[argyllcms] Re: noise and gamut, input profiles with B2A table
From: Graeme Gill <graeme@xxxxxxxxxxxxx>
To: argyllcms@xxxxxxxxxxxxx
Date: Mon, 05 May 2008 13:04:28 +1000
Hello Gerhard,
Graeme, that's actually a good point. I was aready wondering the same
too for a while. Basically we're dealing with a measurement error model
(errors-in-variables (EIV) model) here, since neither the CIE nor the
RGB numbers are error-free, but both are measured numbers and thus
contain measurement errors. My understanding is that usually rather
methods based on total (orthogonal) least squares are used in such a
case.
Yes, this seem logical. I was thinking that it would be possible
with some work, to come up with a generalized estimate of
typical errors by doing some repeatability tests on a range of
devices, although figuring out systematic errors such as quantization
of device values within screening algorithms may take some thought.
The idea was really to come up with a generalized weighting
model to apply to test points. Perhaps it could be used to weigh
input and output error estimates separately as well.
It's a lot of work though, and particular devices may not match a generalized
model that well.
I've no idea though, whether it would be easily possible to adapt
RSPL so that it minimizes the orthogonal error between fitted curve and
the data points, instead of minimizing the error of the dependent
variable only.
I think it comes down to how the smoothness is evaluated with the algorithm.
Currently it is evaluated as the discrepancy in the Y value between
a grid value and the straight line formed from it's neighbors, so (intuitively)
I would imagine that changing this to be a discrepancy in the orthogonal
distance to the straight line would be the type of thing needed.
I did play with something very like this at one point, in an attempt to
create a version of RSPL that was symmetrical with respect to
how smoothness affected the result (ie. that reversing the X,Y
values of the scattered data would result in a smoothed curve that is
a 45 degree reflection), but it complicates the maths a great deal,
and I ended up with an algorithm that needed another layer of
iteration to make it tractable, and worse, it was unstable.
Now maybe these issues could be solved, but that's where I got
to with one attempt!
And yes, if we assume that the CIE measurement errors are
negligibly small compared to the RGB errors, then this leads to the
approach to do the fitting the other way round, i.e. treat the CIE
numbers as independent and the RGB numbers as dependent variable. But
I'm not sure, whether the assumption of negligible CIE measurement
errors is granted either, particularly for batch average targets, which
are not individually measured.
You're probably right, typical IT8 charts are pretty loose with regard
to how well they match the batch averages. I'd imagine though that
there could be a fair amount of noise in the dark values from a typical
cheap scanner, plus the larger errors from the instrument making the
reference measurements, so the errors will probably
multiply at the dark end.
In contrast, a CMYK printer will tend to have the largest device value
uncertainty near white (where small, hard to control tints are being
applied to the paper), while the CIE reading errors will tend to be
largest near the dark end, where less light is being reflected from the
sample.
Thanks for your insightful comments.
Graeme Gill.
