% lens-aging.rnw
% Time-stamp: "lens-aging.rnw"

\documentclass[11pt]{article}

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\RequirePackage[left=1in,top=0.75in,right=1in,bottom=0.75in]{geometry}


%\VignetteIndexEntry{The Effect of the Aging Human Lens on Color Vision}
%\VignetteEngine{knitr::knitr}

\RequirePackage{color}
\definecolor{darkblue}{rgb}{0,0,0.5}
\definecolor{blue}{rgb}{0,0,0.8}
\definecolor{lightblue}{rgb}{0.2,0.2,0.9}
\definecolor{darkred}{rgb}{0.6,0.0,0.0}
\definecolor{red}{rgb}{0.7,0,0}
\definecolor{darkgreen}{rgb}{0.0,0.4,0.0}
\definecolor{lightgray}{rgb}{0.7,0.7,0.7}
\definecolor{darkorange}{rgb}{0.75, 0.45, 0}
\definecolor{purple}{rgb}{0.65, 0, 0.75}
\definecolor{goldenrod}{rgb}{0.80, 0.61, 0.11}
\definecolor{lightyellow}{rgb}{0.98,0.94,0.83}


\RequirePackage{fancyvrb}
\RequirePackage[T1]{fontenc}
\RequirePackage{ae}       % ComputerModern Fonts
\RequirePackage{fancyhdr}
\RequirePackage{float}
\RequirePackage{hyperref}
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  fontsize=\small,
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}

\begin{document}
% \SweaveOpts{concordance=TRUE}

\title{ {\Huge The Effect of the Aging Lens on Color Vision} }
\author{Glenn Davis  \url{    <gdavis@gluonics.com>}}
\maketitle
% \thispagestyle{fancy}

% Setup stuff.
<<setup, echo=FALSE, results="hide">>=
require("knitr",quietly=TRUE)
opts_chunk$set(fig.path="figs/ag2-", fig.align="center",
  fig.width=7, fig.height=7, comment="")
knit_hooks$set(output = function(x, options) {
  paste('\\begin{Soutput}\n', x, '\\end{Soutput}\n', sep = '')
})
options(width=90)
par( omi=c(0,0,0,0), mai=c(0.2,0.2,0.2,0.2) )
if(!file.exists("figs")) dir.create("figs")
@


The goal of this \textbf{colorSpec} vignette is to simulate the effect
of age on human color vision.
The colored figures are best viewed by an observer with age of 32 years, 
and on a display calibrated for sRGB.


% ----------------------------------------------------------------------------
\section*{The Human Lens}

It is well known that the lens in the human eye does not transmit all wavelengths equally;
the transmission at short wavelengths is less, which means the lens is yellowish.
In the UV there is very little transmission;
which is a good thing since the lens protects the retina from UV damage.
It is also well known that the lens gets yellower with age.
When making these colored images it is appropriate to use the
CIE 1931 color matching functions (CMFs).
Unfortunately I could not find the average age of the observers used to
establish the 1931 standard observer (there were 17 of them).
But it \emph{is} known that the average age of the observers used to create the 
CIE 1964 standard observer is 32 years, see \cite{Pokorny}.
So we'll take 32 years for the CIE 1931 standard observer as well.
Featured functions in this vignette are: 
\code{linearize()},
\code{lensAbsorbance()},
\code{extradata()},
\code{applyspec()},
and \code{calibrate()}.

Start the \textbf{R} session and load the \textbf{colorSpec} package,

<<packs, echo=TRUE, message=FALSE>>=
library( colorSpec )
library( spacesXYZ )    # for function standardXYZ()
library( spacesRGB )    # for functions RGBfromXYZ() and plotPatchesRGB()
@

Compute and plot lens transmittance at 32 and 64 years using the model in \cite{Pokorny}.

<<lens1, echo=TRUE, fig.pos="H", fig.height=4, out.width='1.0\\linewidth', fig.cap='Human Lens Transmittance at age=32 and age=64' >>=
lens.trans = linearize( lensAbsorbance( c(32,64), wave=380:780 ) )   
par( omi=c(0,0,0,0), mai=c(0.6,0.7,0.3,0.2) )
plot( lens.trans, color='black', lty=1:2, main=FALSE, legend='topleft' )
@

To compare the color appearance at age 64 to that at age 32,
we need the transmittance at age 64 relative to that at age 32.
We know that object \code{lens.trans} is a matrix, 
so use the standard \textbf{R} matrix subset operation to extract each spectrum.
Then perform the division and plot the ratio.

