Multi-primary display mask-based dithering with low blooming sensitivity

Abstract

To provide multi-primary display mask-based dithering with low blooming sensitivity.SOLUTION: Methods for driving color electrophoretic displays include a plurality of display pixels capable of producing a set of primary colors. The method comprises defining a separation cumulate threshold array, and using the separation cumulate threshold array to identify areas of the electrophoretic display that are better suited for dithering and areas for not dithering areas of the electrophoretic display that exceed the separation cumulate threshold. In one embodiment, the primary colors are cyan, yellow, magenta, and black.SELECTED DRAWING: Figure 6

Description

[Technical Field]

[0001] (Related Applications) This application claims priority to U.S. Provisional Patent Application No. 63 / 276,048, filed November 5, 2021. All patents and publications disclosed herein are incorporated by reference in their entirety.

[0002] The present invention relates to a method and apparatus for rendering color images. More particularly, the present invention relates to a method for multi-color dithering, in which a combination of color intensities is converted into a multi-color surface coverage. [Background technology]

[0003] The term "pixel" is used herein in its conventional sense in the display art to mean the smallest unit of a display that is capable of producing all the colors that the display itself can show.

[0004] Halftoning has been used for decades in the printing industry to represent shades of gray by covering varying percentages of each pixel of white paper with black ink. Similar halftoning schemes can be used with CMY or CMYK color printing systems, where the color channels are varied independently of each other. That is, at each pixel of white paper, any one of the colors (e.g., CMY, e.g., CMYK) can be printed independently at that pixel of the white paper without affecting neighboring pixels.

[0005] However, there are known color systems in which each pixel can display any one of a limited set of primary colors (such systems may hereafter be referred to as “limited palette displays” or “LPDs,” which may be CMY or RGB), but the color channels cannot be varied independently of each other; having a particular color in a first pixel affects the color (i.e., color quality) relative to a target color in one or more immediately neighboring pixels. Such behavior is observed in electrophoretic color displays (EPDs), where the electric field of a first pixel affects the target color in immediately neighboring pixels. This phenomenon is generally known as “blooming.” To some extent, in color EPDs, colors can be spatially dithered to produce the correct color sensation.

[0006] An electronic display typically includes an active matrix backplane, a master controller, local memory, and a set of communication and interface ports. The master controller receives data via the communication / interface ports or reads it from the device memory. Once the data is in the master controller, it is converted into a set of instructions for the active matrix backplane. The active matrix backplane receives these instructions from the master controller and produces an image. In the case of a color EDP, on-device color gamut calculations may require a master controller with increased computing power. Rendering methods for color electrophoretic displays are often computationally intensive, and although the present invention provides a method for reducing the computational load imposed by rendering, as discussed in detail below, the rendering (dithering) step and other steps of the overall rendering process may still impose a significant load on the device computing system.

[0007] The increased computing power required for image rendering reduces the advantages of electrophoretic displays in some applications. In particular, the cost of manufacturing the device increases when the master controller is configured to implement complex rendering algorithms, as does device power consumption. Furthermore, the excess heat generated by the controller requires thermal management. Therefore, in at least some cases, such as when ultra-high resolution images or multiple images need to be rendered in a short period of time, it may be desirable to have an efficient method of dithering multi-color images. Summary of the Invention [Means for solving the problem]

