y.R In T4transport: Tools for Computational Optimal Transport

#### Documented in imagemed22Y

#' Wasserstein Median of Images by You et al. (2022)
#'
#' Given multiple images \eqn{X_1,\ldots,X_N}, the Wasserstein median of
#' order 2 is computed. The proposed method relies on a choice of barycenter computation
#' in that we opt for an algorithm of \code{\link{imagebary15B}}, which uses
#' entropic regularization for barycenter computation. Please note the followings; (1) we only take a matrix as an image so please
#' make it grayscale if not, (2) all images should be of same size - no resizing is performed.
#'
#' @param images a length-\eqn{N} list of same-size image matrices of size \eqn{(m\times n)}.
#' @param weights a weight of each image; if \code{NULL} (default), uniform weight is set. Otherwise,
#' it should be a length-\eqn{N} vector of nonnegative weights.
#' @param lambda a regularization parameter; if \code{NULL} (default), a paper's suggestion
#' would be taken, or it should be a nonnegative real number.
#' @param ... extra parameters including \describe{
#' \item{abstol}{stopping criterion for iterations (default: 1e-8).}
#' \item{init.image}{an initial weight image (default: uniform weight).}
#' \item{maxiter}{maximum number of iterations (default: 496).}
#' \item{print.progress}{a logical to show current iteration (default: \code{TRUE}).}
#' }
#'
#' @return an \eqn{(m\times n)} matrix of the Wasserstein median image.
#'
#' @examples
#' \dontrun{
#' #----------------------------------------------------------------------
#' #                       MNIST Data with Digit 3
#' #
#' # EXAMPLE : Very Small Example for CRAN; just showing how to use it!
#' #----------------------------------------------------------------------
#' data(digit3)
#' datsmall = digit3[1:10]
#'
#' # COMPUTE
#' outsmall = imagemed22Y(datsmall, maxiter=5)
#'
#' # VISUALIZE
#' par(mfrow=c(1,4), pty="s")
#' image(outsmall, xaxt='n', yaxt='n', main="Wasserstein Median")
#' image(datsmall[[3]], xaxt='n', yaxt='n', main="3rd image")
#' image(datsmall[[6]], xaxt='n', yaxt='n', main="6th image")
#' image(datsmall[[9]], xaxt='n', yaxt='n', main="9th image")
#' par(opar)
#' }
#'
#' @concept image
#' @export
imagemed22Y <- function(images, weights=NULL, lambda=NULL, ...){
# --------------------------------------------------------------------------
# CHECK THE INPUT
name.f  = "imagemed22Y"
check.f = check_images(images, name.f)

# --------------------------------------------------------------------------
# GRID AND TRANSFORM
imgsize  = dim(images[[1]])
coordx   = seq(from=0, to=1, length.out=imgsize[2])
coordy   = seq(from=1, to=0, length.out=imgsize[1])
coords   = expand.grid(coordx, coordy)
nsupport = base::nrow(coords)

dxy    = as.matrix(stats::dist(coords))
nimage = length(images)

# --------------------------------------------------------------------------
# OTHER INFORMATION
myp = 2
mymarginal = list()
for (i in 1:nimage){
mymarginal[[i]] = as.vector(t(images[[i]]))
}
mypi      = valid_multiple_weight(weights, nimage, name.f)
mypi      = mypi/base::sum(mypi)
myweights = mypi
if ((length(lambda)==0)&&(is.null(lambda))){
mylambda = 1/(60/(stats::median(dxy)^myp)) # choice of the paper
} else {
mylambda = max(100*.Machine$double.eps, as.double(lambda)) } params = list(...) pnames = names(params) if ("init.image" %in% pnames){ par_init = as.vector(t(params$init.image))
par_init = par_init/base::sum(par_init)
if ((length(par_init)!=nsupport)||(any(par_init < 0))){
stop(paste0("* imagemed22Y : 'init.image' should be of matching size as other images with nonnegative values."))
}
} else {
par_init = rep(1/nsupport, nsupport)
}
if ("print.progress"%in%pnames){
myshow = as.logical(params$print.progress) } else { myshow = TRUE } if ("maxiter"%in%pnames){ myiter = max(1, round(params$maxiter))
} else {
myiter = 496
}
if ("abstol"%in%pnames){
mytol = max(100*.Machine$double.eps, params$abstol)
} else {
mytol = 1e-8
}
round_digit = ceiling(abs(log10(mytol)))

mynthr = max(1, round(params$nthread)) } else { mynthr = 1 } # -------------------------------------------------------------------------- # ITERATIVE PROCEDURE # RUN, WRAP, AND RETURN image_old = par_init for (it in 1:myiter){ # update the relative weight for (i in 1:length(myweights)){ sinkhorn_run = cpp_sinkhorn13(as.vector(mymarginal[[i]]), image_old, dxy, mylambda, myp, 100, mytol) myweights[i] = mypi[i]/as.double(sinkhorn_run$distance) # compute distance by Sinkhorn
}
myweights = myweights/base::sum(myweights)

# update an image
image_new = routine_bary15B(dxy, mymarginal, myweights, myp, mylambda, 100, mytol, FALSE, image_old, mynthr)
image_new = as.vector(image_new)

# compute the error & update
increment = max(as.vector(abs(image_old-image_new)))
if (increment < mytol){
if (myshow){
print(paste0("* imagemed22Y : algorithm terminates at iteration ",it," : increment=",round(increment, round_digit)))
}
return(matrix(image_new, imgsize[1], imgsize[2], byrow=TRUE))
break
}
image_old = image_new
if (myshow){
print(paste0("* imagemed22Y : iteration ",it,"/",myiter," complete : increment=",round(increment, round_digit)))
}
}
return(matrix(image_old, imgsize[1], imgsize[2], byrow=TRUE))
}

# data("digit3")
# data("digit4")
#
# gathered = c(digit3[sample(1:2000, 7)], digit4[sample(1:2000, 3)])
# fbary1   = image15B(gathered, p=1, maxiter=50, print.progress=TRUE)
# fbary2   = image15B(gathered, p=2, maxiter=50, print.progress=TRUE)
# fmedian  = medimage22Y(gathered, print.progress=TRUE, maxiter=20)
#
# par(mfrow=c(1,3), pty="s")
# image(fbary1)
# image(fbary2)
# image(fmedian)
#
# par(mfrow=c(2,5), pty="s")
# for (i in 1:10){
#   image(gathered[[i]])
# }


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T4transport documentation built on April 12, 2023, 12:37 p.m.