This paper makes the case that a powerful new discipline, which we term perception engineering, is steadily emerging. It follows from a progression of ideas that involve creating illusions, from historical paintings and film, to video games and virtual reality in modern times. Rather than creating physical artifacts such as bridges, airplanes, or computers, perception engineers create illusory perceptual experiences. The scope is defined over any agent that interacts with the physical world, including both biological organisms (humans, animals) and engineered systems (robots, autonomous systems). The key idea is that an agent, called a producer, alters the environment with the intent to alter the perceptual experience of another agent, called a receiver. Most importantly, the paper introduces a precise mathematical formulation of this process, based on the von Neumann-Morgenstern notion of information, to help scope and define the discipline. It is then applied to the cases of engineered and biological agents with discussion of its implications on existing fields such as virtual reality, robotics, and even social media. Finally, open challenges and opportunities for involvement are identified.

We propose a perceptual chromatic adaptation transform (CAT) for white balance that makes use of split-quaternions. The novelty of the present work, which is motivated by a recently developed quantumlike model of color perception, consists of stressing the link between the algebraic structures appearing in this model and a certain subalgebra of the split-quaternions. We show the potential of this approach for color image processing applications by proposing a CAT implemented via an appropriate use of the split-quaternion multiplication. Moreover, quantitative comparisons with the widely used state-of-the art von Kries CAT are provided.

This paper introduces a novel interaction method for virtual and augmented reality called look-and-twist, which is directly analogous to point-and-click operations using a mouse and desktop. It is based on head rotation alone and is straightforward to implement on any head mounted display that performs rotational tracking. A user selects features of interest by turning their head to face an object, and then performs a specified rotation along the axis of the looking direction. The look-and-twist method has been implemented and tested in an educational context, and systematic user studies are underway. Early evidence indicates that the method is comparable to, or faster than, the standard dwell time method. The method can be used, for example, with Google Cardboard, and it is straightforward to learn for inexperienced users. Moreover, it has the potential to significantly enrich VR interactions by providing an additional degree of freedom of control, which the binary nature of dwell-based methods lacks.

We propose a perceptual chromatic adaptation transform for white balance that makes use of split-quaternions. The novelty of the present work, which is motivated by a recently developed quantum-like model of color perception, consists at stressing the link between the algebraic structures appearing in this model and a certain sub-algebra of the split-quaternions. We show the potentiality of this approach for color image processing applications by proposing a chromatic adaptation transform, implemented via an appropriate use of the split-quaternion multiplication. Moreover, quantitative comparisons with the widely used state-of-the art von Kries chromatic adaptation transform are provided.

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.

Physical colors, i.e. reflected or emitted lights entering the eyes from a visual environment, are converted into perceived colors sensed by humans by neurophysiological mechanisms. These processes involve both three types of photoreceptors, the LMS cones, and spectrally opponent and non-opponent interactions resulting from the activity rates of ganglion and lateral geniculate nucleus cells. Thus, color perception is a phenomenon inherently linked to an experimental environment (the visual scene) and an observing apparatus (the human visual system). This is clearly reminiscent of the conceptual foundation of both relativity and quantum mechanics, where the link is between a physical system and the measuring instruments. The relationship between color perception and relativity was explicitly examined for the first time by the physicist H. Yilmaz in 1962 from an experimental point of view. The main purpose of this contribution is to present a rigorous mathematical model that, by taking into account both trichromacy and color opponency, permits to explain on a purely theoretical basis the relativistic color perception phenomena argued by Yilmaz. Instead of relying directly on relativistic considerations, we base our theory on a quantum interpretation of color perception together with just one assumption, called trichromacy axiom, that summarizes well-established properties of trichromatic color vision within the framework of Jordan algebras. We show how this approach allows us to reconcile trichromacy with Hering’s opponency and also to derive the relativistic properties of perceived colors without any additional mathematical or experimental assumption. In doing so, we also introduce several novel and mathematically rigorous definitions of chromatic attributes and discuss their counterparts in classical colorimetry. Finally, we underline the important role played by the Hilbert metric in our framework and its compatibility with known experimental data.

