Chromatics, or the science of color, not only studies the description of colors in terms of the physics of electromagnetic radiations, but also their perception through the human eye and cognitive apparatus. Although in purely physical terms colors may be described by as few as three dimensions – such as hue, saturation, and brightness – an open debate remains about how our cognition maps colors and in how many dimensions they encode the distinction between colors according to our perspective. In this work, we study the trade-off between finding an embedding for color perception with the minimal number of dimensions, while maximizing the discrimination between colors. To do so, we designed an experiment where thirteen subjects reported the similarity between twenty colors randomly generated using the Munsell color system. For each subject, we mapped perceived colors in an n-dimensional space, where distances between two colors reflect how different they are according to the subject. We used a least squares optimization to minimize the difference between subject-reported and mapped distances between colors with that dimensionality. We then repeated the process for values from one to nine dimensions. Our results showed an optimal number of dimensions of three when using a cosine similarity measure, which indicates a resemblance to the way the perception of colors is cognitively encoded from mere physical properties of color maps. We discuss the implications and limitations of these results in the light of color theory, and their relevance in both our understanding of the topology of mental concepts and major applications in fields where color theory is important, including composing color scales for designer tools, color psychology in marketing, color matching in interior architecture, and chromatic treatments in post-production of film-making.
Paper link: https://link.springer.com/chapter/10.1007/978-3-031-41862-4_12