I am currently working on image classification methods. One group of preprocessing methods are color space transformations. While there are "traditional" color spaces like RGB (the raw data), HSV, LUV, XYZ, ..., I see any function
$$f:[0, ..., 255]^3 \rightarrow [0, ..., 255]^3$$
as a transformation from one color space in another color space (starting from RGB). Having multiple of those transformation functions $f_i$, I would like to be able to compare them.
Is there a common way to visualize color spaces for comparison? A metric which defines how "close" color spaces are? This measure of "closeness" could be interesting to estimate how much of a difference the choice of color space makes for the classifier.
I thought I could probably take a set of images and use the average euclidean distance of them as one way to compare them. Or just some randomly sampled colors and their average euclidean distance. But I guess there are more sophisticated ways?