[0008] In one aspect, a method of driving a color electrophoretic display has a plurality of display pixels in an array, each display pixel capable of displaying at least three primary colors, the method including receiving an input image, processing the input image to define a separation accumulation at each pixel, defining a separation accumulation threshold array, each element of the array being at least 2 pixels by 2 pixels in size and including a different separation accumulation threshold for each of the three primary colors, and sending instructions to each pixel to display the primary color corresponding to the first separation accumulation threshold exceeded by the separation accumulation at that pixel. In some embodiments, the primary colors at each pixel (i,j) are such that Λk(i,j)>T(i,j), but Λk -1For (i,j)≦T(i,j), the dither function is determined by y(i,j)=Pk. In some embodiments, the dither function uses a blue noise mask (BNM). In some embodiments, processing the input image is implemented by a lookup table. In some embodiments, the input image is passed through a sharpening filter before processing the input image. In some embodiments, the sharpening filter is a finite impulse response (FIR) filter. In some embodiments, processing the input image and generating a color separation accumulation includes using a barycentric coordinate method. In some embodiments, the primary colors are cyan, yellow, magenta, and black. In some embodiments, the primary colors are red, green, blue, and white. In some embodiments, the primary colors are white, red, green, blue, cyan, yellow, magenta, and black. The present invention additionally includes an electrophoretic display configured to perform the methods described above. In some embodiments, the electrophoretic display includes an electrophoretic material having a plurality of charged particles disposed in a fluid and capable of moving through the fluid under the influence of an electric field. In some embodiments, the charged particles and fluid are confined within a plurality of capsules or microcells. The present invention provides, for example, the following. (Item 1) 1. A method of driving a color electrophoretic display having a plurality of display pixels in an array, each display pixel capable of displaying at least three primary colors, the method comprising: receiving an input image; processing the input image to define a separation accumulation at each pixel; defining a separation accumulation threshold array, each element of said array being at least 2 pixels by 2 pixels in size and containing a different separation accumulation threshold for each of said three primary colors; sending instructions to each pixel to display the primary color corresponding to a first separation accumulation threshold exceeded by the separation accumulation at that pixel; A method comprising: (Item 2) The primary colors at each pixel (i,j) are Λk(i,j)>T(i,j) but Λk -1 If (i,j)≦T(i,j), then y(i,j)=Pk The method according to item 1, wherein the (Item 3) Item 10. The method of item 1, wherein the separate cumulative threshold array incorporates a blue noise mask (BNM). (Item 4) Item 1. The method of item 1, wherein processing the input image is implemented by a lookup table. (Item 5) Item 10. The method of item 1, further comprising passing the input image through a sharpening filter before processing the input image. (Item 6) Item 6. The method of item 5, wherein the sharpening filter is a finite impulse response (FIR) filter. (Item 7) Item 10. The method of item 1, wherein processing the input image and defining the separation accumulation includes using a barycentric coordinate method. (Item 8) Item 10. The method of item 1, wherein the primary colors are cyan, yellow, magenta, and black. (Item 9) Item 10. The method of claim 1, wherein the primary colors are red, green, blue, and white. (Item 10) Item 10. The method of item 1, wherein the primary colors are white, red, green, blue, cyan, yellow, magenta, and black. (Item 11) Item 1. An electrophoretic display configured to perform the method according to item 1. (Item 12) Item 12. An electrophoretic display according to item 11, wherein the electrophoretic material comprises a plurality of electrically charged particles disposed in a fluid and capable of moving through said fluid under the influence of an electric field. (Item 13) Item 13. An electrophoretic display according to item 12, wherein the charged particles and the fluid are confined within a plurality of capsules or microcells. [Brief explanation of the drawings]

[0009] The patent or application file contains at least one drawing executed in color.

[0010] [Figure 1] FIG. 1 of the accompanying drawings is an error diffusion model in accordance with the subject matter presented herein.

[0011] [Figure 2] FIG. 2 is an exemplary black and white dithering method using a mask in accordance with the subject matter presented herein.

[0012] [Figure 3] FIG. 3 illustrates various mask designs in accordance with the subject matter presented herein.

[0013] [Figure 4] FIG. 4 illustrates gamut color mapping according to the subject matter disclosed herein.

[0014] [Figure 5] FIG. 5 illustrates a multi-color dithering method using a mask in accordance with the subject matter disclosed herein.

[0015] [Figure 6] FIG. 6 illustrates a multi-color dithering algorithm using a mask in accordance with the subject matter disclosed herein.

[0016] [Figure 7] FIG. 7 is one embodiment of a mask design for multi-color dithering in accordance with the subject matter presented herein.

[0017] [Figure 8]FIG. 8 is one embodiment of a mask design for multi-color dithering in accordance with the subject matter presented herein.

[0018] [Figure 9] FIG. 9 is one embodiment of a mask design for multi-color dithering in accordance with the subject matter presented herein.

[0019] [Figure 10] FIG. 10 is an example of a mask design for multi-color dithering in accordance with the subject matter presented herein. DETAILED DESCRIPTION OF THE INVENTION

[0020] The present invention provides a method for driving a color electrophoretic display having a plurality of display pixels capable of producing a set of primary colors. The set of primary colors can be of any size, but will typically include at least four colors. By defining a separation accumulation threshold array, areas of the electrophoretic display that are above the separation accumulation thresholds can be not dithered, while areas of the electrophoretic display that are more suitable for dithering can be identified.

[0021] Standard dithering algorithms, such as error diffusion algorithms (where the "error" introduced by printing one pixel in a particular color different from the color theoretically desired for that pixel is distributed among neighboring pixels, thereby producing an overall correct color sensation), can be employed with limited palette displays. An extensive literature on error diffusion exists; for a review, see Pappas, Thrasyvoulos N., "Model-based halftoning of color images," IEEE Transactions on Image Processing 6.7 (1997): 1014-1024.

