The non-Riemannian nature of perceptual color space

Bujack, Roxana; Teti, Emily Stark; Miller, Jonah; Caffrey, Elektra; Turton, Terece L.

doi:10.1073/pnas.2119753119

Cited by 11 publications

(24 citation statements)

References 55 publications

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“…Additionally, we have applied our method to a study of diminishing returns in the perception of grays. Bujack et al. (2022) found that even after using a similar MLE approach to model the transformation from absolute strength to perceived strength, modeling a difference scaling function increased accuracy in predicting responses to triads.…”

Section: Discussionmentioning

confidence: 99%

“…There appears to be a slight curvature in the middle region for the plain viewing condition while, for the two light conditions, we see a dramatic effect of diminishing returns. This is perhaps unsurprising given the findings of Bujack et al. (2022) .…”

Section: Application To Empirical Data Setsmentioning

confidence: 98%

“…This analytical approach has recently been applied to color perception, providing strong evidence for the existence of diminishing returns in color perception ( Bujack et al., 2022 ). This work used MOT, where triads were constructed at five discrete centers and the tests varied based on their differences.…”

Section: Application To Empirical Data Setsmentioning

confidence: 99%

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Maximum likelihood estimation of difference scaling functions for suprathreshold judgments

et al. 2022

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Maximum likelihood estimation (MLE) has been used to produce perceptual scales from binary judgments of triads and quadruples. This method relies on Thurstone's theory of a stochastic perceptual process where the perceived difference of two stimuli is the difference in their perceived strengths. It is possible that the perception of a suprathreshold difference is overestimated when adding smaller differences, a phenomenon referred to as diminishing returns. The current approach to construct a perceptual scale using MLE does not account for this phenomenon. We present a way to model the perception of differences using MLE and Thurstone's theory, adapted to allow the possibility of diminishing returns. This method is validated using Monte Carlo simulated responses to experimental triads and can correctly model diminishing returns, the absence of diminishing returns, and the opposite of diminishing returns both in the cases when a perceptual scale is known and when the true perceived strengths of the stimuli are unknown. Additionally, this method was applied to empirical data sets to determine its feasibility in investigations of perception. Ultimately, it was found that this analysis allows for more accurate modeling of suprathreshold difference judgments, a more complete understanding of the perceptual processes underlying comparisons, and the evaluation of Thurstone's theory of difference judgments.

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Section: Discussionmentioning

confidence: 99%

Section: Application To Empirical Data Setsmentioning

confidence: 98%

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Maximum likelihood estimation of difference scaling functions for suprathreshold judgments

et al. 2022

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“…In their paper “The non-Riemannian nature of perceptual color space,” Bujack et al. ( 1 ) tackle the fundamental question of how to structure a color space that explains color differences as well as color matching. By deploying an elegant psychophysical procedure in which observers judged the relative magnitude of pairs of stimulus differences, they show that it is not possible to use either Euclidean or Riemannian geometry to describe both small and large perceptual color differences.…”

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confidence: 99%

“…The question asked by Bujack et al. ( 1 ) is whether it is possible to construct a Riemannian perceptual color space such that integrating the line element along the geodesic between any two points predicts larger perceptual color differences.…”

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Brainard

2022

Proc. Natl. Acad. Sci. U.S.A.

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Helmholtz, Schrödinger, and the First Non‐Euclidean Model of Perceptual Color Space

Roberti

2024

Annalen der Physik

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This paper explores the groundbreaking contributions of Hermann von Helmholtz and Erwin Schrödinger to the geometry of color space ‐a 3D space that correlates color distances with perceptual differences. Drawing upon his expertise in non‐Euclidean geometry, physics, and psychophysics, Helmholtz introduced the first Riemannian line element in color space between 1891 and 1892, inaugurating a new line of research known as higher color metric, a term coined by Schrödinger in 1920. During his tenure at the University of Vienna, Schrödinger extensively worked on color theory and rediscovered Helmholtz's forgotten line element. In his 1920 papers titled “Grundlinien einer Theorie der Farbmetrik im Tagessehen,” published in the Annalen der Physik, Schrödinger elucidated certain shortcomings in Helmholtz's model and proposed his refined version of the Riemannian line element. This study delves into this captivating chapter in the history of color science, emphasizing the profound impact of Helmholtz's and Schrödinger's work on subsequent research in color metrics up to the present day.

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The non-Riemannian nature of perceptual color space

Cited by 11 publications

References 55 publications

Maximum likelihood estimation of difference scaling functions for suprathreshold judgments

Maximum likelihood estimation of difference scaling functions for suprathreshold judgments

Proximity matters

Helmholtz, Schrödinger, and the First Non‐Euclidean Model of Perceptual Color Space

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