(patent pending)


This paper discloses a method and means to forestall the formation of lines along certain directions, particularly horizontal and vertical directions, on a pixelized image display, as there exists in street advertising boards (mostly), airport and train station announcing boards (to a lesser degree), computer monitors and TV displays (almost imperceptible), and other displays characterized by pixelized " dots " which are generally arranged along rows and columns. Of these, the street advertising boards are the most conspicuous example of the offending characteristic, being the ones where the lines are most visible (see figure 1). Indoor information display boards, as in airport and train stations, have smaller pixels, and therefore the lines are less obvious than the lines on public advertisement billboards, and then computers and TV displays are nowadays produced with so small pixels that they are hardly perceptible.

BACKGROUND OF THE DEVICE — field of technology

This device relates to the field of display devices, particularly active display devices, formed by small light emitting elements (pixels), the aggregate of which forms a display image, including characters, and in particular to the displays which are organized in pixels distributed over the surface of the display device. The display surface may be flat or may be a 3-D (3 dimensional) surface, as a spherical surface, or a cylindrical surface, or some other 3-D surface.

BACKGROUND — Discussion of Prior technology

The field of pixelized displays has been characterized by displays which consisted of light emiting elements (pixels) arranged in repeating rows and columns, as a matrix, as seen in Figure 1 below.


            Figure 1a                             Figure 1b                             Figure 1c                             Figure 1d                     Figure 1e
    Click to see modules             Click to see modules             One single unit                 Board at left - detail       Simplified billboard
            in larger pic                       in larger pic               There are no modules           LED - Red-Green-Blue                                                
      Santa Monica Blvd.   Santa Monica Blvd. & Bundy       Santa Monica pier               Santa Monica pier           Sergio's head

                                                                            Click on any picture for an enlarged view of it

The rows and columns are usually evenly spaced. This choice of evenly spaced horizontally and vertically arranged pixels occurred because it is less expensive and easier to manufacture such a type of display on such an organized array than a display with randomly positioned pixels. An example of randomly placed pixels is, for example, the pixels on a pointillist painting by Georges Seurat, in which the individual dots were randomly arranged, besides being of variable size. Below is one of Seurat's paintings: " Dimanche a la Grande Jatte "


The reader may find it interesting to read the following simple article: simple article on Georges Seurat and the pointillism

Yet, the economic advantage of smaller price of manufacture comes at the price of decreased image quality , as there was a good reason, a very good reason indeed, for Seurat and the other pointillist painters never having used colored dots on evenly spaced rows and columns as current billboards displays do. But alas, theirs was a work of art, while pixelized LED bilboard displays are work of money! Still, one is tempted to improve the quality of displays made for money. At least we can improve today’s displays, while we could not improve Seurat’s paintings. Unfortunately LED billboards will never display any social commentary, at least none beyond the shallowness of its own message — which is a meta–commentary.

Figure 1 above shows examples of existing technology LED type of pixelized display. Figures 1a and 1b display actual pictures of street announcing billboards in Los Angeles, while Figures 1c and 1d display a smaller billboard (1c) including a close-up picture showing the individual LEDs (1d) with a cm scale. Then figure 1e shows an oversimplified display of the type used for outdoor advertisement, but one with a extreme smaller number of pixels for sake of simplification: 3 panels along the horizontal direction, 6 panels along the vertical direction, 5 by 2 pixels per panel - keep in mind that each of the pixels at figure 1e is a group of three LEDs, one red, another green and another blue (RGB), as in the picture to the left of it (Figure 1d). While this simplified display shown in figure 1e has 180 pixels, a real-life display has a few million to many million pixels. A vertically oriented displays shown at figure 1a and 1b are approximately 20 meters horizontally by 5 meters vertically (60 ft by 15 ft). The light emitting surface is composed of a large number of relatively small light emitters, typically three types of emitters, as shown in figure 1d, capable of emitting three distinct colors, typically red, green and blue (RGB). Appropriate combinations of each of these colors at a continuously varying light intensity of each of the three colors (RGB), is capable of creating a suitable variety of colored dots, the aggregate of which produces an image when viewed from and beyond a certain distance, which depends on the size of the pixels used for the display. The light emitters themselves are typically mounted on rectangular modules, which can be discerned from the street by the darkened streaks at the supporting frames, which may have a typical dimension of from 40 cm by 20 cm (see figures 1a and 1b). Inside each rectangular module the light emitters are arranged in rows and columns, and the total panel is formed by arranging the rectangles in rows and columns too. Therefore there are two levels of rows & columns: rectangular modules are arranged on a row & column array, and inside each module the LED's are also arranged on another row & column arrangement.

