JPEG: YCrCb <-> RGB conversion precision

Question

I\'ve implemented rgb->ycrcb and ycrcb->rgb conversion using JPEG conversion formulae from
http://www.w3.org/Graphics/JPEG/jfif3.pdf
(the same at: http://en.wikipedia.o

Answer 1

Only about 60% of all RGB values can be represented in YCbCr space when using the same amount of bits for both triplets. This means the most damage happens in RGB->YCbCr when you take a 3*8 bit RGB triplet, convert and round it back to 3*8 bits of precision. The trick is to store the YCbCr triplet at a higher precision until it's time to do forward DCT. There, the data needs to be scaled up anyway, so you can do e.g. 16 bit * 16 bit -> MSB16 multiplies, which are well supported by various SIMD instruction sets.

At the decoder it's the reverse: The results of inverse DCT have to be stored at higher precision until it's time to do the YCbCr->RGB conversion.

This doesn't make the process lossless, but for JPEG, it may buy a few dB of PSNR at the extreme high end of the quality scale, i.e. where the difference can't be seen with a naked eye but can be measured.