# what does it mean to have a decorrelated colour space?

I'm working on the problem of colour transfer between images. In the literature there's a common practice that consists in performing the transformations on images in what is called a decorrelated colour space, such as CIE L* a * b* or YUV. The argument that's given most of the time is that a decorrelated colour space allows us to transform each one of the 3 channels of the image without affecting the other 2 channels, but I don't quite see how so. What is a decorrelated colour space in the first place?. As I conceive it, CIE Lab is decorrelated means that there's an independance between channels, if for example the value of l* grows bigger, this doesn't necessarly imply that the values of a* or b* increase too, but so is the case in rgb I guess. So, what am I missing?

edit: to be clear this answer describes why Lab can be described as a decorrelated color space. This does not imply that decorrelation is the main benefit of using Lab (see many answers on why Lab is useful)

If you plot all the RGB colors of a standard RGB image of the natural world you will notice something (see below), the values tend to fall on a diagonal line that isn't one of the axes of the color space.

In fact if you know the red and green values of a color in RGB color space you could make a good guess as to the blue color, it would be the blue that makes the point fall near that clustered line. This is because the values are all very correlated, they are good predictors of each other.

As I conceive it, CIE Lab is decorrelated means that there's an independence between channels, if for example the value of l* grows bigger, this doesn't necessary imply that the values of a* or b* increase too, but so is the case in rgb I guess. So, what am I missing

So as you can now see, as the values of one RGB dimension increase, the others are also likely to increase.

As it turns out, that clustered diagonal line running through the RGB cube represents the luminance dimension.

In CIE Lab, that luminance dimension we see in the RGB cube as a diagonal running from (0,0,0) to (1,1,1) has been made into one of the axes of the color space. If you know the a* and b* values of a color you still don't know much about the L value. The CIE Lab dimensions are decorrelated from each other because they don't predict each other. • Thank you for your answer, but I'm still a little bit confused. Say we want to transform an image by performing some operations on each one of its channels independently from the other 2 channels. In this case why do we need the 3 channels to be decorrelated? In my opinion, whether a channel helps me predict the value of the other 2 channels is not really that important. In this particular example how does the decorrelation help in getting a better result? – user2651062 Oct 15 '17 at 19:31
• The utility of Lab isn't that the channels are decorrelated that's more of a side effect. Lab is useful because the dimensions are more meaningful for many operations. If you wish to adjust the luminance of a photo, you can do it in Lab by modifying a single channel. The decorrelation in and of itself can be useful for compression schemes, allowing you to compress the less important dimensions separately, but usually this is not the most important attribute of the color space. – Chandler Oct 16 '17 at 20:31