Impact of the completion of Schrödinger’s color theory on Darktable

Software darktable
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I just came across this news from Los Alamos National Laboratory: Research formalizes definitions essential to understanding color perception.

In short, a team of researchers has potentially solved a century-old problem started by Erwin Schrödinger. They’ve mathematically defined how we perceive hue, saturation, and lightness as intrinsic geometric properties, specifically correcting for things like the Bezold-Brücke effect (hue shifts at high intensity).

Most of our current tone-mappers, especially AgX, work to simulate a natural look by manually adjusting how colors desaturate and shift as they get brighter. If this research provides a mathematically “perfect” neutral axis and a “shortest path” for color perception, could it:

  1. Automate AgX Primaries? Instead of us tweaking sliders to avoid “the notorious six” color shifts, could the module use this new geometry to calculate the path to white automatically?
  2. Fix Gamut Mapping? Since the research proves color space is non-Riemannian, does this mean our current methods for handling out-of-gamut colors are fundamentally inefficient?

I’m curious to hear from the devs and color science enthusiasts here - could this lead to a more theoretically grounded version of AgX or a brand new scene-referred module?

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you might outline the solution found by the researchers and the difference to the existing darktable solution for the developer so they doesn’t need to spend too much effort to answer your question :wink:

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To be clear, the details in this research is above my understanding. That’s why I was wondering if any of the experts in here have any opinions on it.

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Odd name for posting here. More suited to Reddit

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@jdc is very knowledgeable on color science.

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A disclaimer I have very little knowledgeable about color science and just little bit more on differential geometry, so I use the seconds to guide the first.

I did a quickly read of the paper, its is very interesting but is focused on building a well defined mathematical framework to further studies on color perception.

I quick resume of the Mathematical concepts, mathematicians like to group concepts together to reuse theorem and definitions, this allow us to build on previous work. One of those set of concepts is Riemannian Geometry, that is a set of points (a manifold) and a special object, the metric, that allow us to define angles and distance. You can think about something like a sphere, the surface is curved so the normal definition of distance (the Euclidean Geometry) don’t work, but one important point: in small patches the normal definition is a good approximation.

The point this paper try to understand: is the space of color perception well described by a Riemannian Space or not?

First you need to define this space, the connection with color science is that in small patches its is defined by CIERGB and the distance is the ΔE2000 metric. You use this space to define other concepts like “Whats is Hue? Saturation?”. Schrödinger also defined a Riemannian metric (you can think of this metric a nice way to glue many copies of ΔE2000 ) that make this space a Riemannian Space.

To understand how well this work the authors do some check against know effects. The first one is Bezold-Brücke Effect, were the authors found that if the definition from Schrödinger for Hue and Saturation is changed it works.

The big problem is the effect of Diminishing Returns, were large differences appears small than the sum of small partial differences. This is a problem because on thing that make a space a Riemannian Space is that you can go along a path and collect the small changes and this is the change on the whole path. The presence of Diminishing Returns points to the fact that what measures distance of colors is non-Riemannian. This was a discussed previous in a work of some of the authors in this paper.

The authors propose that even if the metric is non-Riemannian there is an approximation that is Riemannian that is “close enough”, they did some experiments are participants choose a “neutral gray” to allow they to measure this.

This last part is not 100% clear to me yet, but from what I understand when they factor out “selection bias” the found the metrics to be very close.

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@chaimav

Thank you for referencing my skills.

It’s a complex subject that I’ve been interested in for about 20 years.

To simplify drastically, there are two major problems :

  • The mathematical (or Cartesian) part based on color matrices, illuminants, spectral colors, and the Observer 2° or 10°. These calculations, hidden behind different names depending on the software (Rawtherapee is very different from Darktable), use either RGB, XYZ, or Lab values. There are no truly ‘bad’ references in terms of workspaces.

  • The physiological aspect cannot be reduced to ‘Bezold-Brücke effect’ alone, which is extremely reductive.

I have followed the work of researchers who, for the past 30 years, have sought to model the effects of the eye/brain interaction. One of the most advanced models is CIECAM (from 1997 to 2020) which takes into account in particular :

  • simultaneous contrast
  • the Hunt’s effect.
  • Stevens’s effect.
  • Helmholtz-Kohlrausch’s effect.
  • Chromatic adaptation.
  • etc.

CIECAM has been using the 3-process workflow since 1997:

  • Scene conditions, which, in summary, takes into account the shooting conditions: Absolute luminance, Mean luminance, Surround,…
  • Image adjustments : It corresponds to the treatment of correlated variables (J, C, h, H, Q, M, s, ac, bc) for various purposes : action on lightness (J), brightness (Q), chroma (C), saturation (s), color level (colorfullness M), the hue angle h, as well as ac et bc. It is quite possible to build an images editing software around those variables…
  • Viewing conditions : which, in summary, takes into account the viewing conditions: Absolute luminance, Mean luminance, Surround,…

CIECAM is fully integrated into RawTherapee…but here we’re using Darktable. Nevertheless, I remain open to any discussion or exchange on these topics, both from a Cartesian and a physicological perspective.

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