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

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

Benamou J, Carlier G, Cuturi M, Nenna L, Peyré G (2015). “Iterative Bregman Projections for Regularized Transportation Problems.” SIAM Journal on Scientific Computing, 37(2), A1111--A1138. ISSN 1064-8275, 1095-7197.

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)

if (FALSE) {
# 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)
}