[argyllcms] Re: Version 0.53 - Gamut mapping warning message.

> --- Ursprüngliche Nachricht ---
> Von: Roger Breton <graxx@xxxxxxxxxxxx>
> An: argyllcms@xxxxxxxxxxxxx
> Betreff: [argyllcms] Re: Version 0.53 - Gamut mapping warning message.
> Datum: Sat, 17 Dec 2005 21:55:22 -0500
> 
> My hypothesis is that there is a relationship between the "linearity" or

Roger, no doubt, there is. But I think the main reason is, that nobody
is willing to print and measure a "reasonable" number of patches (say
100000..1000000), which might be required to sample the behaviour of
a "non-well-behaved" device accurately enough. For instance, the ECI
chart has less than 1500 patches - and this is really *not much*.
Since CMYK is 4-dimensional, 1500 samples are on average just approx
6.2 samples per dimension, or only 5.2 intervals per dimension (!).

If you do a non-parametric regression (that's what Argyll does, when
CLUT profiles are created), then what other characteristics but a
smooth curve would you assume between these *very sparsely* sampled
points? But the smoothness assumption can be only fulfilled by a
well-linearized device.

Unfortunately, in order to double the sampling resolution for each
dimension, you need to use 16 times as many patches (i.e. 2^4). And
for instance 25 samples per dimension would require 390625 patches.

Only a more sophisticated parametric device model (with a rather
low number of parameters) would make a parametric regression possible,
requiring less data points. But then you need to have the a priori
knowledge, that the given device does follow the chosen model
(e.g. matrix + gamma, gain, offset is known to be able to model CRT
monitors reasonably well). Thus, for a device with completely unknown
characteristics, this is rather not an option either.

> good behavior or mononicity

Non-monotonicty is IMO a different issue and does not only apply
to badly-behaved devices. Even for a well linearized CMYK-printer,
IMO monotonicity isn'n granted in general. E.g. CMYK(0,0,20,0) is
darker than CMYK(0,0,0,0), but CMYK(0,0,20,100) is usually rather
brighter then CMYK(0,0,0,100), which implies non-monotonicity; i.e.
in some regions of the gamut the gradient dL/dY (where L=lightness
and Y=yellow) is positive, and in other regions it is negative.

> of a device and it profilability,

Regards,
Gerhard

-- 
Gerhard Fuernkranz
nospam456@xxxxxx

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