k-means clustering on RGB or HSV scale?

Question

I want to segment an image but someone told me that the Euclidean distance for RGB is not as good as HSV -- but for HSV, as not all H, S, V are of the same range so I need to normalize it. Is it a good idea to normalize HSV and then do clustering? If so, how should I normalize on HSV scale?

Thanks

Answer 1

As HSV components are signify Hue, Saturation and gray intensity of a pixel they are not correlated to each other in terms of color, each component have its own role in defining the property of that pixel, like Hue will give you information regarding color (wavelength in other terms) Saturation always shows how much percentage of white is mixed with that color and Value is nothing but magnitude of that color(in other term Intensity), that is why all components of HSV space not follow same scale for representation of the values while hue can goes negative(because these are cyclic values) on the scale as well but intensity (V) will never goes negative, so normalization will not help in clustering much, the Better idea is you should apply clustering only on Hue if you want to do color clustering.

Now why Euclidean is not good for multi-channel clustering is because its distribution along mean is spherical(for 2D circular) so if it can not make any difference between (147,175,208) and (208,175,147) both will have same distance from the center, its better to use Mahalanobis Distance for distance calculation because it uses Co-variance matrix of the components which makes this distance distribution Parabolic along the mean.

so if you want to do color segmentation in RGB color space use mahalanobis distance(but it will computationally extensive so it will slows down clustering process) and if you want to do clustering in HSV color space use Hue for the segmentation of colors and than use V for fine tuning of segmentation output.

Hope it will help. Thank You

Answer 2

Hue is cyclic.

Do not use the mean (and thus, k-means) on such data.