It is interesting to observe that it is widely known that horizontal and vertical lines are psychologically more disturbing then lines at an angle with the horizontal which is different than 0 dgs and 90 dgs. Of course that no straight lines is the most psychologically pleasing, this being why the architecture of Oscar Niemayer is what it is. These comments explain the underlying motivation for the changes we are proposing for the LED billboards.

This increased feeling of disturbance probably occurs because only modern man cause horizontal and vertical lines, which do not exit in nature at all, and H. sapiens brains developed before things were made in mass production just to make more money for some 1% in Beverly Hills or Park Avenue. Indeed, it is known from the work on the mechanism of vision, e.g. the collaborative work by Francis Crick and Christof Koch, that our brains detect straight lines in hardware, or, in other words, there are neural mechanisms that detonate signals when the image entering the brain contains straight lines. Note that this now known to be true automatic detection of straight lines is different than the detection of the letters, as you do while reading these astonishing statements, as it appears that letters are detected in software (but there is no proof that this is so, other than that there is not evolutionary time for the process of letter recognition to be done in hardware). Look at the following pictures, figure 2 below, which can be enlarged clicking on them. I suspect that they are enlargements of newspaper photos, from some old newspaper, in line with the theater being part of a museum, but I do not know for sure. They are pointillist in the sense that the image is made from dots, but in this case the dots (or points) are generated automatically according to the local darkness. They used to be at the Billy Wilder Theater, which is part of the Hammer Museum, in Westwood, but they are no longer there. It is very interesting that whoever made the system to determine the points was aware that horizontal and vertical lines are more disturbing than lines at an angle, so the system is such that the line of dots are at 45 dgs and 135 dgs with the horizontal, still mutually perpendicular, but not horizontal and vertical! The pixels are still arranged on an x-y grid but the grid is tilted by 45 dgs. Just look carefully. It is very interesting, very, very interesting. Don't ask me why the LED boards still organize the pixels along horizontal/vertical orientations, when it is well known that if these lines were at 45/135 dgs. it would be more pleasing to look at them.


            Figure 2a                                           Figure 2b                                     Figure 2c                                       Figure 2d

Advancing what is described in more detail below, the improvement we are proposing are (1) the use of variations from the rectangular module shape and hexagonal modules instead of plain rectangular modules, which breaks the darkened lines caused by the module's frames (lines 110h and 110v at figure 1e, also see figures 1a and 1b), running from side-to-side and from top-to-bottom of the displaying surface, and (2) a number of variations of the internal arrangement of the light emitting pixels within each module, which breaks the other type of streak on the light emitters, which is the vertical or horizontal linear continuation of the pixels from one module to the next. Note that our proposals for improvement on the LED billboards still lend themselves to mass production. This will be explained in the sequel.

Another example of disturbing perceptual feelings caused by the displayed image is shown in figure 3a below, where the yellow line, which is slightly off from the horizontal, is depicted as a stairway, causing a disturbing sensation on humans watching it. Note that the problem here is not the lack of sufficient resolution of the particular screen, because the resolution is the same across the whole screen but the coastline, which is displayed with the same resolution as the yellow line showing the airplane path, generates no uneaseness at all! Our proposed variation on the LED placement improves on this disturbing visual effect too.

Figures 3b, 3c and 3d are calculated illuminated red pixels from a straight X-Y pixel distribution (3b) and from a modified X-Y pixel distribution (3c) added to a random noise of so-many% (I forgot how much, having calculated it 2.5 years ago... :) , but I think it was 5% noise in the coordinate value). Than figure 3d shows both 3b and 3c on top of each other and also magnified for better comparison.


