# Enhancing Color Scales for Active Data Physicalizations
## 2 Theoretical Background
### Color Systems, Color Perceptual Distance, and Farnsworth-Munsell Test  
This article used some color spaces, among which the following stand out: RGB, HSV or HSL, CIELAB, and Munsell. RGB is widely used in the display of electronic devices. In this article, it is used in the LED strip configuration embedded in the data physicalization and in estimating the RGB color visible in the data physicalization via a webcam. The HSV and HSL color systems are an alternative to RGB as they come closer to how humans describe the perception of color [23]. In this article, they are used to present the results of color choice and the color palettes proposed. Another system used is CIELAB, a color space widely used to evaluate colors, and it correlates color values with visual perception very well [24]. This article uses the color parameters in CIELAB to calculate the perceptual distance between two colors and estimate their similarity [25]. Finally, the Munsell color space specifies a color in hue (basic color), value (lightness), and chroma (color intensity) and presents a wide chromatic and tonal variety of colors. In this article, the Munsell color system is used to apply the Farnsworth-Munsell test [26], both in digital and physical environments, pointing out potential colors to compose the data physicalization color palettes. In 1976, the International Commission on Illumination (ICI), aiming to have a metric to measure the difference between two colors, introduced the concept of Delta E [27]. Thus, \(\Delta E\) (DeltaE or dE) is the measure of change in visual perception between two colors. In the same year, the ICI also proposed the CIELAB color system and the first version for calculating Delta E (DeltaE 76) using CIELAB color parameters. New versions of Delta E were proposed to correct some inconsistencies in previous versions, and the most recent is DeltaE 2000 [28]. Although DeltaE 2000 presents a more complex calculation, it is also more accurate, mainly due to more precise lighting calculations. It also considers the issue of perceptual non-uniformity of the human visual system; that is, the human eye is more sensitive to certain colors than others. Color tolerance is the metric that describes the limit of the difference between two colors: a reference color and the target color we want to measure its similarity to. Generally speaking, there is no standard for the Color Tolerance Range, which varies depending on the industry or purpose [25]. Therefore, it is possible to imagine that these values for colors in data physicalization will also be different, as it will depend on the material and how the color is proposed in physicalization, among other factors. However, a table of generic values commonly used in the absence of more specific standards can be seen in Table 1. Thus, this article considers that colors are similar if they have perceptual distances between them less than or equal to 5. Proposed by [PERSON], the Farnsworth-Munsell 100 test is a vision test whose objective is to evaluate the test participant's ability to identify and order colors with minimal differences in hue, considering value and chroma constants [30]. The Munsell color system describes the color hue values used in the test and is often used to test for color blindness [31]. The most common initial configuration is to use 100 hue values grouped into four blocks of 25 colors distributed horizontally, but other values are possible. Each block has two reference colors at the ends, and they are fixed (Figura 3a). These colors should guide the test participant in ordering the other colors of the set, and each block is presented individually [24; 32]. Currently, the test can be found in both physical and digital versions. After applying the test, the error counting stage begins, identifying colors positioned incorrectly in each color block (Figura 3b). The greater the distance of the color from its original position, the greater the error value.