[argyllcms] Re: inter-instrument matching tables
- From: Gerhard Fuernkranz <nospam456@xxxxxx>
- To: argyllcms@xxxxxxxxxxxxx
- Date: Mon, 14 Nov 2011 02:49:11 +0100
Hi Graeme,
I tried to map artificially corrupted spectral readings to the original ones, using a
simple linear principal component regression in spectral space, and IMO the results seem
quite promising (for one particular "medium" of course, i.e. for one
paper/ink/printer/dpi/halftoning/etc. combination).
"Artificially corrupted" means 1) Argyll FWA applied + 2) convolution with a low-pass
filter kernel in order to simulate a different bandwith of the other instrument + 3) non-linear
distortion along the wavelength axis in order to simulate a bad wavelength calibration of the other
instrument. Eventuelly the "corrupted" readings differed from the original ones by 11dE
avg, 56dE max.
Still a linear PCR in spectral space, using 10...20 principal components, like
% compute correction matrix M
% training set, measured with 2nd instrument
spectral_readings = [
...
];
% same chart measured with 1st (reference) instrument
reference_readings = [
...
];
% number of principal components
num_pc = 15;
[u,s,v] = svd(spectral_readings);
basis = v(:,1:num_pc);
M = basis * ((spectral_readings * basis) \ reference_readings);
% apply correction to spectral readings measured with 2nd instrument
estimated_reference_readings = readings * M;
was able to obtain corrected residual errors of less than 0.05dE avg (and
spectral reflectance residuals of 0.0005% RMS).
[ Not correctable is of course random noise in the measurements. Btw, since the readings
of both instruments are supposed to be noisy, we are dealing with "errors in
variables" here, so eventually total least squares should be preferred to the
ordinary least squares used in the above code snippet. ]
Geometric differences certainly result in different readings. However,the
measurements of a a typical print do not seem to have an effective rank of more
than 15..20, and this rank already includes all effects of the printing
technology and also all effects of the instrument used for the measurements.And
two spectral data sets with a rank of 20 each (measured by two instruments with
possibly two different geometries) can be mapped to each other with a matrix,
which is effectively just a 20x20 matrix. Given say 2000 data points, it should
be well possible to estimate a model with just 20 parameters quite robustly
(note, many RSPLs used to build CLUT profiles have rather hundred to several
hundred effective parameters).
Regards,
Gerhard
Am 13.11.2011 23:37, schrieb Graeme Gill:
Roberto Michelena wrote:
4) make some sort of "Lab-to-Lab" link profile for each instrument to
"match" the master one (DTP-70).
Hi,
I'm not sure how well such a thing would work. It may work OK
for a particular paper, ink & instrument pair, but it's hard to say.
More serous corrections would work on spectral data, and the main
complexity would be the allowance for illuminant differences interacting
with FWA/OBA, where quite complex modeling would be needed (such as
exists in the Argyll FWA compensation). In addition there may
be geometric differences (where the nature of the light direction,
detector direction sensitivity, and the relative sizes of
the illuminated and detected regions differ), and I'm not
sure how these sorts of differences manifest in the actual readings.
Graeme Gill.
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