We show how to adapt the almost forgotten work of Yilmaz about the relativity of color perception to perform a color correction of digital images through a three-dimensional version of Lorentz boosts used in the special theory of relativity. Even in this preliminary version, the resulting algorithm is robust and it outperforms the classical physically-based diagonal illuminant correction techniques in terms of ability to remove color cast.

In the context of autonomous driving, a scenario is described by a set of parameters of the autonomous vehicle and its environment, for example: fast lane, high speed, right turn, sun etc.. The work of the experts allowed to identify parameters that can constitute scenarios. The objective of the proposed topic is to develop a mathematical method to generate the most relevant 1000 scenarios obeying multiple necessities. A scenario is a set of parameters obeying to certain needs. These necessities have been defined, including logical rules between parameters (e.g. a sunny day and a cloudy weather cannot coexist in the same scenario), or even the elaboration of weightings from two parameters (criticality and probability). Generating scenarios without prior work leads to a combinatorial explosion of solutions. The objective of our research work is to use mathematical tools to provide a set of relevant solutions.

The Naka-Rushton equation that models the transduction from electromagnetic energy carried by a photon to difference of potential of the membrane of a retinal photoreceptor has been used for two decades in tone mapping algorithms to compress the range of high dynamic range (HDR) images. Up to now, only its analytical properties of linear fractional transformation have been considered and exploited. In this paper, we recast the Naka-Rushton equation in the abstract setting of Möbius transformations, pointing out the hidden geometric properties of Naka-Rushton formula and discussing their pertinence to what a tone mapping algorithm is expected to comply.

In 1962, H. Yilmaz published a very original paper in which he showed the striking analogy between Lorentz transformations and the effect of illuminant changes on color perception. As a consequence, he argued that a perceived color space endowed with the Minkowski metric is a good approximation to model color vision. The contribution of this paper is twofold: firstly, we provide a mathematical formalization of Yilmaz's argument about the relationship between Lorentz transformations and the perceptual effect of illuminant changes. Secondly, we show that, within Yilmaz's model, the color space can be coherently endowed with the Minkowski metric only by imposing the Euclidean metric on the hue-chroma plane. This fact motivates the need of further investigation about both the proper definition and interrelationship among the color coordinates and also the geometry and metrics of perceptual color spaces.

Théorie et applications d’une nouvelle formulation de l’espace des couleurs perçues. Cette thèse porte sur une nouvelle approche mathématique de la perception des couleurs et ses premières applications au traitement d'images. Alors que la littérature existante suggère à la fois la nature hyperbolique des espaces couleurs et l'importance du mécanisme d'opposition de Hering dans le processus de la vision, il n'existe aucun modèle mathématique intégrant naturellement ces caractéristiques. L'approche présentée dans cette thèse, partant de l'axiomatisation de Newton, Grassmann, Helmholtz, Schrödinger et Resnikoff, conduit à une structure algébrique qui est le pendant réel de celle utilisée en mécanique quantique, qui présente des caractéristiques hyperboliques et encode l'opposition de Hering dans les matrices de Pauli réelles. Ces similitudes avec les théories modernes de la physique peuvent être expliquées à un niveau intuitif par le fait que la perception des couleurs est un processus basé sur la dualité entre le contexte de mesure et l'appareil d'observation, dans la mesure où cela n'a aucun sens de parler d'une couleur perçue sans spécifier les conditions dans lesquelles elle a été mesurée. Les couleurs perçues ne sont en effet pas absolues, mais relatives aux conditions d'observation. Ce manuscrit donne une vue d'ensemble de cette nouvelle théorie en mettant l'accent sur ses aspects relativistes. De plus, des définitions rigoureuses des attributs colorimétriques classiques (dont la teinte, la saturation, la luminosité...) sont fournies dans ce cadre. D'autre part, cette thèse comprend également des applications de ce nouveau formalisme, à travers des algorithmes de traitement d'images en couleur. Ces derniers sont destinés à faire en sorte que l'appareil photo numérique imite le comportement du système visuel humain. Deux premières applications sont présentées : un boost de Lorentz normalisé utilisé comme transformée d'adaptation chromatique pour la balance des blancs, c'est-à-dire l'algorithme qui émule l'adaptation aux conditions d'illumination, et quelques premières applications de constructions classiques provenant de la géométrie hyperbolique au tone mapping.