Equivalence between 3-points DCT and HSV color transform
===

I was looking to perform a color decorrelation on a RGB image. I know that various color spaces present various decorelation power, used notably to perform image compression.

The optimal decorrelation is the KLT transform. The DCT can be a close approximation, and is interesting regarding the computing time of the transform.

A 3-point DCT can then be used to decorrelate the colors of the image, like what is done here : http://www.ipol.im/pub/algo/ys_dct_denoising/ (the *Color Decorrelation* part).

They use an orthonormal basis to perform that 3-point DCT.

When you look at the C++ code, they hardcoded it like that : 

        const float DCTbasis3x3[3][3] = {
	{   0.5773502588272094726562500000000000000000,
	    0.5773502588272094726562500000000000000000,
	    0.5773502588272094726562500000000000000000,     },

	{   0.7071067690849304199218750000000000000000,
	    0.0000000000000000000000000000000000000000,
	   -0.7071067690849304199218750000000000000000, },

	{   0.4082483053207397460937500000000000000000,
	   -0.8164966106414794921875000000000000000000,
	    0.4082483053207397460937500000000000000000      }};

You can also see them in other papers, like that one : http://www.cis.pku.edu.cn/faculty/vision/haopengwei/Papers/ICPR00.pdf (**Comparative Study of Color Transforms for Image Coding and Derivation of Integer Reversible Color Transform** - page 2 )

Those values are related to the values used for the HSV color transform (more specifically the HSI color space)! For example, on this arxiv paper : arxiv.org/ftp/arxiv/papers/1107/1107.4396.pdf, on page 2, you can see the matrix used in the HSI transform.

Does that mean that performing a 3-point DCT transform on a RGB image is the same as performing a RGB2HSI  transform ?
Is there an equivalence between projecting on a 3 vector DCT basis, and 3 vector HSI basis ?