Hi, Doug:
Tying to understand how the profile calculations are done. In the first case, does it take the set of 729 input values and compare against the measured values and do some sort of best-fit regression to cover the whole color space.
Argyll's colprof and XRite's I1Profiler use slightly different approaches. With the defaults, I1Profiler tends to do a close fit when the target RGB patches are widely spaced while Colprof does not. I1Profiler profiles tend to be a bit more accurate for small patch counts but a bit less accurate when the patch count gets above about 2000. As to how it generates the "smart patches" I can't say other than I expected them to produce better results than just a larger patch set. A lot of the added patches are near neutrals but the larger patch set I compared the optimized set with produced slightly better color accuracy and materially better near neutral accuracy. Since I1Profiler's optimize pass produces over 300 near neutrals while my generic, large profile only had 134 near neutrals I'm rather shocked that the results weren't better rather than worse.
Then does it keep the original data at this point or tosses them away? If later, then when the next set of 640 patches are added, the subsequent analysis is done with predicted values from the first icc profile (with its inherent error) combined with the new measurements. Is that how it is done? If it is, perhaps this would be the source of a kind of statistical "hysteresis" over the third profile where the all patches were analyzed in one shot.
I1Profiler's optimize pass adds the number of smart patches you enter to the ones from the original set. This test used 729 original patches and in the optimize pass I added 640 additional patches which were about half color and half near neutrals. These are combined and the new profile is created from them.
Basically, what I did was create a profile with the 729 base patch set and a second profile by combining them with the 640 patches. The third profile was made using the generic (not tuned to the printer) patch set which was the 729 set with an additional 512 patches centered in the device rgb cubes as well as 134 near neutral to improve B&W performance. There is a description of this process
here. These produce slightly better profiles relative to their patch size but it isn't huge. Just a bit better.
All the patches for the three targets were combined, duplicates removed, and additional, independent patches added to create a set of 3, 957 count target pages. The accuracy results were done using only the independent patches since comparing accuracy using the same patches that profiles are created from is very misleading. Profiles that match the values from which they were created are not only unreliable, but they can actually invert things. A solid way to measure accuracy is to print a different set of patches using absolute intent, measure them and compare the measured results.
My approach here is a bit different and provides a way to measure profile accuracy for both colors and near neutrals for a large number of patch sets with the same, independent set of RGB values. That same measured set can then be used doing a reverse lookup. That is finding the Lab values that produce the exact RGB device values for each profile. This would be the same as if one had those Lab values in an image and printed them using Abs. Intent and measured them then produced a dE 2000 difference.