psyphy (version 0.3)

SS.RGBcalib: Self-Start Functions for Fitting Luminance vs Grey Level Relation on CRT displays

Description

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.

Usage

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

Value

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

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

Author

Kenneth Knoblauch

Details

The model $$ Lum(GL) = Blev + \beta_i * GL^\gamma $$ 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.

References

~put references to the literature/web site here ~

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)