                                                                                                            Figure 3a


                                Figure 3b                                                     Figure 3c                                                         Figure 3d

                          Calculated red LEDs                           Calculated red LEDs                                       Both 3b and 3c together
                  on a perfect XY distribution               on an XY distribution with random noise           also magnified for better comparison


It is an objective of the device to decrease the inaccuracies and imperfections introduced in images produced by light emitters regularly organized in rows and columns, particularly the artificially produced visible continuous lines of light, particularly along the horizontal and vertical directions, which are common in current technology of lighted displays.


As explained above, the causes of the streak lines across the LED billboards stem from two main causes, namely (1) the continuation of the necessarily darker borders around the rectangular modules, even if subtle, as seen in the actual pictures of street billboards shown at figures 1a and 1b above, and (2) the continuation, from edge–to–edge, of the identically positioned LEDs within each module, rectangular or not. The two problems being distinct, they require distinct solutions, so let us start with the first problem, the problem created by the frame continuation of the rectangular modules.

DETAILED DESCRIPTION streaks caused by the frames of the modules

There exists one simple solution that deviates so very little from the current billboards, which are depicted at figures 4b and 4c, that it should be mentioned first. This simpler solution has the advantage of requiring less modifications on the current system, though they lack completeness. Figure 4a depicts the module arrangement in all the existing street billboards, for all the the author know. There are two slight variations, as seen in figure 4b and 4c, which consists of moving each alternate row (or column) to the midpoint line of the previous row (or column). In these two figures, 4b and 4c we have added a smaller rectangle on the top–left corner to fill–in the vacant space, making an overall rectangular displaying surface. Such filler–ins may, and perhaps should, be used throughout the billboard, to produce a perfect rectangular surface, as expected by the viewers, but the fillers–in are just a variation and improvement on the main design, which consists of breaking the lines of the frames, so we do not develop on them here. Other variations are possible, e.g. , displacing the rows (or columns) by less than half of their dimension, or by more than half of their dimension, as in figure 5a and 5b below. Doing so it causes that the positional repetition of the edges becomes further away, so it may be claimed to be superior to displacing the row (column) by half of its dimension. We do not want to enter in such fine discussions here, but only leave it as a possibility which, like many others, as mix and match, as medium-sized regions of 4b type next to other medium sized regions of 4c type, and more, all of which are a trade–off between the difficulty of implementing it and the advantage obtained from implementing it. The disadvantage of this simpler solution is that it can break either only the vertical lines (4b) or only the horizontal lines (4c), but not both.


                  Figure 4a                                         Figure 4b                                     Figure 4c

A more complete solution to the first problem of continuing frame lines across the image surface is to use regular hexagonal modules instead of the current choice of rectangular modules. Figure 5 below show this preferred geometry. Hexagonal modules have been proposed before, though the author have never seen any such hexagonal modules.


                                                                                                        Figure 5
                                                                                                Hexagonal modules

Any other possibilities? Mathematics teach us that there are only three regular geometric figures that fill the space: regular, or equilateral triangles, rectangles, and regular or equilateral hexagons. Squares also fill the space, and I am not counting them because they are a special case of the rectangles, when the sides happen to be equal. We are now discarding the equilateral triangles because they are a subset of the hexagons, which are a particular combination of 6 equilateral triangles around a common point, which is the center of the hexagon. It is possible, though, to use triangles for all that we are proposing with the hexagons; we just made a choice to disregard them for simplicity. Before leaving the equilateral triangles in the dust we want to leave it recorded that we are aware that they create less problems at the billboard edges than the hexagons create, because triangles are simpler geometric figures than the hexagons are. At the same time, triangular modules, though geometrically possible, do increase the ratio of the perimeter to the surface area, which should be decreased for best results, because the perimeter do create darker lines. And, of course, as it is well known in mathematics, among the set of regular polygons, the larger is the number of sides the smaller is the total perimeter for a given fixed area, and consequently, for any given fixed total billboard area, the triangles do create a longer total accumulated line of frames around them than the hexagons do, which is a disadvantage of triangular modules over hexagonal modules.

