Hi Harry, in a theoretic world, if the density of a cube does not match the density of the measurement, other factor will came in play to see if make a denser cube will make sense in order to have the maximum precision allowed by your device display.
If you like a bit of technicality behind it...
One of the way to look at it, is the interpolation error of the LUT itself when applied to another image or LUT transformations: if the point you want to transform is indeed coincident with one of the original lattice you have a 100% precision, if you are in the middle of the lattice cube you have the minimum precision and the order of the error can be visible: this depend upon few factors: the lut distorsion, the precision in measurements, the clamping, the way a LUT is applied to a picture (usually a theathedrical, pyramidal or a trilinear math): the statistical delta from the book (colors appearance models) of a 17x17x17 equally spaced respect the real value can be in the order of 5% in the worst case scenario.
To give you an example, imagine in the diagonal of LightSpace CMS cube where it lies the greyscale representation: 17 diagonals point will represent it. Regardless in how much precision in the measurement you place there, only 17 points will be your reference. In your case, only 5 point will be. pretty much all the LUT interpolations make linear math, so if you look at your 5x5x5 is a 4 segment line. How a SCurve is represented then? poorly.
So, a LUT helps, a lot, but it is not a 100% precise model. the bigger is the density of the lattice the better accuracy you get. up o the point that some fo the samples (in the blacks) can be smaller that the tool you use to measure the sample itself making the process even more silly....
A 5x5x5 cube will have only a certain precision in display a transformation but the measurement that we do with LightSpace CMS has more than enough for most of the representation as Steve showed in the above link.
you can have two way to approach a 5x5x5 matrices: either you measure only that, or you measure a denser cube and scale that down to 5x5x5. As long as the point that you try to measure is NOT an inbetween of the measured lattice you are OK. luckily, a 17x17x17 (vertices) cube, represent a 16 single side cubes lattice and a 5x5x5 (vertices) cube represent a 4 single side cubes: the point of the 5x5x5 are indeed exactly represented in the model.
A 10x10x10 (vertices) represent a 9x9x9 single cubes per side and that will NOT be coincident to your 5x5x5 models, so you will have a faster measurement but on top of the imprecision of a lesser dense cube you will find an interpolation error in order to make your cube: the worst case shows up in a odd-by-one scenario: devices that support 16x16x16 will have only two point perfectly represented in the original lattice and all the other are inbetween with the bulk of the interpolated ones smack right in the middle of the color space you want to represent.
I will check with Steve if we can make a case where only a 5x5x5 can be measured to speed up the process.
-Walter |