[argyllcms] interpolation reversibility

  • From: Roberto Michelena <colorsync@xxxxxxxxx>
  • To: argyllcms@xxxxxxxxxxxxx
  • Date: Fri, 4 Nov 2005 09:23:56 -0500


Let me ask this which has been floating on my mind for some time:
When you do a reverse interpolation (as in your -G option), will it be
100% coincident with it's corresponding forward one? In other words,
Lab->CMYK->L'a'b will result in perfect match between Lab and L'a'b
when both are made from the same table (A2B), using the reverse
mapping method as in "-G" option?

To put it in perspective (why is it important):

Take a pair of devices and their measurements, e.g. Press and Proofer.
You get two profiles, ICCPress and ICCProof with also contain the
measurements (albeit smoothed) in their A2B tables.
Make a link via standard method, abscol; ICCLink1
Make a link via -G method, abscol; ICCLink2

process a set of arbitrary CMYKpress source values through ICCLink1
and you get CMYKproof1
process the same set through ICCLink2 and you get CMYKproof2

Now process CMYKProof1 through ICCProof A2B and you get LabProof1
Do the same with CMYKProof2 and you get LabProof2

Process CMYKpress through ICCPress A2B and you get LabPress

comparing LabProof1 to LabPress, and LabProof2 to LabPress, should
yield a closer match for LabProof2, right? this would indicate the
reverse interpolation (-G) is more precise than the double
interpolation incurred when building B2A and then linking to it.
(it'd be interesting to see this numbers!)

The question is, will LabProof2 be an exact match to LabPress? in
other words, the reverse interpolation is mathematically coincident
with the forward one?

Because if not, the link created by -G (ICCLink2) could still be
improved by pure mathematical iteration (function to optimize:
deviation from LabPress) without the need of reprinting targets.

I mean, we are always assuming (and I believe it's a fine assumption)
that the prediction of LabPress and LabProof given by interpolation on
their respective A2B tables is the most exact tool we have. Not that
it's exact, but it is more accurate than all other tables and
interpolations we use. So if we make these match in a link, that link
would be as accurate as one can get without further printing, right?

-- Roberto Michelena

Other related posts: