Keeping the design principles discussed in the previous Section in mind, two theoretical sub-pixel architectures were constructed.82 These new structures can be used for the multi-primary display due to employing more than three primaries.
The first architecture consists of hexagonal logical pixels. Each logical pixel is divided into six equal triangles as sub-pixels, with six primary colours, see Figure II/7. Three of the primary colours may be the common red, green and blue primaries (P1, P3, P5) and the additional ones may be chosen as other chromaticities (P2, P4, P6), e.g. yellow, cyan, and magenta, thus enlarging the colour gamut of the display. The arrangement on the right is the rotated version of the arrangement on the left (by 30 degrees counter-clockwise).
The logical pixel of the second architecture consists of seven sub-pixels of hexagon shape with seven colour primaries (Figure II/8). The shape of the whole pixel looks like a flower in which the chromaticities and the order of the six primaries (P1, P2, P3, P4, P5, P6) may be identical to the previous architecture. A seventh colour primary or even white sub-pixel may be placed in the middle (P7) to enhance the overall brightness of the display (indeed it will desaturate the colours, but for a special purpose it might be acceptable). In this case, the chromaticity of white should be carefully chosen to match the chromaticity of white generated by the additive mixture of the other six sub-pixels. Including an additional white colour primary is often used in recent DLP (Digital Light Projection) projection displays to increase output luminance.
Figure II/7. A possible six-primary architecture for sub-pixel rendering. Left: Original arrangement, right: original arrangement rotated by 30 degrees counter-clockwise
Figure II/8. Seven-primary architecture for sub-pixel rendering. Top: Arrangement of the primary colours, bottom: a sequence of sub-pixels taken from the architecture: this is the thinnest possible horizontal line containing all primary colours
If the pixels (consisting of 6 or 7 sub-pixels) are arranged in the way as shown in Figure II/7 and Figure II/8 then the display plane will be covered so that no neighbouring sub-pixels of the same colour will emerge, according to the design principle described in Section 2.1. Optimizing the chromaticities of the primaries for multi-primary display83 to achieve optimal balance between the appropriate peak luminance and the purity of colours the device is capable to exhibit, though out of the scope of this work, is a another valuable field regarding the multi-primary displays. Recently, colour appearance based approach has led to better results than considering simply the often confusing 2D representation of the CIE chromaticity diagrams colour gamut is usually measured on.84
Compared with other sub-pixel architectures, these new structures are claimed to have less colour fringe error (CFE) due to the possibility of a more uniform placement of the
primary colours on the hexagonal grid. (The result of a sample CFE calculation is shown in Table II/2 and will be discussed below more in detail.) Hexagonal structures have increased rotational symmetry and, thus, it is easy to avoid adjacent sub-pixels of the same colour on the grid. It is also possible to display thin grey or white lines in many directions, according to the design principle described in Section 2.3.
Table II/1. Comparison of the hexagonal architectures and the RGB-stripe layout
RGB-stripe Hexagon (6 prim.)
Hexagon (7 prim.)
Hexagon (6 prim. Rot.)
number of sub-pixels 324 300 304 312
MTF vertical 6 7.5 6 5
MTF horizontal 4.5 3.5 8 6
vertical addressability 12 15 38 25
horizontal addressability 9 18 16 12
The latter property of both new architectures makes the value of their MTF (defined in Section 2.2) higher than that of the common RGB-stripe, for many directions. Unlike for the case of the RGB-stripe, addressing neighbouring sub-pixels in case of the hexagon structures along an imaginary line will not result in colour blocks of the same primaries.
Consequently, displaying e.g. vertical black and white lines, sub-pixels can be used instead of whole physical pixels, such that half of the sub-pixels are lit in a pixel (e.g. P4 P3 P2
from one pixel and P5 P6 P1 from the upper right neighbouring pixel in Figure II/7).
A comparison of the vertical and horizontal MTF and addressability of the hexagon structures and classical RGB-stripe is shown in Table II/1, for the example shown in Figure II/9. Due to the dissimilar geometric covering properties of different polygons (triangles, rectangles and hexagons) it is not easy to compare these architectures. The first row of Table II/1 contains the number of sub-pixels in the same rectangular area for all layouts shown in Figure II/9 (first only the architecture is of interest, discard the rendered letters). For a reasonable comparison, we have included approximately the same number of sub-pixels (between 300 and 324) for each of the four sub-pixel layouts shown in Figure II/9. The second row of Table II/1 shows the vertical MTF of the four sub-pixel layouts.
According to the simplified definition of MTF to display devices (see Section 2.2), this is
the maximum number of vertical black and white line pairs in the rectangular area shown in Figure II/9. The third row of Table II/1 shows the horizontal MTF of the four sub-pixel layouts, similar to the vertical one. The fourth row of Table II/1 shows vertical addressability. This is the maximum number of displayable (thin) horizontal lines of any colour (including black and white), in different positions in the rectangular area shown in Figure II/9. The fifth row of Table II/1 shows horizontal addressability. This is the maximum number of displayable (thin) vertical lines, similar to the previous one.
As can be seen from Table II/1, the addressability of the RGB stripe is exactly twice as its MTF, for a given direction (vertical or horizontal) but the addressability of the hexagon patterns is usually higher than twice the MTF of the same direction. This feature of the hexagon patterns originates in the nature of the texture of triangles and hexagons. Unlike the grid of squares, triangles and hexagons cover the plane so that it is possible to represent thin lines not only at the centre of the logical pixels (surrounded by thick black lines in Figure II/7 and Figure II/8) but also between two such pixels, e.g. by using the rightmost sub-pixels of the left pixel and the leftmost sub-pixels of the right pixel.
Figure II/9. Sub-pixel rendered black Arial and Times New Roman “n” letters on white background. Arial letters are in the first row and Times New Roman letters are in the second row. Architectures: first column - original continuous image, 2nd column - RGB-stripe, 3rd column - six-primary, 4th column - seven-primary, 5th column - six-primary rotated.
For example in the arrangement depicted in Figure II/7, shifting the hexagonal pixel grid (designated by the thick black lines) by one sub-pixel, other hexagonal pixels can be formed, each of them comprising all of the 6 colour primaries. As pointed out above, this does not increase the MTF of the structure but it enables a more accurate spatial positioning of the lines.
It can also be seen that, for the case of the 7 primary hexagon structure, not only the whole “flower shape” can be used to represent rows but also the altering sequence of one and two sub-pixels involving all seven primaries (see the bottom part of Figure II/8). This in turn increases vertical addressability.
In Figure II/9, black sub-pixel rendered Arial and Times New Roman type lowercase letters “n” on white background are also shown. According to the concept of sub-pixel rendering, these letters “n” are composed of those sub-pixels only of which major part is inside the outline of the letter “n” (the geometric centres of the sub-pixels were consider) regardless of their primary colours. To quantify CFE for the four different layouts shown in Figure II/9, a calculation method will be applied, which is derived from the general formula of Eq. (II/1), for the special case of black letters on white background. Since the stroke width of the letters “n” is similar to the width of the logical pixels in all four layouts in Figure II/9, the colour fringe error (CFE) can be quantified by considering the number of sub-pixels of each of the different colour primaries inside the letters “n”. For minimum CFE, the number of sub-pixels of the different colour primaries should be equal inside the letters “n” to be able to produce “white” in the neighbourhood of the letters “n”. If these numbers are different from each other then there will be a chromatic difference between
“white” and the actual chromaticity of the background of the letter, corresponding to the concept of Eq. (II/1).
The percentage values of these numbers of sub-pixels of different colour primaries inside the letters “n” (related to the total number of sub-pixels inside the letters “n”) are listed in Table II/2, together with the mean percentage value, its standard deviation (STD), and the maximum deviation from the mean. Assuming an ideal case (thus ignoring sub-pixel rendering), the percentage values in any row should be equal, and the STD should be zero. Thus, these STD values can be considered as an alternate measure of CFE, for these special examples shown in Figure II/9. Concerning the rotational symmetry of the hexagon architectures it is not astonishing that they perform better than the RGB-stripe in this sense.
In the RGB-stripe layout the number of blue sub-pixels is almost twofold inside the letters
“n” compared to the red and green ones (designated by bold percentage values in Table
II/2). This causes a visible colour fringe error on the RGB-stripe based architectures. For all other architectures in Table II/2, the percentage values deviate less. They show a more uniform participation of the sub-pixels of different colour primaries inside the letters “n”.
As can be seen from Table II/2, the 7-primary architecture (see Figure II/8) has overall the smallest STD value (0.6) and it is for the case of rendering the Arial type. For the Times letter, however, the 6-primary architecture of the original arrangement performed the best (STD=0.9). It would be hard to adjudge the performance of the six and seven primary layouts compared to each other on the grounds of the above character rendering example.
They both seem to perform better for either font type (Times or Arial).
Table II/2. A sample CFE calculation. Number of sub-pixels of each of the different colour primaries inside the letters “n” (shown in Figure II/9) related to the total number of sub-pixels inside the letters “n” as percentage values. Numbers 1 to 7 in the second row represent the colour primaries, letters r, g, and b below these numbers are for the primaries of the RGB-stripe: red, green, and blue.
Percentage of the number of sub-pixels of the color primaries inside the letters “n” rendering was performed without low-pass filtering, only the basic concept was followed.
In practice, however, low-pass filtering is always applied to the RGB stripe architecture using sub-pixel rendering,70-72 for less CFE. By applying a 2D low-pass filtering to the hexagon architectures in more than one direction, it is expected that the visual performance of hexagon architectures would be further improved, especially for text rendering, but this is only a hypothesis based on the elemental calculations for the example shown.
From the above it can be concluded that adding more primaries to the modern displays and break up with the conventional arrangement of the building elements of the screen
besides the increased gamut sub-pixel rendering is also achievable that is predicted to outperform of the RGB-stripe in quality. In the next Section a rendering method is introduced that is equivalent to sub-pixel rendering but is an approach based on theoretic colorimetric considerations and the dedicated property of the HVS being more sensitive merely to intensity changes than to colour.