# K means clustering of image with k=1 vs mean of all pixels

I have relatively uniformly colored images and I extracted colors using k-means. k means 1 showed the best results for my modeling purposes, k means 2 not so much, and with k-means 3 there ceased to be differences between some channels of samples.

Is this a reasonable approach and is it technically different from calculating the mean of all pixels in the image.

Can it be said that I took the mean of all pixels if the result is the same?

Welcome to CrossValidated! If when you say "k-means 1" you mean a k-mean algorithm with only 1 cluster, then I think the centers of the cluster are represented by the multivariate mean vector, i.e. the vector that contains the mean of all the variables you input in the k-means.

See below, the centers of the kmeans() function are equal to the means of the two variables:

set.seed(123)
x <- rbind(matrix(rnorm(100, sd = 0.3), ncol = 2),
matrix(rnorm(100, mean = 1, sd = 0.3), ncol = 2))
colnames(x) <- c("x", "y")
cl <- kmeans(x, 1)

mean(x[,1]);mean(x[,2])
cl\$centers