Categorical colour geometry

The color communication game

There is clear diversity among speakers of a typical language in how colors are named. What is the impact of this diversity on the people's ability to communicate about color? Is there a gap between a person's general understanding of the color terms in their native language and how they understand a particular term that denotes a particular color sample? Seventy English-speaking dyads and 63 Somali-speaking dyads played the Color Communication Game, where the "sender" in each dyad named 30 color samples as they would in any color-naming study, then the "receiver" chose the sample they thought the sender intended to communicate. English speakers played again, under instructions to intentionally communicate color sample identity. Direct comparison of senders' samples and receivers' choices revealed categorical understanding of colors without considering color naming data. Although Somali-speaking senders provided fewer color terms, interpersonal Mutual Information (MI) calculated from color naming data was similarly below optimal for both groups, and English-speaking dyads' MI did not improve with experience. Both groups revealed superior understanding of color terms because receivers showed better exactly-correct selection performance than was predicted by simulation from their senders' color-naming data. This study highlights limitations on information-theoretic analyses of color naming data.

The non-Riemannian nature of perceptual color space

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, recognized by the International Commission for Weights and Measures, does not account for diminishing returns in color difference perception.

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.

RGB Colors and Ecological Optics

Object color space is highly structured due to optical constraints (radiant power non-negative, reflectance factors between zero and unity) and ecological context (daylight illuminant). In this setting trichromacy induces a natural geometry through a unique spectral tripartition. Different from null-context colorimetry, one gains two desirable relations: The colorimetric coordinates are coarse-grained spectral reflectance factors and there is a direct link to color experiences, since RGB–coordinates provide ostensive definitions. The framework allows one to deal with subtractive color mixture, source variation, effects of metamerism and relations between scenes and image data in a unified, structured manner. In ecological contexts, colors are effectively object properties. The formal framework is linear algebra and convex geometry. Applications in human biology, computer graphics, design, etc., are immediate.

Color-Patterns to Architecture Conversion through Conditional Generative Adversarial Networks

Often an apparent complex reality can be extrapolated into certain patterns that in turn are evidenced in natural behaviors (whether biological, chemical or physical). The Architecture Design field has manifested these patterns as a conscious (inspired designs) or unconscious manner (emerging organizations). If such patterns exist and can be recognized, can we therefore use them as genotypic DNA? Can we be capable of generating a phenotypic architecture that is manifestly more complex than the original pattern? Recent developments in the field of Evo-Devo around gene regulators patterns or the explosive development of Machine Learning tools could be combined to set the basis for developing new, disruptive workflows for both design and analysis. This study will test the feasibility of using conditional Generative Adversarial Networks (cGANs) as a tool for coding architecture into color pattern-based images and translating them into 2D architectural representations. A series of scaled tests are performed to check the feasibility of the hypothesis. A second test assesses the flexibility of the trained neural networks against cases outside the database.

Evo-Devo Strategies for Generative Architecture: Colour-Based Patterns in Polygon Meshes

Parametric design in architecture is often pigeonholed by its own definition and computational complexity. This article explores the generative capacity to integrate patterns and flows analogous to evolutionary developmental biology (Evo-Devo) strategies to develop emergent proto-architecture. Through the use of coloured patterns (genotype) and the modification of polygonal meshes (phenotype), a methodological proposal is achieved that is flexible to changes and personalization, computationally efficient, and includes a wide range of typologies. Both the process and the result are oriented towards computational lightness for a future and better integration of the workflow in genetic algorithms. Flow-based programming is used to replicate genetic properties such as multifunctionality, repeatability and interchangeability. The results reinforce the biological strategies against other more computationally abstract ones and successfully execute the parallels of universal mechanisms in Evo-Devo that are present in life.

Computing the relevant colors that describe the color palette of paintings

In this paper, we introduce an innovative parameter that allows us to evaluate the so-called "relevant colors" in a painting; in other words, the number of colors that would stand out for an observer when just glancing at a painting. These relevant colors allow us to characterize the color palette of a scene and, on this basis, those discernible colors that are colorimetrically different within the scene. We tried to carry out this characterization of the chromatic range of paints according to authors and styles. We used a collection of 4,266 paintings by 91 painters, from which we extracted various parameters that are exclusively colorimetric to characterize the range of colors. After this refinement of the set of selected colors, our algorithm obtained an average number of 18 relevant colors, which partially agreed with the total 11-15 basic color names usually found in other categorical color studies.

Reconciling the statistics of spectral reflectance and colour

The spectral reflectance function of a surface specifies the fraction of the illumination reflected by it at each wavelength. Jointly with the illumination spectral density, this function determines the apparent colour of the surface. Models for the distribution of spectral reflectance functions in the natural environment are considered. The realism of the models is assessed in terms of the individual reflectance functions they generate, and in terms of the overall distribution of colours which they give rise to. Both realism assessments are made in comparison to empirical datasets. Previously described models (PCA- and fourier-based) of reflectance function statistics are evaluated, as are improved versions; and also a novel model, which synthesizes reflectance functions as a sum of sigmoid functions. Key model features for realism are identified. The new sigmoid-sum model is shown to be the most realistic, generating reflectance functions that are hard to distinguish from real ones, and accounting for the majority of colours found in natural images with the exception of an abundance of vegetation green and sky blue.