<<lens2, echo=TRUE, fig.pos="H", fig.height=4, out.width='1.0\\linewidth', fig.cap='Human Lens Transmittance at age 64 relative to age 32' >>=
lens.64 = lens.trans[ ,2] / lens.trans[ ,1]
lens.64 = colorSpec( lens.64, wavelength(lens.trans), 'transmittance' )
specnames(lens.64) = "trans.64 / trans.32"
par( omi=c(0,0,0,0), mai=c(0.6,0.7,0.3,0.2) )
plot( lens.64, main=TRUE, legend=FALSE, ylab='Relative Transmittance', col='black' )
@

Think of this curve as defining a pair of glasses with a yellowish tint.
In this vignette, going from an age of 32 years to 64 years is equivalent to
putting on these tinted glasses.


% ----------------------------------------------------------------------------
\section*{The Macbeth ColorChecker with Observer Age 32}

We first read the spectra of the \emph{ColorChecker} target.  
This data has been kindly provided in CGATS format by \cite{Pascale}.
\emph{ColorChecker} is a Registered Trademark of X-Rite, and X-Rite is a Trademark. 

<<target, echo=TRUE, message=FALSE>>=
path = system.file( 'extdata/targets/CC_Avg30_spectrum_CGATS.txt', package='colorSpec') 
MacbethCC = readSpectra( path, wave=wavelength(lens.64) ) 
MacbethCC = MacbethCC[ order(MacbethCC$SAMPLE_ID), ]
print( extradata(MacbethCC), row.names=F )
@

Note that \code{MacbethCC} is organized as \code{'df.row'} 
and contains extra data for each spectrum, notably the coordinates of the patch rectangle.

Now build the "material responder" from Illuminant D65 and the 1931 CMFs:

<<lee10, echo=TRUE, message=FALSE >>=
D65.eye = product( D65.1nm, "artwork", xyz1931.1nm, wave=wavelength(lens.64) )
#   calibrate so the perfect-reflecting-diffuser is the 'official XYZ'
#   scale XYZ independently
prd = neutralMaterial( 1, wavelength(lens.64) )
D65.eye = calibrate( D65.eye, stimulus=prd, response=standardXYZ('D65'), method='scaling' )
@
Calculate XYZ and then RGB:
<<lee11, echo=TRUE, fig.pos="H", fig.height=5, out.width='1.0\\linewidth', fig.cap='Rendering with Illuminant D65 and xyz1931.1nm, at age=32' >>=
XYZ = product( MacbethCC, D65.eye, wave=wavelength(lens.64) )
RGB = RGBfromXYZ( XYZ, space='sRGB', which='scene' )$RGB  # this is *signal* sRGB
# add the rectangle data to RGB, so they can be plotted in proper places
patches = extradata(MacbethCC)
patches$RGB = RGB
patches.first = patches   # save this reference object for later
#  display in proper location, and use the sRGB display transfer function
par( omi=c(0,0,0,0), mai=c(0.2,0.2,0.2,0.2) )
plotPatchesRGB( patches, space='sRGB', which='signal', back='gray20', labels=FALSE )
@
This figure has the colors as perceived by the 1931 standard observer.



\section*{The Macbeth ColorChecker with Observer Age 64}

Make new responder by inserting the hypothetical pair of tinted glasses
(defined by \code{lens.64} in Figure 2)
between target and the eye, and then recalculate RGBs.

