Monday, August 15, 2022

New understanding of color perception theory

From a news article about a recent paper that casts doubt on the traditional understanding of how human color perception works: "Math error: A new study overturns 100-year-old understanding of color perception":

A new study corrects an important error in the 3D mathematical space developed by the Nobel Prize-winning physicist Erwin Schrödinger and others, and used by scientists and industry for more than 100 years to describe how your eye distinguishes one color from another. The research has the potential to boost scientific data visualizations, improve TVs and recalibrate the textile and paint industries.

The full paper appears in the Proceedings of the National Academy of Sciences vol. 119 no. 18 (2022). It is titled "The non-Riemannian nature of perceptual color space" authored by Dr. Roxana Bujack and colleagues at Los Alamos National Lab.

The scientific community generally agrees on the theory, introduced by Riemann and furthered by Helmholtz and Schrödinger, that perceived color space is not Euclidean but rather, a three-dimensional Riemannian space. We show that the principle of diminishing returns applies to human color perception. This means that large color differences cannot be derived by adding a series of small steps, and therefore, perceptual color space cannot be described by a Riemannian geometry. This finding is inconsistent with the current approaches to modeling perceptual color space. Therefore, the assumed shape of color space requires a paradigm shift. Consequences of this apply to color metrics that are currently used in image and video processing, color mapping, and the paint and textile industries. These metrics are valid only for small differences. Rethinking them outside of a Riemannian setting could provide a path to extending them to large differences. This finding further hints at the existence of a second-order Weber–Fechner law describing perceived differences.


The key observation that this paper rests on is the concept of "diminishing returns". Statistical analysis of experimental data collected in this paper suggests that the perceived difference between pairs of colors A, B and C that lie along a single shortest path (geodesic) do not satisfy the additive equality.

A commentary by Dr. David Brainard (U. Penn.) about this paper was published in PNAS and is available here:

Some of the caveats noted in this commentary piece:

First, the authors make a first principles assumption that the achromatic locus is a geodesic and use this in their choice of stimuli. This assumption is intuitively appealing in that it would be surprising that the shortest path in color space between two achromatic stimuli would involve a detour through a chromatic stimulus and back. However, the achromatic locus as a geodesic was not empirically established, and more work could be considered to shore up this aspect of the argument. Second, the data were collected using online methods and combined across subjects prior to the analysis. This raises the question of whether the aggregate performance analyzed could be non-Riemannian even when the performance of each individual subject was itself Riemannian. Although it is not immediately obvious whether this could occur, it might be further considered as a possibility. press release:

LANL press release:

PNAS paper:


  1. Additional comments here:

  2. Is light more like a wave or a particle) What does the new understanding of color perception theory say about this?

  3. a) Yes.
    b) This study has no relevance to wave-particle duality. It is about models for human colour perception.


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