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SIAM Journal on Imaging Sciences

A Quantum Information-Based Refoundation of Color Perception Concepts

Michel Berthier, Nicoletta Prencipe, Edoardo Provenzi

Published Nov 21, 2022• 11 citations
Publisher

Abstract

In this paper we deal with the problem of overcoming the intuitive definition of several color perception attributes by replacing them with novel mathematically rigorous ones. Our framework is a quantum-like color perception theory recently developed, which constitutes a radical change of view with respect to the classical Commission Interntional de l'Éclairage models and their color appearance counterparts. We show how quantum information concepts, (e.g., effects, generalized states, postmeasurement transformations, and relative entropy) provide tools that seem to be perfectly fit to model color perception attributes such as brightness, lightness, colorfulness, chroma, saturation, and hue. An illustration of the efficiency of these novel definitions is provided by the rigorous derivation of the so-called lightness constancy phenomenon.

DOI
10.1137/22m1476071

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In this paper we deal with the problem of overcoming the intuitive definition of several color perception attributes by replacing them with novel mathematically rigorous ones. Our framework is a quantum-like color perception theory recently developed, which constitutes a radical change of view with respect to the classical Commission Interntional de l'Éclairage models and their color appearance counterparts. We show how quantum information concepts, (e.g., effects, generalized states, postmeasurement transformations, and relative entropy) provide tools that seem to be perfectly fit to model color perception attributes such as brightness, lightness, colorfulness, chroma, saturation, and hue. An illustration of the efficiency of these novel definitions is provided by the rigorous derivation of the so-called lightness constancy phenomenon.
In this paper we deal with the problem of overcoming the intuitive definition of several color perception attributes by replacing them with novel mathematically rigorous ones. Our framework is a quantum-like color perception theory recently developed, which constitutes a radical change of view with respect to the classical CIE models and their color appearance counterparts. We show how quantum information concepts, as e.g. effects, generalized states, post-measurement transformations and relative entropy provide tools that seem to be perfectly fit to model color perception attributes as brightness, lightness, colorfulness, chroma, saturation and hue. An illustration of the efficiency of these novel definitions is provided by the rigorous derivation of the so-called lightness constancy phenomenon.
Starting from the foundational axiomatization of the perceptual color space initiated by Schrödinger in 1920 and eventually refined by Resnikoff in 1974, Berthier, Provenzi and their collaborators have recently proposed a reformulation of perceptual color attributes within the framework of quantum information. Their work is based on the Jordan algebra formalism of quantum theories and, more specifically, on a quantum system described by a spin factor over the field of real numbers. This theoretical framework is not that of ordinary quantum mechanics, mainly because it requires dealing with rebits, whereas the latter uses qubits. The aim of this paper is to show that this difference in no way hinders the implementation of experimental protocols for testing the validity of the predictions of the color perception model. In particular, we show how to compute the quantum information based perceptual attributes of perceived colors in terms of qubit density matrices.
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.
This paper is devoted to the study of the Markovian dynamics of open two-state quantum systems defined over the real numbers. Its aim is twofold. On the one hand, we provide a complete mathematical description of such dynamics when the affine component of the quantum channel semigroup is Markovian. We describe Lindblad and Kraus operators, orthogonal evolutions by means of Jordan algebra derivations, as well as solutions of the GKSL dissipative equation and their effect on the relative entropy. On the other hand, we are interested in an original application to color perception that motivates this analysis. Using a recent novel model in which perceived colors are given by Lüders measurements on the state space of a rebit, we show how the chromatic distortion induced by a non-neutral illuminant can be modeled by a Markovian rebit channel that progressively reduces color distinguishability. This colorimetric effect is illustrated through simulations on digital images, offering a concrete demonstration of the relevance of Markovian rebit evolution for modeling perceptual phenomena.
Difficulties in algorithmic simulation of natural thinking point to the inadequacy of information encodings used to this end. The promising approach to this problem represents information by the qubit states of quantum theory, structurally aligned with major theories of cognitive semantics. The paper develops this idea by linking qubit states with color as fundamental carrier of affective meaning. The approach builds on geometric affinity of Hilbert space of qubit states and color solids, used to establish precise one-to-one mapping between them. This is enabled by original decomposition of qubit in three non-orthogonal basis vectors corresponding to red, green, and blue colors. Real-valued coefficients of such decomposition are identical to the tomograms of the qubit state in the corresponding directions, related to ordinary Stokes parameters by rotational transform. Classical compositions of black, white and six main colors (red, green, blue, yellow, magenta and cyan) are then mapped to analogous superposition of the qubit states. Pure and mixed colors intuitively map to pure and mixed qubit states on the surface and in the volume of the Bloch ball, while grayscale is mapped to the diameter of the Bloch sphere. Herewith, the lightness of color corresponds to the probability of the qubit’s basis state «1», while saturation and hue encode coherence and phase of the qubit, respectively. The developed code identifies color as a bridge between quantum-theoretic formalism and qualitative regularities of the natural mind. This opens prospects for deeper integration of quantum informatics in semantic analysis of data, image processing, and the development of nature-like computational architectures.