It may be asked now if there are any other possibilities that involve irregular polygons. It is, of course, completely possible to fill any given surface with arbitrarily shaped polygons . One example of this are the small paving stones covering the sidewalks in many older cities in Europe and South America today, and old Roman and Inca roads in Europe and South America (and in other places too). One example of small paving stones is the famous Copacabana beachfront, designed by Burle Marx, great artist he was, as seen here, next to the sitting statue of the great poet and writer Carlos Drummond de Andrade: CopacabanaSidewalk1 , CopacabanaSidewalk2 . Also many old walls in Europe and elsewhere are made with arbitrarily shaped stones, as this old stone wall at the fortress Knin, in Croatia , and this old barn . Both cases sometimes include a masonry filler, but this is not necessary if the worker were to invest enough time to fit each stone to the exact shape of the existing hole contour, as I have seen myself being done in Copacabana. Therefore it is possible to use arbitrarily shaped modules to fill in the billboard surface. But these are not acceptable from the industrial perspective, because industrial production requires boring repetitive mass-produced modules, not beauty and human warmth, so we sadly discard this possibility which we prefer. The next question is then if there are any other irregular polygon shaped modules that are easily produced industrially and that fills the displaying surface. The answer to this is yes, as per figures 5b, 5c, 5d and etc. These are just a few out of an infinite number of shapes. Figures 5e, 5f and 5g display a possible solution for the module frame continuity that uses the lateral displacement shown in figure 4b, it being just a variation of figure 4b, which already prevents up-and-down frame lines on the billboard, to which it is added a modified top and a matching modified bottom on each module, so modified as to match the neighboring modules, as a male-female pair. In this case displayed at figure 5e, 5f and 5g, each row of modules is upside-down with respect to the row above it and to the row below it - but this is not required for all cases. In some cases a single module that is flipped is sufficient, other cases require two different modules or more than two. The resulting array of modules shown in figures 5e to 5m does fill all the billboard area and shows no continuous line across the surface along any direction. These modules can also be mass produced and it is easy to program. The variations at the top and bottom sides have to be tilted more than approximately 10 dgs to forestall the line continuation, but this is just a subjective ballpark figure, not science. There are other variations on the same theme, smaller or larger modifications of the variations shown here at figure 5. We believe that the best solution is the smaller departure from the rectangular module that is capable of breaking the line continuation accross the display surface or the hexagonal module.


            Figure 5a, 5b                     Figure 5c, 5d                     Figure 5e, 5f, 5g                     Figure 5h, 5i, 5j                     Figure 5k, 5l, 5m

DETAILED DESCRIPTION streaks caused by the alignments of the individual LEDs

Having disposed of the first problem, which is the line continuation at the frame edges, we now turn our attention to the second problem, which is a possible clever LED arrangement within each module for the amelioration of the image quality of the LED billboards. Our quest for a better LED arrangement ought to stay within the boundaries dictated by the industrial production and perhaps within the boundaries set by the computer, and also the time to write the code. As an introductory remark we note that the objective here is to disrupt the continuation of the position of the LEDs, and that, given that the distance between the LEDs is small, the position disruption ought to be also small, a slight deviation from an ideal arrangement.

Before we start the description of the LED arrangement within the modules. we want to discuss the possibilities that are available. We will discuss the possibilities assuming circularly shaped LED groups (pixels), which is not the case, as they often are square-shaped or rectangularly-shaped, as per figure 1d, which is a close-up of the small board shown in figure 1c, but this can be trivially adjested as needed. So, let us continue assuming circularly-shaped LEDs, keeping in mind that an adjustment will be required at the end.

Confining ourselves to densely packed circles, there are two geometric arrangements that are most suitable (others are possible too, but we will confine ourselves to these two arrangements). These are the checker-board arrangement and the hexagonal-close-packed arrangement. They are shown in figure 6a and 6b below. Note that figures 6a and 6b revert to the rectangular module, which we chose to allow the reader to concentrate on the LED arrangements. Our best proposal uses either a modified rectangular module, or a hexagonal module, not a regular rectangular module.

Figure 6a displays the checker-board arrangement, which mimic a checker-board or a chess-board. Figure 6a displays a simplified billboard with rectangular modules arranged in 6 rows and 3 columns, each module with 18 LEDs arranged on 3 rows by 6 columns. Figure 6b displays the hexagonal-close-packed arrangement (HCP), so called because it is the arrangement that packs the maximum number of circles possible in a fixed surface area. In an HCP arrangement, the center of each circle is in the centerline of the line above and of the line below it. In this simplified, idealized billboard there are 18 modules organized on a 6 rows by 3 columns arrangement, each module with 17 LEDs arranged on a 3 rows by 5 or 6 columns arrangement.


