The Quattro Sensor and Luma

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

Eric Fossum wrote:

Reminds me of the old saying, give me 6 parameters and I can fit an elephant, and 2 more and I can make him eat peanuts.

Or, something like that. Anyway, no doubt one can fit practically anything given enough parameters, esp. non-linear ones. One has to ask then about sensitivity to variability and of course noise, or YSNR, to be exact. I suppose it depends on the fitting parameters.

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:

r = 4.07161
g = -7.55536
b = -0.22193
r^2 = -2.91354
g^2 = 5.67019
b^2 = 0.38947
r*g = 1.31829
r*b = 0.44178
g*b = 3.84469

sqrt(SSE) = || y-y_calc || = 0.15818

correlation(y,y_calc) = 0.99723

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

r = -0.26851
g = 1.31593
b = -0.27386

|| y - y_calc || = 1.1371

correlation(y, y_calc) = 0.84477

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

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