# Defining the PSNR for images in CIE-LUV or CIE-XYZ or CIE-HCL spaces

In image compression applications, we know that for an 8-bit 0 to 255 level grayscale image the PSNR (peak signal to noise ratio) can be defined through the MSE as:

$$MSE=\frac{1}{mn}{\displaystyle \sum_{i=1}^{m-1}\sum_{j=0}^{n-1}[I(i,j)-K(i,j)]^{2}}$$

$$PSNR=10*log_{10}(\frac{MAX_{I}^{2}}{MSE}) =20*log_{10}(\frac{MAX_{I}}{\sqrt{MSE}})$$

where I is the original 2D image and K is the reconstructed image (decompressed). Typically, we have $$MAX_I=255$$. My question is how does one define PSNR (or even SNR for that matter) in the CIE-LUV or CIE-XYZ or CIE-HCL spaces?

• You question is already answered here: Defining the SNR or PSNR for color images Oct 9, 2023 at 9:03
• Thanks! According to that document, it appears that in LUV space, we use the color difference by looking at the Eucliden distance between the two images. Is it not the case that L will dominate, or do we scale the spaces by the maximum ranges? I also found this work on Visual Information Fidelity that I had not seen before. It works on images. Oct 9, 2023 at 13:23