# What is the name of this color transformation?

This is a question regarding color transformation in images. I have this color transformation matrix I am using to convert an RGB image to a color space whose name I do not know:

T = [(1/3) (1/3) (1/3); (1/2) 0 (-1/2); (-1/2) 1 (-1/2)]


What is the name of this color transform? I think I once saw somewhere that it is called KL transform because it was close to a KLT computed over a large collection of images, but I am not sure...

## 2 Answers

I do not know the name of your transformation $T$, but it can't be the Karhunen-Loeve transform: The Karhunen-Loeve transform is image specific and its transformation matrix is a rotation matrix (see for example the KLT in Mathematica).

Given the values in your matrix, it seems to attempt to separate between intensity (first row) and color (the other two rows, spanning the remaining hyperplane) while being optimized for speed.

• Yes, I agree with you regarding that this is not the KLT itself, but as I said I once saw that they referred to it as such in a paper. I thought that the last two rows give rise to an opponent color model (R-B and 2G-R-B). – smichak Feb 28 '12 at 8:21

Just found the paper that referred to this transformation:

Y.I. Ohta, T. Kanade, T. Sakai. Color information for region segmentation, Comput. graphics Image Process. 13 (1980) 222—241.

It is indeed called the K-L space as it is an static approximation of the (dynamic) image specific KLT calculated over a large set of images. The main reason is that the eigenvectors remain approximately the same for a large set of natural color images.