"What is a CIImage that qualifies as a "K x 1" image?"
This filter uses an algorithm called K-means, which is the name of a classic method for determining the k dominant colors in an image, a.k.a. the "palette" of the image. (Look up "k-means clustering" on google for the details).
Let's set k = 5 for example's sake. I've found this to be a good number of colors to capture the essential look of an image.
Because you want the filter to give you the 5 most important colors in the image, it needs 5 "seed" colors to kick off its algorithm. These seeds are simply meant to be hints you supply in order to help the algorithm converge on the optimal answer faster—they don't have to be the "right" colors. (Determining the right colors is the algorithm's job, after all!)
As an initial guess, why not just take the 5 pixel colors found in (say) the center and the corners of the image? Or black, red, green, yellow and blue?
OK, but how do you supply these 5 hints to the CIFilter? An NSArray of five NSColor objects might be the most obvious way. Unfortunately, however, CIFilter doesn't like that kind of input, so instead it requests that you give it a 5-by-1 pixel image, where each pixel, reading right from left, is the corresponding color. Yes, it's a tiny, tiny image. You can generate it in code or in Photoshop or in Pixelmator.
Caveat: I don't have MacOS 15 yet so I'm only speaking from my experience with processing images. I haven't had a chance to use CIKMeans yet. Hope this helps though.