After last week’s meeting, I was curious to see if I could solve @daniele’s tonal compression function for arbitrary mid grey and diffuse white intersections.
After a lot of trial and error (mostly error), I managed something.
- d_{0} → d_{1} maps input middle grey x to output middle grey y.
- w_{0} → w_{1} maps input white x to output white y.
- p adjusts contrast
- t_{0} adjusts toe / shadow / flare compenstation.
- s_{x} and s_{y} are the input and output domain scales for the intersection points.
If t_{0} = 0, the input → output mapping is exact. If t_{0}>0, the input → output mapping will be changed slightly, depending on where the toe pivot p_{t} is set.
I tried for a long time to solve for the intersections with toe pivot adjustment integrated, but the equations become unmanagebly complex and beyond my capabilities. With the compression and toe equations separate, they are both much simpler.
I was able to solve the toe equation for 2 intersects at d_{1} and w_{1}, however this causes undesireable behavior, because as you increase t_{0}, values between d_{1} and w_{1} increased.
I settled on a compromise where the toe compression function pivots around a single value p_{t}, which can be set to taste. If it’s set at 1.0, d_{0} gets a bit darker when t_{0} is increased. If it’s set to 0.1, w_{1} gets a bit brighter when t_{0} is increased.
I’m pretty sure there is a better and/or simpler way to do these things, but I’m just doing what I can with my current math ability. Any suggestions I would be happy to hear them!
As usual, here’s a Nuke node implementation as well, for testing:
ToneCompress_v2.nk (2.8 KB)
I’ve included a few “eye matched” non-scientific presets for SDR and a few different flavors of HDR.