# [argyllcms] Re: Absolute minimum number of patches for a matrix/TRC monitor profile

• From: Gerhard Fuernkranz <nospam456@xxxxxx>
• To: argyllcms@xxxxxxxxxxxxx
• Date: Fri, 05 Feb 2010 11:09:04 +0100

```Graeme Gill wrote:
> Gerhard Fuernkranz wrote:
>> Shouldn't four suffice? The three primaries should be enough to
>> determine the matrix and also the WP, and additionally e.g. a middle
>> gray for finding the gamma.
>
> As I understand it you need RGB + W to determine the matrix, as RGB on
> their own don't set the channel scale factors
> (see icc/icc.c icmRGBprim2matrix()).

Well, an additive matrix model is XYZ = RGB * M, and solving for M
requires only 3 linearly independent (RGB,XZY) pairs. You need the
"complete" XYZ of the primaries though (including their luminance, and
not just the chromaticity). But measurements include the luminance
anyway. And white is just the sum of the XYZ of the primaries, so it can
be computed from the primaries [although of course in practice, displays
may not be aware of this rule and the measured primaries may not sum up
exactly to the measured white. Still, if the measured white isn't
reasonably close to the sum, one's alarm bells should ring.].

> If it's a pure Gamma curve then perhaps you only need one gray patch
> to set that, although adding black gives a more
> complete picture of the device, and makes it safer if the model has an
> offset component (as the shaper type profile might).

Sure, for more robustness and in order to account for random errors in
the measurements we can never have enough patches, and more patches will
eventually also enable us to use a model with more degrees of freedom.
The basic assumption is certainly that the device follows the chosen
model well enough. If this is not a case, then the model may fit pretty
well (if not exactly) at the few measured "anchor points", while the
prediction errors in other regions may still be high. If we can't live
with the result, then we need to switch to a more appropriate model,
with more degrees of freedom, but then in turn the minimum number of
required patches for estimating the model will increase as well...

[ Btw, actually a matrix + single gamma model is already overdetermined
by primaries + middle gray, and IMO one could even derive matrix +
triple-gamma from these four points. ]

Regards,
Gerhard

```
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