Derivation of Kb, Kr for YCbCr systems - AVS Forum
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post #1 of 20 Old 04-01-2012, 05:30 AM - Thread Starter
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How are the parameters Kb and Kr derived? They're defined for both Rec.601 and Rec.709 but how were they arrived at? I haven't found any papers or links that discuss it. Anyone know, or know where to find it?
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post #2 of 20 Old 04-01-2012, 08:48 AM
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http://en.wikipedia.org/wiki/YCbCr

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post #3 of 20 Old 04-01-2012, 10:35 AM - Thread Starter
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I don't see anything on that page that lists how the numbers are arrived at. It just says what they are for Rec.601 and Rec.709. Note that I'm looking for Kb and Kr, not Cb and Cr
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post #4 of 20 Old 04-01-2012, 11:07 AM
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Are you asking how the defined constants for both 601 and 709 came about in the ITU-R Recommendation? There was a document I read one time that discussed how they arrived at that but remembering where may be difficult. I'm not even sure why it matters though...

Have you searched the documents at the itu website? http://www.itu.int/rec/R-REC-BT/en

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post #5 of 20 Old 04-01-2012, 11:18 AM - Thread Starter
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Quote:
Originally Posted by turbe View Post

Are you asking how the defined constants for both 601 and 709 came about in the ITU-R Recommendation? There was a document I read one time that discussed how they arrived at that but remembering where may be difficult. I'm not even sure why it matters though...

Have you searched the documents at the itu website? http://www.itu.int/rec/R-REC-BT/en

That's exactly what I'm asking. If you could remember where you read it, I'd be infinitely thankful. I've Google searched over the website, but haven't found anything promising.
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post #6 of 20 Old 04-01-2012, 11:23 AM
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I vaguely remember reading about that on microsoft's development network sites, it's been some time.. I believe it was when working on a project converting in and out of RGB... I suggest you try searching for those conversion documents. also try using the terms 'luma coefficients' with your search... good luck...

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post #7 of 20 Old 04-01-2012, 01:32 PM
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Poynton's book, Digital Video and HD: Algorithms and Interfaces, may be what you are looking for

here's an related excerpt/page from the book:
http://books.google.com/books?id=dSC...cients&f=false

For 709's, see page 369

Also see:
HERE and HERE

Hope that helps...

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post #8 of 20 Old 04-03-2012, 10:22 AM - Thread Starter
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Unfortunately there's nothing in there about how to get Kb and Kr yourself...
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post #9 of 20 Old 04-04-2012, 02:58 AM
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Try this link into the Poynton book.

http://books.google.com/books?id=dSC...cients&f=false

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post #10 of 20 Old 04-04-2012, 08:34 AM
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Quote:
Originally Posted by ams2990 View Post

Unfortunately there's nothing in there about how to get Kb and Kr yourself...

Why would you need to?

Are you inventing your own new standard?

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No, but I am doing research on the mathematics of colorimetry for my Master's. Kb and Kr are some of the few values that I haven't figured out how to re-derive.
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post #12 of 20 Old 04-04-2012, 03:00 PM
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I believe the values are somewhat arbitrary depending on how you want to allocate the bits for red/green/blue reproduction, shifting the values around give more/less bits to represent each channel.

For rec.601 they appear to be somewhat arbitrary.
For rec.709 they use the normalized Y values for the Red and Blue primaries, which in theory should provide a equal distribution of bits.

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post #13 of 20 Old 04-04-2012, 04:14 PM
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Quote:
Originally Posted by sotti View Post

I believe the values are somewhat arbitrary depending on how you want to allocate the bits for red/green/blue reproduction, shifting the values around give more/less bits to represent each channel.

For rec.601 they appear to be somewhat arbitrary.
For rec.709 they use the normalized Y values for the Red and Blue primaries, which in theory should provide a equal distribution of bits.

The rec.601 coefficients are not arbitrary. If they were arbitrary, why use 0.299 and not just 0.3?

They are calculated the same way as rec.709. They're both calculated from the reference primaries and the reference white chromaticities.

The calculation in the Poynton link I gave above is from SMTPE RP177-1993.

However, they certainly could be arbitrary. The only reason to have precise values is to make the black and white version of the image accurate. But backwards compatibility to black and white TV's is not much concern today.

