Quality Measurement of Existing Color Metrics using Hexagonal Color Fields

In the area of colorimetry there are many color metrics developed, such as those based on the CIELAB color space, which measure the perceptual difference between two colors. However, in software applications the typical images contain hundreds of different colors. In the case where many colors are seen by human eye, the perceived result might be different than if looking at only two of these colors at once. This work presents an alternative approach for measuring the perceived quality of color metrics by comparing several neighboring colors at once. The colors are arranged in a two dimensional board using hexagonal shapes, for every new element its color is compared to all currently available neighbors and the closest match is used. The board elements are filled from the palette with specific color set. The overall result can be judged visually on any monitor where output is sRGB compliant.


Introduction
In the software applications there are applications where several colors need to be compared in order to determine the color that better matches the given sample.For instance, in stereo vision the colors from two separate cameras are compared to determine the visible depth.In image compression algorithms the colors of neighboring pixels are compared to determine what information should be discarded or preserved.Another example is color dithering -an approach, where color pixels are accommodated in special way to improve the overall look of the image.For instance, in Floyd-Steinberg dithering [1] and Riemersma dithering [2] the color is compared to several existing matches and closest match is used; the difference between original color and used match is calculated and propagated to other pixels.
In order to measure the difference between the given colors, each of them has to be specified in a common system, usually referred to as color space.In computer applications it is very common to use RGB color space.However, since RGB color space is rather subjective in terms of specification, of which several exist (such as sRGB, see Rec. 709 [3]), several other color spaces were developed that are also thought to be more perceptually uniform (an important property for measuring color differences).The most commonly used formal color spaces are CIE XYZ, CIELAB and CIELUV [4].If the original color is specified in RGB color space and that specification is known, the color can be converted to CIE XYZ without losing precision through gamma correction and linear transformation [5].The transformation from CIE XYZ to CIELAB and/or CIELUV is made through a series of transforming functions (see [4] or [5]).Once the colors have been represented in CIELAB color space, several color difference equations exist (see [6], [7], [8] and [9]).
Alternatives to CIELAB and CIELUV in terms of perceptual accuracy exist, such as DIN99 color space [10] with its associated color difference formulas [11], ATD95 color space [12] and HCL color space [13].
The aforementioned color spaces and their associated metrics have their strengths and weaknesses (see [5] and [14]) in terms of quality and performance.In this work the focus is made on the quality factor in practical applications -where color metrics are used in typical software applications.There are recent works that evaluate the quality of the different color metrics based on specific sample data (see [6] and [15]).However, as much as scientific background is important for a given color metric, its practical application's  In the hexagonal field the order at which the cells are filled with the colors from the source palette is important and affects the final result.There is a finite but significantly large number of all possible ordering schemes on two-dimensional field, starting from linear schemes (from left to right, from top to bottom) to pseudo random ordering such as Hillbert Curve [16].In this work a radial ordering scheme was used -the initial cell was considered to be in the middle and its neighbors were filled in clockwise manner until the entire field has been filled or the colors from the source palette have been exhausted.

The analysis of resulting fields
Once the hexagonal color field has been generated using the approach described earlier, the resulting image was analyzed by (f) color metrics with the reference palette (g).
The above set of images was generated with the source palette with 1280 random colors on hexagonal field of dimensions 32x32.The experiments used the color metrics based on CIELAB [4], CIELUV [17] and HCL [13], and color difference formulae DIN99 [10], CIEDE2000 [9], and ATD95 [12].
strengths and weaknesses are of high priority to a software engineer.The experiments Quality Measurement of Existing Color Metrics using Hexagonal Color Fields 25 described in this work provide insight on how each color metric performs when working with colors typically displayed on a standard computer display.In the reality the human eye perceives a large variety of colors simultaneously and this work provides an alternative approach for testing the existing colors metrics with three or more colors at the same time.1 Palette Exhaust on Hexagonal Field In order to measure the quality performance of the given metric, a fixed palette of colors is given.The color values were specified using two techniques -first involved uniform distribution of red, green and blue values in sRGB color space and second using random color generation using linear number distribution.The colors were extracted from the palette one by one depending on the quality comparison described later on until all colors have been exhausted.The initial color that was looked for on the palette is gray (CIELAB coordinates corresponding to L*=50, a*=0 and b*=0).The different choice for the initial color produces different results and middle gray was selected as a reasonable average between the entire set of all possible colors.The colors were filled on a hexagonal two-dimensional field.The hexagonal shape of field cells was chosen over triangular or square shapes because it has the largest entropy of all three.The different entropy levels are illustrated on the Fig. 1.

Fig. 1 .
Fig. 1.The entropy of triangular (a), square (b) and hexagonal (c) cell shapes.The number of neighbors is marked with different colors to the given red cell in the middle.
The hexagonal field with unsorted reference palette is shown in the last image (only the first 1024 colors shown).The images were Quality Measurement of Existing Color Metrics using Hexagonal Color Fields 27 created by extracting colors from the original palette and filling the destination grid, starting from the center.Each color from the input palette is compared to the neighbor colors of the location where it will be placed and the best match is selected.It can be observed that the overall color distribution varies depending on the chosen color metric, although the observed image is similar (looks like a series of colored patches).The best color matching results appear closer to the center of the image and become worse to the edges as the remaining color options left in the source palette become sparse.The final score chart made by calculating the average of the human observant scores is illustrated on the Fig. 3.

Fig. 3 .
Fig. 3. Average score for the different color metrics using the experimental image set 1 as judged by 10 human observers.

Fig. 5 .3
Fig. 5. Average score for the different color metrics using the experimental image set 2 as judged by 10 human observers.