The Quattro Sensor and Luma

Started Jul 18, 2014 | Discussions thread
Joofa Senior Member • Posts: 2,791
Re: Results for a linear model

Mark Scott Abeln wrote:

Joofa wrote:

That is true. However, there are a few nice things about this particular model:

  • The model is linear despite having nonlinear parameters. Therefore, fast, analytic methods can be used for solution.
  • All 'extra' nonlinear parameters were derived from the basic T,M,L parameters. Hence, no new parameters were provisioned.

Here are the model coefficients:

correlation(y,y_calc) = 0.99723

For comparison the following are the coefficients for a model with r,g,b parameters only:

correlation(y, y_calc) = 0.84477

Bigger coefficients in the earlier model may mean more susceptibility to noise, however.

[From your other post]: And since folks often use the Colorchecker target with its 18 colors, this is one place where using as few parameters as possible — which would be 6 independent parameters — will avoid the problem of over-specification, and even in this situation I think this is cutting it close since we are only dealing with 18 colors.

When camera sensitivities are quite different from the 'standard' color matching functions it may be helpful to use extra higher order terms.

If you add more parameters, you can get the correlation to 1. But that would be an example of overfitting data. But we know that we can’t get perfect correlation in principle,

Several issues here as explained below:

  • In the results presented I don't see much overfitting.
  • We are typically dealing with an overdetermined system here. So the number of parameters is typically quite less than the measurements.
  • In this particular model that I used all of the 'extra' parameters were in fact actually derived from the same basic T, M, L curves. This is a significant point. I'm not adding parameters that are derived from variables other than T, M, L.
  • If what you are saying were correct then we can essentially never use polynomial regression, splines, and many other linear, but higher order approximation techniques. However, we know that these techniques are used frequently, with a judicious use of the number and order of parameters.

because the sensor does not measure the same proportions of frequencies of light as does the typical human eye, which is a metamerism problem.

We haven't projected to any typical 3D space yet.

As mentioned elsewhere, there isn’t a good physical or psychological justification for the variables used.

That is not true. Popular undergrad textbook on color science by Billmeyer, Saltzman, and Berns in fact mentions using higher order terms for determining color correction matrices (CCM) from color charts, in a way similar to the model that I used.

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