imagebary15B: Barycenter of Images according to Benamou et al. (2015)

In T4transport: Tools for Computational Optimal Transport

Barycenter of Images according to Benamou et al. (2015)

Description

Using entropic regularization for Wasserstein barycenter computation, imagebary15B finds a barycentric image X^* given multiple images X_1,X_2,\ldots,X_N. 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.

Usage

imagebary15B(images, p = 2, weights = NULL, lambda = NULL, ...)

Arguments

images	a length-N list of same-size image matrices of size (m\times n).
p	an exponent for the order of the distance (default: 2).
weights	a weight of each image; if NULL (default), uniform weight is set. Otherwise, it should be a length-N vector of nonnegative weights.
lambda	a regularization parameter; if NULL (default), a paper's suggestion would be taken, or it should be a nonnegative real number.
...	extra parameters including abstol stopping criterion for iterations (default: 1e-8). init.image an initial weight image (default: uniform weight). maxiter maximum number of iterations (default: 496). nthread number of threads for OpenMP run (default: 1). print.progress a logical to show current iteration (default: TRUE).

Value

an (m\times n) matrix of the barycentric image.

References

\insertRef

benamou_iterative_2015T4transport

See Also

bary15B

Examples

#----------------------------------------------------------------------
#                       MNIST Data with Digit 3
#
# EXAMPLE 1 : Very Small  Example for CRAN; just showing how to use it!
# EXAMPLE 2 : Medium-size Example for Evolution of Output
#----------------------------------------------------------------------
# EXAMPLE 1
data(digit3)
datsmall = digit3[1:2]
outsmall = imagebary15B(datsmall, maxiter=3)

## Not run: 
# EXAMPLE 2 : Barycenter of 100 Images
# RANDOMLY SELECT THE IMAGES
data(digit3)
dat2 = digit3[sample(1:2000, 100)]  # select 100 images

# RUN SEQUENTIALLY
run05 = imagebary15B(dat2, maxiter=5)                    # first 5 iterations
run10 = imagebary15B(dat2, maxiter=5,  init.image=run05) # run 5 more
run50 = imagebary15B(dat2, maxiter=40, init.image=run10) # run 40 more

# VISUALIZE
opar <- par(no.readonly=TRUE)
par(mfrow=c(2,3), pty="s")
image(dat2[[sample(100,1)]], axes=FALSE, main="a random image")
image(dat2[[sample(100,1)]], axes=FALSE, main="a random image")
image(dat2[[sample(100,1)]], axes=FALSE, main="a random image")
image(run05, axes=FALSE, main="barycenter after 05 iter")
image(run10, axes=FALSE, main="barycenter after 10 iter")
image(run50, axes=FALSE, main="barycenter after 50 iter")
par(opar)

## End(Not run)

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