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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?

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Yes - if you are taking k-means with k=1, it's the same as calculating the mean of all pixels in the image. Attention to the channels though - you should be taking the means of all pixels per channel, to end up with three channels, so one mean for R, one for G, and one for B, assuming you're in RGB colorspace.

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