SS.RGBcalib function

Self-Start Functions for Fitting Luminance vs Grey Level Relation on CRT displays

This selfStart model evaluates the parameters for describing the luminance vs grey level relation of the R, G and B guns of a CRT-like display, fitting a single exponent, gamma, for each of the 3 guns. It has an initial attribute that will evaluate initial estimates of the parameters, Blev, Br, Bg, Bb and gamm. In the case of fitting data from a single gun or for a combination of guns, as in the sum of the three for calibrating the white, the parameter k is used for the coefficient. Both functions include gradient and hessian attributes.

SS.calib(Blev, k, gamm, GL)
SS.RGBcalib(Blev, Br, Bg, Bb, gamm, Rgun, Ggun, Bgun)

Arguments

• Blev: numeric. The black level is the luminance at the 0 grey level
• k: numeric, coefficient of one gun for fitting single gun
• Br: numeric, coefficient of the R gun
• Bg: numeric, coefficient of the G gun
• Bb: numeric, coefficient of the B gun
• gamm: numeric, the exponent, gamma, applied to the grey level
• GL: numeric, is the grey level for the gun tested, covariate in model matrix in one gun case
• Rgun: numeric, is a covariate in the model matrix that indicates the grey level for the R gun. See the example below.
• Ggun: numeric, is a covariate in the model matrix that indicates the grey level for the G gun
• Bgun: numeric, is a covariate in the model matrix that indicates the grey level for the B gun

Details

The model

where i is in {R, G, B}, usually provides a reasonable description of the change in luminance of a display gun with grey level, GL. This selfStart

function estimates $\gamma$ and the other parameters using the nls function. It is assumed that grey level is normalized to the interval [0, 1]. This results in lower correlation between the linear coefficients of the guns, $\beta_i$ , than if the actual bit-level is used, e.g., [0, 255], for an 8-bit graphics card (see the example). Also, with this normalization of the data, the coefficients, $\beta_i$, provide estimates of the maximum luminance for each gun. The need for the arguments Rgun, Ggun and Bgun is really a kludge in order to add gradient and hessian information to the model.

Returns

returns a numeric vector giving the estimated luminance given the parameters passed as arguments and a gradient matrix and a hessian array as attributes.

References

~put references to the literature/web site here ~

Author(s)

Kenneth Knoblauch

See Also

nls

Examples

data(RGB)

#Fitting a single gun
W.nls <- nls(Lum ~ SS.calib(Blev, k, gamm, GL), data = RGB,
                                subset = (Gun == "W"))
summary(W.nls)

#curvature (parameter effect) is greater when GL is 0:255
Wc.nls <- nls(Lum ~ SS.calib(Blev, k, gamm, GL*255), data = RGB,
                                subset = (Gun == "W"))
MASS::rms.curv(W.nls)
MASS::rms.curv(Wc.nls)
pairs(profile(Wc.nls), absVal = FALSE)
pairs(profile(W.nls), absVal = FALSE)

#Fitting 3 guns with independent gamma's                
RGB0.nls <- nlme::nlsList(Lum ~ SS.calib(Blev, k, gamm, GL) | Gun,
                data = subset(RGB, Gun != "W"))
summary(RGB0.nls)
plot(nlme::intervals(RGB0.nls))

# Add covariates to data.frame for R, G and B grey levels
gg <- model.matrix(~-1 + Gun/GL, RGB)[ , c(5:7)]
RGB$Rgun <- gg[, 1]
RGB$Ggun <- gg[, 2]
RGB$Bgun <- gg[, 3]
RGB.nls <- nls(Lum ~ SS.RGBcalib(Blev, Br, Bg, Bb, gamm, Rgun, Ggun, Bgun), 
                                      data = RGB, subset = (Gun != "W") )
summary(RGB.nls)
confint(RGB.nls)