Hello Ernst, you wrote:
Given successive changes in pigment qualities through time I wonder how it works if say you have several reds in that target that are based on different pigments ranging from the 12th century up to now. They have to be selected as an average of used pigments through time and by that are a compromise again. Would it not be better to make more targets with pigments that represent a certain period in time and/or type of art? Still a rough classification considering the different speeds in adapting new pigments per area. What was ground by Jan van Eyck in 1420 may not have been in use in Russia two centuries later.
As far as my experience goes, the properties of the "ideal" training set are more affected by the properties of sensor and light source than by typical pigments. Sets of spectra that cover large parts of the metamer mismatch regions of a sensor or observer can be found or produced with historic paints as well as with modern colorants (e.g with color formulation systems, printing inks, ...). As soon as there are more than 3 basis colors to be considered, the chances to improve reproduction accuracy by excluding "unrealistic" areas from the metamer mismatch regions decrease dramatically. And at least when we regard paintings, arbitrary mixes of more than 3 basis colors even in one original are quite common. Even if you restrict the basis of your training- and test-sets to just 4 colors (e.g. if you print all test- and training-sets with just one particular CMYK printer), but make use of the whole space spanned by this basis (i.e. if you don't use a fixed separation rule), you will note that there are situations where different CMYK values result in the same response for one of your "observers" (camera or human observer), but in distinct responses for the other observer. As soon as this happens, the mapping between camera and observer space can not be unambiguous anymore. And as soon as there is more than one CMYK value that induces a certain camera or observer response, you can find /an infinite number/ of CMYK values that induce exactly the same response for one of the observers (but different responses for the other one). If you can e.g. print the same shade of gray once with pure black and once with pure CMY, you can find an arbitrary number of CMYK combinations "in between" that also result in the same Lab value, but in different RGB values. The set of spectra that result in the same camera or observer response is the metamer set that induces this response. It is infinite, closed and convex. The projection of the metamer set for a certain camera response onto the observer space is the metamer mismatch region. Also this region is closed and convex. There are several strategies to select patches for the training set: you can e.g. select just one typical representative for each mismatch region (e.g. a CMYK patch with an "average" separation), you can include extrema (e.g. pure CMY and pure K) or you can create separate training sets for different applications (separations). Error-minimizing mappings can benefit from the fact that mismatch regions are often elongated and oriented along a certain axis. Klaus Karcher