                                                                                Figure 6a                                       Figure 6b
                                                              LED Checkerboard arrangement         LED HCP arrangement
                                                                                            Click to see enlarged figures

Of course that the reader will not be impressed at all after looking at the figure 6 above. After all, the HCP (Hexagonal Close Packed) arrangement still suffers from horizontal continuation of LED from board to board, so, is it worth? The answer to this comes naturally if one looks at the same checkerboard and HCP LED distribution, but now within hexagonal modules, as shown below in figure 7.


                                                                                Figure 7a                                       Figure 7b
                                                              LED Checkerboard arrangement         LED HCP arrangement
                                                                                            Click to see enlarged figures

The reason for the improvement of the image quality at figure 7 when compared with figure 6 is that on a hexagon of side l, the vertice-to-vertice distance is 2 * l (2 times l), actually 2 * l * cos (60 dgs) + l, while the distance from side-to-side is 2 * l * cos (30 dgs.) = 1.732 * l. It follows that the vertical and horizontal dimensions of the hexagonal modules are incomensurate. Now, looking at the modules as columns, each column of hexagonal modules is vertically displaced with respect to its neighboring column of hexagonal modules by exactly half of the height of each module (that is, by l * cos (30 dgs.) = 0.866 * l. If the reader inspect the rows, the LED row at the center of any module, running from vertice-to-vertice, does not continue the LED row at either side neighbor, which is valid for both cases, the checkerboard and the HCP.

With this we come to a closing of the solution to the second problem, which is the problem of the alignment of the individual LEDs. We then bring together here a simplified figure of the exiting displays and an also simplified drawing of our proposed improvement with both the hexagonal module and the HCP pixel arrangement. The reader is requested to look at a repetition of figure 6a and of figure 7b, side-by-side, and to make his/her own conclusion.


                                                                                Figure 6a                                       Figure 7b

The reader may now be wondering about the possibility of mixing these variations, with the objective of causing more changes on the pattern of pixel distribution. Of course that it is perfectly possible to built a billboard such that some modules are populated with LEDs distributed as an HCP while other modules are populated with LEDs distributed as a checkerboard. One such implementation is seen here, figure 8a which is implemented on an hexagonal module, but it could be implemented on a rectangular module equally well. Other possibility is to rotate the HCP-populated hexagonal modules by + or - 60 dgs, which causes another degree of relative positional variation from one pixel group to another. Such a variation is seen here, figure 8b , also implemented for a hexagonal module but that could be applied to a rectangular module as well. Then finally, it is possible to built modules populated by LEDs that are partly arranged as checkerboard and partly arranged as HCP. Internal combinations of checkerboard and HCP can be made with various fractions of each, and they can also differ by the order they appear, which then create a very large number of differences between each module.


                                                                                Figure 8a                                       Figure 8b
                                                        Combination checkerboard with HCP     All HCP with some rotated HCP
                                                                                            Click to see enlarged figures

Our proposal, based on an analysis of the numerous possibilities explained above, is that the best visual effect is obtained with either hexagonal or modified rectangular modules populated with either HCP or a mixture of HCP and checkerboard arrangements of LED. If the modules are of the hexagonal type, then, upon assembly, some of these will be tilted by +60 dgs, others by -60 dgs, others not tilted, see Figure 8b , which then creates three variations on the pattern, adding to the effect of the interruptions of the light emitter lines, and that this is enough to cause a better image when compared with the existing LED billboards. We propose it, as a balance between the complexity of implementation and image improvements obtained. Given that quality of image is a subjective evaluation, other implementations will be implemented, including the ones we discussed above, but not limited to them, alone or in combination, with our best choice of Hexagonal modules with HCP pixel arrangement.

Another possibility, which is described in the patent application which is already allowed and will issue soon, is to use what we call pseudo-HCP and pseudo-checkerboard, either alone or in combination. We call a pseudo-whatever an arrangement that breakes the regular whatever arrangement by a small but non-negligible distance, therefore disrupting the otherwise regularity. This is already described in our patent to issue soon (around November 2015) and hopefully will be added here before that.


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