Hi David,
David Neary wrote:
I'll conduct some tests some time and try and figure out just how bad these quantisation errors could be.
Great - quantitative data will really help.
I've done some testing - I wrote a little program that puts every possible 8-bit RGB colour through an lcms transform. A frequency table is kept of every colour that comes out the other side, which gives us some idea of how many codes are "lost" - how badly the dynamic range is reduced.
First, as a control subject, I analyzed the gamma function at 1.1 and 0.6. The results are as follows:
Gamma 1.1 Code use tally: 00: 1707993 01: 13481272 02: 1529388 03: 0 04: 57834 05: 0 06: 0 07: 0 08: 729 09: 0
In other words, 13,481,272 colours are mapped with a 1:1 ratio, so can be transformed back again without loss. 1,707,993 colours are missing from the destination set, and just under 1,600,000 colours are arrived at from multiple source colours.
Gamma 0.6 Code use tally: 00: 7647887 01: 4251528 02: 3700404 03: 0 04: 1073574 05: 0 06: 0 07: 0 08: 103823 09: 0
Gamma 0.6 is considerably more destructive, only 1/4 of the codes maintain a 1:1 mapping.
Now for AdobeRGB <-> sRGB:
sRGB -> AdobeRGB1988 Code use tally: 00: 8102616 01: 4172676 02: 3175714 03: 438068 04: 538838 05: 66267 06: 124002 07: 23117 08: 48831 09: 87087
AdobeRGB1988 -> sRGB Code use tally: 00: 8012181 01: 8325155 02: 156167 03: 54498 04: 10468 05: 58725 06: 15054 07: 2108 08: 2129 09: 140731
This isn't as bad as I'd feared, but still considerably worse than either of the gamma tests.
In both cases nearly half the codes in 8-bit RGB space are lost!
This in effect reduced 24-bit RGB to 23-bit RGB. As I said, this isn't as bad as I'd feared - I was expecting to see a loss of nearly 1-bit per channel; in fact we lose only approximately 1-bit over the whole image.
If anyone's curious enough to want the source of my test program, just ask :)
All the best, -- Alastair M. Robinson
