Abstract
In this paper, we provide an overview on the foundation and first results of a very recent quantum theory of color perception, together with novel results about uncertainty relations for chromatic opposition. The major inspiration for this model is the 1974 remarkable work by H.L. Resnikoff, who had the idea to give up the analysis of the space of perceived colors through metameric classes of spectra in favor of the study of its algebraic properties. This strategy permitted to reveal the importance of hyperbolic geometry in colorimetry. Starting from these premises, we show how Resnikoff’s construction can be extended to a geometrically rich quantum framework, where the concepts of achromatic color, hue and saturation can be rigorously defined. Moreover, the analysis of pure and mixed quantum chromatic states leads to a deep understanding of chromatic opposition and its role in the encoding of visual signals. We complete our paper by proving the existence of uncertainty relations for the degree of chromatic opposition, thus providing a theoretical confirmation of the quantum nature of color perception.
Highlights
The central core of this paper is the concept of space of colors perceived by a trichromatic human being, or color space, for short
We have shown how Resnikoff’s idea to abandon metameric classes of spectra and study the color space solely through its algebraic properties can be further refined by exploiting the properties of formally real Jordan algebras
This leads to a real quantum theory of color vision that permits to rigorously define colorimetric attributes and to understand chromatic opponency by means of quantum features
Summary
The central core of this paper is the concept of space of colors perceived by a trichromatic human being, or color space, for short. The work of H.L. Resnikoff, that we will briefly recall, is related to the aforementioned geometrical and metric structure of the perceived color space. That we will briefly recall, is related to the aforementioned geometrical and metric structure of the perceived color space It is a foundational work, without direct algorithmic applications and it requires a non trivial acquaintance with theoretical physics and pure mathematics. We start providing an outlook on the color perception theory inspired by Resnikoff’s insights that we have developed through the papers [6,7,8,9,10,11] These are quite technical and dense works, here we prefer to privilege clarity of exposition and, for this.
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