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post #14 of 20 Old 04-04-2012, 04:43 PM
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Quote:
Originally Posted by dr1394 View Post

The rec.601 coefficients are not arbitrary. If they were arbitrary, why use 0.299 and not just 0.3?

They are calculated the same way as rec.709. They're both calculated from the reference primaries and the reference white chromaticities.

The calculation in the Poynton link I gave above is from SMTPE RP177-1993.

However, they certainly could be arbitrary. The only reason to have precise values is to make the black and white version of the image accurate. But backwards compatibility to black and white TV's is not much concern today.

Ron

That could be the difference between rec.709 and rec.601 then, because they are pretty significantly different.

the Kb of 0.114 would be an extremely bright blue which given the chromacity of the SMTPE-C primaries doesn't jive with a D65 white point. But that may be the appropriate value for getting black and white compatibility right.

Where in rec.709 using the actual linear Yn components gives better bit distribution.

Arbitraty may have been to strong a word.

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post #15 of 20 Old 04-04-2012, 05:08 PM
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Quote:
Originally Posted by sotti View Post

That could be the difference between rec.709 and rec.601 then, because they are pretty significantly different.

the Kb of 0.114 would be an extremely bright blue which given the chromacity of the SMTPE-C primaries doesn't jive with a D65 white point. But that may be the appropriate value for getting black and white compatibility right.

Where in rec.709 using the actual linear Yn components gives better bit distribution.

Arbitrary may have been to strong a word.

Be aware that the luma coefficients in rec.601 are not based on the SMPTE-C primaries. They are actually based on the NTSC 1953 primaries and white point.

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post #16 of 20 Old 04-04-2012, 06:09 PM
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Quote:
Originally Posted by dr1394 View Post

Be aware that the luma coefficients in rec.601 are not based on the SMPTE-C primaries. They are actually based on the NTSC 1953 primaries and white point.

Ron

Ahhhhh, well that would make a huge difference then. Good point.

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post #17 of 20 Old 04-04-2012, 08:29 PM
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The mismatch between the luma coefficients and primaries in rec.601 is part of the reason that Poynton was against changing the luma coefficients in rec.709. If you don't care about black and white fidelity (and we already don't in rec.601), then the rec.601 coefficients are just as good as the rec.709 coefficients for transforming between RGB and YCbCr.

Even "arbitrary" coefficients (like Kr = 0.3, Kb = 0.1) would work fine. In fact, this was done in the new YCgCo color space where Kr = Kb = 0.25 (when luma and chroma bit depths are equal). Here's a paper on YCgCo:

http://escher.elis.ugent.be/publ/Edocs/DOC/P105_213.pdf

But rec.709 was built from scratch, so the luma coefficients are "theoretically" correct.

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post #18 of 20 Old 04-04-2012, 08:59 PM
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Another paper on YCgCo with the coding gains of different luma coefficients. Note that rec.601 is slightly better than rec.709.

http://wftp3.itu.int/av-arch/jvt-sit...o/JVT-I014.doc

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post #19 of 20 Old 04-04-2012, 09:00 PM
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Quote:
Originally Posted by dr1394 View Post

Be aware that the luma coefficients in rec.601 are not based on the SMPTE-C primaries. They are actually based on the NTSC 1953 primaries and white point.

Ron

yes, that's clear in the posts linked above

he needs to let us know what is known..

1 = Kr + Kg + Kb (709: Kr = 1 - (.7152 + .0722) - 601: Kr = 1 - (0.5864 + 0.1146))


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The coefficients in the luma equation are based upon the sensitivity of human vision to each of the RGB primaries standardized for coding

i.e. if he has xyY, he needs to convert to XYZ first (Y=1 of course)

if he is asking about the % of R G B in regards to the last quote above, I look forward to his dissertation posted publicly.

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post #20 of 20 Old 04-05-2012, 05:03 AM - Thread Starter
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Quote:
Originally Posted by turbe View Post

I look forward to his dissertation posted publicly.

Only a Master's, unfortunately, not a Ph.D., so you'll have to wait a few more years to get your hands on a dissertation with my name on it.

Also, I got my hands on a copy of SMTPE RP177, which contains all of the information required to re-derive the YCbCr conversion equations. Thanks dr1394 for pointing me in the right direction!
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