<<lee20, echo=TRUE, fig.pos="H", fig.height=5, out.width='1.0\\linewidth', fig.cap='Rendering with Illuminant D65 and xyz1931.1nm, at age=64 without adaptation' >>=
D65.eye.64 = applyspec( D65.eye, function(y) {lens.64 * y} )
XYZ = product( MacbethCC, D65.eye.64, wave=wavelength(lens.64) )
patches = extradata(MacbethCC)
patches$RGB = RGBfromXYZ( XYZ, space='sRGB', which='scene' )$RGB  # this is *signal* sRGB
par( omi=c(0,0,0,0), mai=c(0.2,0.2,0.2,0.2) )
plotPatchesRGB( patches, space='sRGB', which='signal', back='gray20', labels=FALSE )
@
As expected, the result has a yellow tint.
Now make a plot that compares the effective responsivities.
<<lee21, echo=TRUE,  fig.pos="H", fig.height=5, out.width='1.0\\linewidth', fig.cap='comparison of effective responsivities, at age=32 and age=64' >>=
#   the effective responsivities for age=32
par( omi=c(0,0,0,0), mai=c(0.6,0.7,0.3,0.2) )
specnames( D65.eye ) = sprintf( "%s.32", c('x','y','z') )
plot( D65.eye,  lty=1, legend='top' )
#   the effective responsivities for age=64
specnames( D65.eye.64 ) = sprintf( "%s.64", c('x','y','z') )
plot( D65.eye.64,  lty=2, add=TRUE, legend='topright' )
@

But these figures are only appropriate for the instant in time that the change was made, 
and before the eye and brain have had the time to adapt.
In electronic camera terms, there is no "white balance" yet.

So now calibrate and adapt to D65 using the \emph{Bradford Method}.
This method is regarded as being a good model for the way that the
human eye and brain achieve \emph{color constancy}, see \cite{Lindbloom}.
<<lee22, echo=TRUE, fig.pos="H", fig.height=5, out.width='1.0\\linewidth', fig.cap='Rendering with Illuminant D65 and xyz1931.1nm, at age=64 after chromatic adaptation' >>=
prd = neutralMaterial( 1, wavelength(lens.64) )
XYZ.D65 = spacesXYZ::standardXYZ('D65')
D65.eye.64 = calibrate( D65.eye.64, stimulus=prd, response=XYZ.D65, method='Bradford' )
XYZ = product( MacbethCC, D65.eye.64, wave=wavelength(lens.64) )
patches = extradata(MacbethCC)
patches$RGB = RGBfromXYZ( XYZ, space='sRGB' )$RGB        # this is *signal* sRGB
par( omi=c(0,0,0,0), mai=c(0.2,0.2,0.2,0.2) )
plotPatchesRGB( patches, space='sRGB', which='signal', back='gray20', labels=FALSE )
@
The tint is now gone.
But it hard to compare colors in this figure with the ones way back in Figure 3.
So combine the original age=32 rendering with the age=64 rendering
by splitting each square into 2 triangles.
<<lee23, echo=TRUE, fig.pos="H", fig.height=5, out.width='1.0\\linewidth', fig.cap='Rendering with both age=32 (Figure 3), and age=64 (Figure 6)' >>=
par( omi=c(0,0,0,0), mai=c(0.2,0.2,0.2,0.2) )
#  draw full squares from Figure 3
plotPatchesRGB( patches.first, space='sRGB', back='gray20', labels=F )
#  overwrite the squares with triangles by setting shape= and add=
plotPatchesRGB( patches, space='sRGB', labels=F, shape='bottomright', add=T )
@
The top-left triangle has the color from Figure 3
and the bottom-right triangle has the color from Figure 6.
There are minor differences in the \textbf{Red} and \textbf{Magenta} patches,
and some smaller differences in a few others.

Here are the responsivity functions \emph{after} adaptation:
<<lee30, echo=TRUE,  fig.pos="H", fig.height=5, out.width='1.0\\linewidth', fig.cap='comparison of effective responsivities' >>=
par( omi=c(0,0,0,0), mai=c(0.6,0.7,0.3,0.2) )
plot( D65.eye,  lty=1, legend='top', main=FALSE )
plot( D65.eye.64, lty=2, add=TRUE, legend='topright' )
@
So despite the fairly radical yellowing of the lens with age (in Figure 2),
this adaptation model shows that the perceived colors are not all that different.
Great !


% \pagebreak

\bibliographystyle{alpha}
\bibliography{lens-aging}


% ----------------------------------------------------------------------------


\section*{Appendix}
This document was prepared \today \quad with the following configuration:
<<finish, echo=FALSE, results="asis">>=
knit_hooks$set(output = function(x, options) { x })
toLatex(sessionInfo(), locale=FALSE)
@


\end{document}
