rgb-noise: Build a spline approximation to the Lightroom camera tone curve

rgb-noise: Get spline approx to LR camera TC.r

# Plot log-log of LR and our camera tone curves
ggplot(lin.rgb.and.tif) +
      geom_point(aes(x = (mean)/255, y = tif.mean.cam/255, 
                     group = channel, colour = channel),
                 size = 1.5) +
      ggtitle('LR Camera tone curve\nFor Nikon D7000') +
      xlab('linear sRGB gray (log10)') + ylab('LR camera TC sRGB gray (log10)') +
      scale_x_log10() +
      scale_y_log10() +
      geom_line(aes(x=x, y=y), data=my.cam.tc, color='darkblue', linetype='dashed')

# The curve is the same regardless the channel
green.df <- subset(lin.rgb.and.tif, channel == 'green')
# sort the points
green.df <- green.df[with(green.df, order(mean)), ]
# Get a composite of LR at the left and our camera TC at the right
combo.df <- data.frame('x' = green.df$mean/255, 'y' = green.df$tif.mean.cam/255)
# Add my camera TC to the data frame
combo.df$my.cam <- my.cam.tc.fun(combo.df$x)
# From 37.5 and ahead interpolate from LR cam to my cam TC
rows.for.interpol <- which(combo.df$x >= 0.375)
combo.df$lr.cam <- combo.df$y
my.cam.w <- (combo.df[rows.for.interpol, 'x'] - 0.375)/(0.914635-0.375)
combo.df[rows.for.interpol,'lr.cam'] <- 
  with(combo.df[rows.for.interpol,], my.cam.w*my.cam + (1-my.cam.w)*y)

# switch to the log10 scale
combo.df <- with(combo.df, data.frame('x'=log10(x), 'y'=log10(lr.cam)))
                 
# Pass a smooth spline over the LR tone curve points
log10.lr.tc.sp <- smooth.spline(x = combo.df$x, 
                                y = combo.df$y, 
                                all.knots = TRUE)

# plot the spline approximation with the source data
dom.range <- range(combo.df$x)
dom <- seq(dom.range[1],dom.range[2],length.out=512)
log10.lr.tc.df <- data.frame(x=dom, y=predict(log10.lr.tc.sp, dom)$y)

# Log-log plot of the approximation and the source data
ggplot(green.df) + 
  geom_point(aes(x=log10(mean/255), y=log10(tif.mean.cam/255)), 
             color='red', alpha=0.4, size=2.2) +
  geom_line(aes(x, y), data=log10.lr.tc.df) + 
  ggtitle('LR Camera Tone Curve\nFor Nikon D7000') +
  xlab('linear sRGB Gray') + ylab('Lightroom camera sRGB gray') +
  scale_x_continuous(breaks = seq(-3, 0, 1), 
                              labels=c('0.1%', '1%', '10%', '100%')) +
  scale_y_continuous(breaks = seq(-3, 0, 1), 
                              labels=c('0.1%', '1%', '10%', '100%')) +
  # Also plot our camera tone curve
  geom_line(aes(x=log10(x), y=log10(y)), 
            data=my.cam.tc, linetype='dashed',  color='blue')

# Make a composite with the LR approximation at the left and our camera TC at the right
lr.tc.df <- as.data.frame(10^log10.lr.tc.df)
# Add 'my camera TC' to the data frame
lr.tc.df$my.cam <- my.cam.tc.fun(lr.tc.df$x)
#-- Interpolate from 37.5% to 100% from LR camera to 'my camera'
rows.for.interpol <- which(lr.tc.df$x >= 0.375)
lr.tc.df$lr.cam <- lr.tc.df$y
# Interpolation weights
my.cam.w <- (lr.tc.df[rows.for.interpol, 'x'] - 0.375)/(0.91463- 0.375)
lr.tc.df[rows.for.interpol,'lr.cam'] <- 
  with(lr.tc.df[rows.for.interpol,], my.cam.w*my.cam + (1-my.cam.w)*y)
lr.tc.df <- rbind(lr.tc.df, data.frame(x=1, y=1, my.cam=1, lr.cam=1))

# Pass a natural spline over the composite curve
lr.tc.spfun <- splinefun(lr.tc.df$x, y=lr.tc.df$lr.cam, method='natural')

# Get a curve with evenly spaced points
get.sp.tc <- function(spfun, step, x.range=c(0,1)) {
  first.deriv <- function(x) {
    spfun(deriv=1, x=x)
  }
  func <- function(x) {
    spfun(x=x)
  }

  x.min <- x.range[1]
  x.max <- x.range[2]
  
  current.value <- x.min
  tone.curve <- data.frame('x' = x.min, 'y'= func(x.min))

  while (current.value < x.max) {
    deriv <- first.deriv(current.value)
    dx <- step / sqrt(1+deriv*deriv)
    current.value <- current.value + dx
    x <- min(current.value, x.max)
    tone.curve <- rbind(tone.curve, data.frame('x' = x, 'y'= func(x)))
  }
  # result;
  tone.curve
}

# Compute evenly spaced LR cam TC points
lr.cam.tc <- get.sp.tc(lr.tc.spfun, 1/512)
write.csv(lr.cam.tc, 'lr-cam-tc.csv', row.names = FALSE)

# Plot the approximation, the LR camera TC data and our original camera TC
ggplot(lr.cam.tc) +
  geom_point(aes(x=(mean)/255, y = tif.mean.cam/255), 
             color='red', alpha=0.25,  data=green.df) +
  geom_line(aes(x=x, y=y)) +
  ggtitle('LR Camera tone curve') +
  xlab('linear sRGB gray') + ylab('Lightroom camera sRGB gray') +
  geom_line(aes(x=x, y=y), data=my.cam.tc, color='darkblue', linetype='dashed') +
  scale_x_continuous(breaks = seq(0, 1, 0.25), 
                              labels=c('0%', '25%', '50%', '75%', '100%')) +
  scale_y_continuous(breaks = seq(0, 1, 0.25), 
                              labels=c('0%', '25%', '50%', '75%', '100%'))