シュレーディンガーらが開発した色の見え方を表現する3次元数学的記述からのパラダイムシフトにより、より鮮やかなコンピューターディスプレイ、テレビ、印刷物、テキスタイルなどを実現できる可能性がある。 A paradigm shift away from the 3D mathematical description developed by Schrödinger and others to describe how we see color could yield more vibrant computer displays, TVs, printed materials, textiles and more
2022-08-10 アメリカ・ロスアラモス国立研究所(LANL)
This visualization captures the 3D mathematical space used to map human color perception. A new mathematical representation has found that the line segments representing the distance between widely separated colors don’t add up correctly using the previously accepted geometry. The research contradicts long-held assumptions and will improve a variety of practical applications of color theory.
心理学、生物学、数学を融合させたこの研究で、ブジャックたちは、リーマン幾何学を用いると、大きな色差の知覚が過大評価されることを発見した。なぜなら、人は大きな色の違いを、大きく離れた2つの色調の間にある小さな色の違いを合計した場合の合計よりも小さく感じるからだ。
リーマン幾何学では、この効果を説明することはできません。この結果は、画像およびビデオ処理、カラー マッピング、塗料および繊維産業で現在使用されているカラー メトリックに適用されます。リーマンの設定の外でそれらを再考することは、それらを大きな違いに拡張する道を提供する可能性があります.
この発見は、認識された違いを説明する 2 次の Weber-Fechner 法則の存在をさらに示唆しています。
<関連情報>
- https://discover.lanl.gov/news/0810-color-perception
- https://www.pnas.org/doi/10.1073/pnas.2119753119#sec-8
知覚的色空間の非リーマン性 The non-Riemannian nature of perceptual color space
Roxana Bujack , Emily Teti, Jonah Miller, Elektra Caffrey, and Terece L. Turton
Proceedings of the National Academy of Sciences Published:April 29, 2022
DOI:https://doi.org/10.1073/pnas.2119753119
Significance
For over 100 y, the scientific community has adhered to a paradigm, introduced by Riemann and furthered by Helmholtz and Schrodinger, where perceptual color space is a three-dimensional Riemannian space. This implies that the distance between two colors is the length of the shortest path that connects them. We show that a Riemannian metric overestimates the perception of large color differences because large color differences are perceived as less than the sum of small differences. This effect, called diminishing returns, cannot exist in a Riemannian geometry. Consequently, we need to adapt how we model color differences, as the current standard, ΔE<?XML:NAMESPACE PREFIX = “[default] http://www.w3.org/1998/Math/MathML” NS = “http://www.w3.org/1998/Math/MathML” />ΔE, recognized by the International Commission for Weights and Measures, does not account for diminishing returns in color difference perception.
Abstract
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.
