img2measure: Extract a discrete measure from a gray-scale image matrix

In T4transport: Tools for Computational Optimal Transport

Extract a discrete measure from a gray-scale image matrix

Description

This function takes a gray-scale image represented as a matrix X and converts it into a discrete measure suitable for optimal transport computations in a Lagrangian framework. Pixel intensities are normalized to sum to one, and the nonzero pixels are represented as weighted points (support and weights).

Usage

img2measure(X, threshold = TRUE)

Arguments

X	An (N,2) nonnegative matrix representing a gray-scale image, where each entry corresponds to a pixel intensity.
threshold	A logical flag indicating whether to threshold very small weights smaller than machine epsilon.

Value

A named list containing

support

an (M\times 2) matrix of coordinates for the nonzero pixels, where each row is a point (x,y).

weight

a length-M vector of weights corresponding to the nonzero pixels, summing to 1.

Examples

#-------------------------------------------------------------------
#                           Description
#
# Take a digit image and compare visualization.
#-------------------------------------------------------------------
# load the data and select the first image
data(digit3)
img_matrix = digit3[[1]]

# extract a discrete measure
img_measure = img2measure(img_matrix, threshold=TRUE)
w  <- img_measure$weight
w_norm <- w / max(w)          # now runs from 0 to 1
col_scale <- gray(1 - w_norm) # 1 = white, 0 = black

# visualize
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,2), pty="s")
image(img_matrix, xaxt="n", yaxt="n", main="Image Matrix")
plot(img_measure$support, 
     col = col_scale, xlab="", ylab="",
     pch = 19, cex = 0.5, xaxt = "n", yaxt = "n",
     main = "Extracted Discrete Measure")
par(opar)

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