7 cube

A Cube or BCC?
But either are well below the 33 size of the LUT, so changing the LUT size will basically do nothing, although as you have seen the larger LUT may be worse as there is more interpolation happening.
Or the increased interpolation could smooth things more, so be a bit better.
Either is equally possible.

Steve

I have misunderstood your question. I have not done any profile, but relied on LUT conversion from one gamut to another one. The relevant LUT conversion depends on the LUT generation size.

Doing a colour space to colour space conversion is totally different.
It performs a mathematical conversion, not at all the same as using a profile.
Any difference in the results will be down to rounding variations in the LUT generation, and as above could go either way.

So what did you mean by 7 Cube?

Steve

the 343 patches I have used to compare the outcomes

Ah - you would need a lot more patches to get a viable comparison.
But as the approach you used is not valid, it is irrelevant.

Steve

So, I have repeated the approach starting from real (synthetic, as being generated with Virtual probe and for the 66 cube case with tricks), profiles.
I have generated profiles on an ST2084 rec2020, and generated a LUT for producing a DCI P3 with an Alternative WP. Then I have used the generated LUT as active LUT and run a 10^ verification.
I am reporting here the dEs for the following cases:
1. 66 vertices LUT:
a) BCC 14^
b) CC 17^ (a) and b) have approximately the same number of patches)
c) CC 33^
d) CC 66^
2. 33 vertices LUT:
a) BCC 14^
b) CC 17^ (a) and b) have approximately the same number of patches)
c) CC 33^
d) CC 66^
Then I have tried something of more realistic: Instead of using as active the generated LUT, I have converted with the LG 33 option and used it as active LUT. With the same verification profile I have verified the following cases:
3. 17^ generated from:
a) 33 vertices LUT converted to 33 LG
b) 66 vertices LUT converted to 33 LG
66^ generated from:
c) 33 vertices LUT converted to 33 LG
d) 66 vertices LUT converted to 33 LG
See here grouped the 1 and 2 cases:

My comments:
1. Using an high number of vertices is beneficial when the profile is not so effective (14 Bcc case and 17 cube case). In the other case the improvement is marginal.
2. 17 ^ profile looks definitely more effective than 14 bcc one.

Here the outcome of 3:

My comments:
1. As for 1 and 2 cases, sing an high number of vertices is beneficial when the profile is not so effective. Otherwise it is marginal.
2. 3.a and 2.b dE numbers are practically the same.

My overall conclusion is: there is an advantage in increasing the number of LUT vertices, but don't expect that a quite perfect LUT will become more perfect.

Sorry, but none of this actually means anything, as all you a are seeing/testing are edge patches that are borderline between the source and destination colour spaces.

And larger patch sets have more borderline patches... While BCC patch sets automatically have fewer.

Unfortunately, there is no valid/useful information here.

Steve

The goal is not comparing Bcc with normal cubes, but measuring the effect of the increase of number of LUT vertices, as the title of the thread suggests

No - that is all part of the same thing.
Having more patches due to larger vertices just changes the number of points that become edge borderline cases.

Steve

For my testing, for the verification part, I am using a 10^3 profile. Should I use a different one?

Would not makes any real difference...
I appreciate and understand what you are trying to do, but using synthetic profiles via the Virtual probe is not doing what you want/think.
You need a real profile with volumetric non-linear issues to gain any benefit/understanding of what using different profile/LUT sizes actually mean.

In simple, terms, a perfect display can be calibrated to any other colour space with just gamma and matrix adjustments.
Using ever larger LUTs or ever larger profiles would do basically nothing.

You will likely see difference if targeting a colour space larger than the display can't actually cover, especially if you use Gamut Mapping.
But that is not a true validation of the calibration accuracy.

The true calibration comparison would be to verify the target colour space WITHIN the actual colour space the display can cover.
And then with a virtual probe the results would be all but identical in all cases.

Steve

Yes, I understand what you mean, and my first thought was using a real profile (or a modified version of the Virtual Probe).
But, it looked to me not practical also for logistical reasons and technical reasons (My Oled is not brilliant in term of Luminosity drifting).
For this reason I have chosen for conversion a challenging synthetic profile:
.
17 cubes gives middling outcomes and I have something good for 33 and 66 cubes.

Modifying a synthetic profile rarely works, as any modifications will likely be noting like the actual issues found with displays with volumetric non-linear issues.
It really just isn't going to be a valid test again.

What you could possibly do is use a LUT generated from an inverse calibration, so the LUT mimics the display's errors, as a 'Virtual LUT' for such tests...

Steve