imageinterp: Interpolation between Images

In T4transport: Tools for Computational Optimal Transport

Interpolation between Images

Description

Given two grayscale images represented as numeric matrices of identical size, compute interpolated images along a 2-Wasserstein geodesic connecting them. The function interprets each image as a discrete probability distribution on a common (m\times n) grid, computes an exact optimal transport plan, and constructs intermediate measures by pushing the plan through the linear interpolation map z=(1-t)x+t y (displacement interpolation / McCann's interpolation).

Usage

imageinterp(image1, image2, t = 0.5, ...)

Arguments

image1	a grayscale image matrix of size (m\times n) with nonnegative entries.
image2	another grayscale image matrix of size (m\times n) with nonnegative entries.
t	a scalar or numeric vector in [0,1] specifying interpolation times. t=0 returns image1, t=1 returns image2.
...	extra parameters including eps positivity floor applied after normalization (default: 1e-15). Larger values can improve robustness. abstol tolerance used for internal mass checks (default: 1e-12). print.progress logical; if TRUE, print basic diagnostics (default: FALSE).

Details

Because the interpolated support locations generally do not coincide with the original grid points, the resulting distribution is projected back onto the grid by depositing transported mass to the nearest grid location. This is a simple and robust "re-binning" step, analogous in spirit to how histinterp re-bins interpolated quantile samples.

Value

If length(t)==1, a single (m\times n) matrix representing the interpolated image. If length(t)>1, a length-length(t) list of (m\times n) matrices.

Examples

#----------------------------------------------------------------------
#                  Digit Interpolation between 1 and 8
#----------------------------------------------------------------------
# LOAD DATA
set.seed(11)
data(digits)
x1 <- digits$image[[sample(which(digits$label==1),1)]] 
x2 <- digits$image[[sample(which(digits$label==8),1)]]

# COMPUTE
tvec <- seq(0, 1, length.out=10)
path <- imageinterp(x1, x2, t = tvec)

# VISUALIZE
opar <- par(no.readonly=TRUE)
par(mfrow=c(2,5), pty="s")
for (k in 1:10){
  image(path[[k]], axes=FALSE, main=sprintf("t=%.2f", tvec[k]))
} 
par(opar)

T4transport documentation built on Jan. 11, 2026, 9:07 a.m.