# ABANICCO: A New Color Space for Multi-Label Pixel Classification and Color Analysis
## 5 Methods
### Geometric Knowledge Generation  
The purpose of this step was to create a simplified color space for color classification and naming. We chose to work with CIELAB color space, due to its advantageous properties, as explained in Section 2.3. The first task was to find the exact location of the pure hues in the color wheel within the CIELAB color space. As color space dimensions are decorrelated, the luminance component is unnecessary for understanding a given color's chromatic content: this meant that we could discard the luminance dimension, and work on the reduced AB two-dimensional space. To find the location of the main crisp or pure hues in this reduced color space, we selected an example of a complete color wheel, including hue modifications. We calculated the double AB histogram, showing the location of the crisp hues. The resulting geometrical distribution radiated from a center point, as shown in Figure 2A. The skeletonization of the double histogram provided endpoints and branches following a circular path. Due to their disposition, the lines between the center of the dual histogram and each endpoint could be used to represent the bases of the pure chromogens. Figure 11 provides a better look at this representation. Once we knew where the pure bases were, the next task was to find the boundaries between them. We considered two options for locating the boundaries between the crisp color categories: angle bisectors and classification methods. Both were tried out before moving to the next step, to decide on the best approach. The classification methods were more complex to use, needed training, and took longer to provide results, and the obtained classifications were unsatisfactory, both in resulting boundaries and classes created. An example of these unsatisfactory boundaries applied to natural images was the obtained segmentations of a gradient of colors in Figures 22 and 23. We observed how the machine learning classifiers failed to create appropriate boundaries between the three present colors, each generating a single class of arbitrary length instead of the expected classes of set length obtained by the bisectors approach: these results, together with the simplicity and efficiency of the bisectors approach, explain why we chose it over other classification methods. The experiments carried out to determine the best method are described in Appendix A, and the obtained segmentation of the whole range of hues in Figures 22 and 23. Using angle bisectors, we obtained precise color regions that, for simplicity, were then grouped according to color perception, shape, CIELAB construction, and the Berlin and Kay theories [27; 33], in 10 groups: Green; Yellow; Light Orange; Deep Orange; Red; Pink; Purple; Ultramarine; Blue; and Teal. It is important to note that neutrals (black, white, and gray) and near-neutral brown were not present in this classification, as they are not pure chromatic colors. In the CIELAB color space, the pure hues are located far from the center, and are radially distributed. All modifications of these hues then fall gradually closer to the center, with the shades having lower luminance than the tints, and the achromatic colors falling in a gradient aligned on the L axis. This can be seen in the CIELAB diagram of Figure 1C. In our reduced AB space, this meant that the neutral colors, black, white, and gray were located in the center of the space. The shades and tones of orange, commonly named brown, were located close to the center, within the red, orange, and yellow areas. Figure 2 shows how this area corresponded to the lower left corner of the upper right quadrant in the AB space (consistent with the mixed range of yellows and reds), close to the L axis (due to theirnear-achromacity); therefore, brown shades could be aligned with any pure chromogen bases between red and warm yellow, depending on the angle and distance from the center. The final task was the incorporation of browns and neutral as two extra classes.