The Quattro Sensor and Luma

Started Jul 18, 2014 | Discussions thread
Mark S Abeln
Mark S Abeln Forum Pro • Posts: 20,341
Re: Results for a linear model

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.

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

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

At best we can hope for is to derive the best model of the underlying phenomena that we can, as well as a good measure of error for the model.

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