RNLmodel {colourvision}

Receptor Noise Limited Models (Vorobyev & Osorio 1998)

Description

Receptor noise limited colour vision models (Vorobyev & Osorio 1998; Vorobyev et al. 1998) extended to any number of photoreceptor types.

Usage

RNLmodel(model = c("linear", "log"), photo=ncol(C)-1,
         R1, R2=Rb, Rb, I, C,
         noise = FALSE, v=NA, n=NA, e=NA,
         interpolate = TRUE, nm = seq(300, 700, 1),
         coord="colourvision")

Arguments

model

Linear ("linear"; Vorobyev & Osorio, 1998), or log-linear ("log"; Vorobyev et al. 1998) RNLmodel version. model="log" is preferred.

model="linear" can be used only if comparison is to be made between two very similar colours.

photo

Number of photoreceptor types. Model accepts any number of photoreceptor types (>=2). For instance, dichromatic: photo=2; trichromatic: photo=3; tetrachromatic: photo=4, etc. Default gets number of photoreceptor types from C argument.

R1

Reflectance of observed objects. A data frame with first column corresponding to wavelength values and following columns with reflectance values. R1 must be in the same scale as R2 and Rb(percentage or proportion).

R2

Reflectance to be compared against R1. R2=Rb if comparison is to be made against the background. A data frame with two columns only: first column corresponding to wavelength values and second column with reflectance values. R2 must be in the same scale as R1 and Rb(percentage or proportion).

Rb

Background reflectance. A data frame with two columns only: first column corresponding to wavelength values and second column with reflectance values. Rb must be in the same scale as R1 and R2 (percentage or proportion).

I

Irradiance spectrum. A data frame with two columns only: first column corresponding to wavelength values and second column with irradiance values. Irradiance values must be in quantum flux units.

C

Photoreceptor sensitivity curves, from lowest to longest lambda-max. A data frame: first column corresponding to wavelength values and following columns with photoreceptor sensitivity values (see function photor).

noise

Logical. Whether receptor noise is provided (noise = TRUE) or calculated from photoreceptor relative abundances (noise = FALSE).

e

Receptor noise of each photoreceptor type. Used when noise = TRUE

n

Relative number of each photoreceptor type in the retina. Usually increases with lambda-max. Used to calculate e when noise = FALSE.

v

Noise-to-signal ratio of a single photoreceptor. Used to calculate e when noise = FALSE.

interpolate

Whether data files should be interpolated before further calculations. See approx.

nm

A sequence of numeric values specifying where interpolation is to take place. See approx.

coord

Whether colour locous coordinates should be calculated by the method (coord="colourvision") by Gawryszewski (2018), or by alternative (coord="alternative"; available for 2-4 photoreceptor types only) methods (Hempel de Ibarra et al. 2001; Renoult et al. 2017).

Details

The receptor noise limited model was originally developed to calculate \Delta S between two reflectance curves directly, without finding colour locus coordinates (e.g. x,y; Vorobyev and Osorio 1998). This function uses later formulae to find colour loci in a chromaticity diagram (similarly to Hempel de Ibarra et al. 2001; Renoult et al. 2015).

In lack of a direct measurement, receptor noise (e_i) can be estimated by the relative abundance of photoreceptor types in the retina, and a measurement of a single photoreceptor noise-to-signal ratio:

e_i=\frac{\nu}{\sqrt{\eta _i}}

where \nu is the noise-to-signal ratio of a single photoreceptor, and \eta is the relative abundance of photoreceptor i in the retina. Alternatively, noise may be dependent of the intensity, but this possibility is not implement in colourvision yet. Noise dependent of intensity usually holds for low light conditions only (Vorobyev et al. 1998).

Value

ei

Noise of photoreceptor channels.

Qri_R1

Photoreceptor photon catch values from R1, after the von Kries transformation (see function Qr).

Qri_R2

Photoreceptor photon catch values from R2, after the von Kries transformation (see function Qr).

Ei_R1

Photoreceptor outputs from the stimulus (R1)

Ei_R2

Photoreceptor outputs from R2

Xi_R1

Coordinates in the colour space for R1

Xi_R2

Coordinates in the colour space for R2. Equals zero when R1=Rb

deltaS

Euclidean distance from R1 to R2. It represents the conspicuousness of the stimulus (R1) in relation to the background when R1=Rb.

Author(s)

Felipe M. Gawryszewski [e-mail]

References

Gawryszewski, F.M. 2018. Colour vision models: Some simulations, a general n-dimensional model, and the colourvision R package. Ecology and Evolution, 10.1002/ece3.4288.

Hempel de Ibarra, N., M. Giurfa, and M. Vorobyev. 2001. Detection of coloured patterns by honeybees through chromatic and achromatic cues. J Comp Physiol A 187:215-224.

Renoult, J. P., A. Kelber, and H. M. Schaefer. 2017. Colour spaces in ecology and evolutionary biology. Biol Rev Camb Philos Soc, doi: 10.1111/brv.12230

Vorobyev, M., and D. Osorio. 1998. Receptor noise as a determinant of colour thresholds. Proceedings of the Royal Society B 265:351-358.

Vorobyev, M., D. Osorio, A. T. D. Bennett, N. J. Marshall, and I. C. Cuthill. 1998. Tetrachromacy, oil droplets and bird plumage colours. J Comp Physiol A 183:621-633.

See Also

photor, RNLthres, CTTKmodel, EMmodel, GENmodel

Examples

#1
## Photoreceptor sensitivity spectra
##with lambda max at 350nm, 450nm and 550nm:
C<-photor(lambda.max=c(350,450,550))

##Grey background
##with 7 percent reflectance from 300 to 700nm:
Rb <- data.frame(300:700, rep(7, length(300:700)))

## Read CIE D65 standard illuminant:
data("D65")

##Reflectance data of R1 and R2
R1.1<-logistic(x=seq(300,700,1), x0=500, L=50, k=0.04)
R1.2<-logistic(x=seq(300,700,1), x0=400, L=50, k=0.04)
w<-R1.1[,1]
R1.1<-R1.1[,2]+10
R1.2<-R1.2[,2]+10
R1<-data.frame(w=w, R1.1=R1.1, R1.2=R1.2)

R2<-logistic(x=seq(300,700,1), x0=550, L=50, k=0.04)
R2[,2]<-R2[,2]+10

## Run model 
model<-RNLmodel(photo=3, model="log",
       R1=R1, R2=R2, Rb=Rb, I=D65, C=C,
       noise=TRUE, e = c(0.13, 0.06, 0.12))
       
#plot       
plot(model)

#2
#Pentachromatic animal
## Photoreceptor sensitivity spectra
##with lambda max at 350,400,450,500,and 550nm:
C<-photor(lambda.max=c(350,400,450,500,550))

##Grey background
##with 7 percent reflectance from 300 to 700nm:
Rb <- data.frame(300:700, rep(7, length(300:700)))

## Read CIE D65 standard illuminant:
data("D65")

##Reflectance data of R1
R1<-logistic(x=seq(300,700,1), x0=500, L=50, k=0.04)
R1[,2]<-R1[,2]+10

#RNL model
RNLmodel(photo=5, model="log",
       R1=R1, R2=Rb, Rb=Rb, I=D65, C=C,
       noise=TRUE, e = c(0.13, 0.06, 0.12, 0.07, 0.08))