[0022] This application is a continuation of U.S. Patent Nos. 5,930,026, 6,445,489, 6,504,524, 6,512,354, 6,531,997, 6,753,999, 6,825,970, 6,900,851, 6,995,550, 7,012,600, 7,023,420, 7,034,783, 7,061,166, 7,061,662, 7,116,466, 7,119,772, 7,177,066, 7,193,625, 7,202,847, 7,242,514, No. 7,259,744, No. 7,304,787, No. 7,312,794, No. 7,327,511, No. 7,408,699, No. 7, No. 453,445, No. 7,492,339, No. 7,528,822, No. 7,545,358, No. 7,583,251, No. 7,602 ,374, No. 7,612,760, No. 7,679,599, No. 7,679,813, No. 7,683,606, No. 7,688,2 No. 97, No. 7,729,039, No. 7,733,311, No. 7,733,335, No. 7,787,169, No. 7,859,742 , No. 7,952,557, No. 7,956,841, No. 7,982,479, No. 7,999,787, No. 8,077,141, No. No. 8,125,501, No. 8,139,050, No. 8,174,490, No. 8,243,013, No. 8,274,472, No. 8,2 No. 89,250, No. 8,300,006, No. 8,305,341, No. 8,314,784, No. 8,373,649, No. 8,384 ,658, No. 8,456,414, No. 8,462,102, No. 8,514,168, No. 8,537,105, No. 8,558,78 No. 3, No. 8,558,785, No. 8,558,786, No. 8,558,855, No. 8,576,164, No. 8,576,259 , No. 8,593,396, No. 8,605,032, No. 8,643,595, No. 8,665,206, No. 8,681,191, No. 8 ,730,153, No.8,810,525, No.8,928,562, No.8,928,641, No.8,976,444, No.9,0 No. 13,394, No. 9,019,197, No. 9,019,198, No. 9,019,318, No. 9,082,352, No. 9,171,Nos. 508, 9,218,773, 9,224,338, 9,224,342, 9,224,344, 9,230,492, 9,251,736, 9,262,973, 9,269,311, 9,299,294, 9,373,289, 9,390,066, 9,390,661, and 9,412,314, and U.S. Patent Application Publication Nos. 2003 / 0102858, 2004 / 0246562, 2005 / 0253777, 2007 / 0091418, 2007 / 0103427, 2007 / 0176912, 2008 / 0024429, 2008 / 0024482, 2008 / 0136774, 2008 / 0291129, 2008 / 0303780, 2009 / 0174651, 2009 / 0195568, No. 2009 / 0322721, No. 2010 / 0194733, No. 2010 / 0194789, No. 2010 / 0220121, No. 2010 / 0265561, No. 2010 / 0283804, No. 2011 / 0063314, No. 2011 / 0175875, 2011 / 0193840, 2011 / 0193841, 2011 / 0199671, 2011 / 0221740, 2012 / 0001957, 2012 / 0098740, 20 No. 13 / 0063333, No. 2013 / 0194250, No. 2013 / 0249782, No. 2013 / 0321278, No. 2014 / 0009817, No. 2014 / 0085355, No. 2014 / 0204012, No. 201 No. 4 / 0218277, No. 2014 / 0240210, No. 2014 / 0240373, No. 2014 / 0253425, No. 2014 / 0292830, No. 2014 / 0293398, No. 2014 / 0333685, No. 2014 / Also related to Nos. 0340734, 2015 / 0070744, 2015 / 0097877, 2015 / 0109283, 2015 / 0213749, 2015 / 0213765, 2015 / 0221257, 2015 / 0262255, 2015 / 0262551, 2016 / 0071465, 2016 / 0078820, 2016 / 0093253, 2016 / 0140910, and 2016 / 0180777. These patents and applications may hereinafter, for convenience, be collectively referred to as the "MEDEOD" (Method of Driving an Electro-Optic Display) Application and are incorporated herein by reference in their entirety.

[0023] EPD systems exhibit certain peculiarities that must be taken into account when designing dithering algorithms for use in such systems. Inter-pixel artifacts are a common feature in such systems. One type of artifact is caused by so-called "blooming," in both monochromatic and colorimetric systems, where the electric field generated by a pixel electrode tends to affect an area of ​​the electro-optic medium wider than that of the pixel electrode itself, thereby, in effect, spreading the optical state of one pixel into part of the area of ​​an adjacent pixel. Another type of crosstalk is experienced when driving adjacent pixels results in a final optical state in the inter-pixel area that is different from that reached by either of the pixels themselves; this final optical state is caused by the average electric field experienced within the inter-pixel region. A similar effect is experienced in monochromatic systems, but because such systems are one-dimensional in color space, the inter-pixel region usually displays a gray color state intermediate between the states of the two adjacent pixels, and such intermediate gray color state does not significantly affect the average reflectance of the region, or it can be easily modeled as, in effect, blooming. However, in a color display, the inter-pixel regions can display colors that are not present in any of the adjacent pixels.

[0024] The aforementioned problems in color displays have serious consequences for the gamut and linearity of predicted colors by spatially dithering the primary colors. Consider attempting to generate a desired orange color using a spatially dithered pattern of saturated red and yellow colors from the primary color palette of an EPD display. Without crosstalk, the combination required to generate orange can be perfectly predicted in the far field using the laws of linear additive color mixing. Because red and yellow lie on the gamut boundary, this predicted orange color should also lie on the gamut boundary. However, if the aforementioned effects cause (for example) a bluish band in the inter-pixel region between adjacent red and yellow pixels, the resulting color will be much more neutral than the predicted orange. This results in a “dip” at the gamut boundary, or more accurately, a scalloping, since the boundary is actually three-dimensional. Thus, simple dithering approaches not only fail to accurately predict the required dithering, but may also attempt to generate an unavailable color (because the color lies outside the achievable gamut), as in this case.

[0025] It may be desirable to be able to predict the achievable color gamut through extensive measurement or advanced modeling of patterns. This may not be feasible when the number of device primaries is large or when crosstalk errors are large compared to the errors introduced by quantizing pixels to the primaries. The present invention provides a dithering method that incorporates a model of blooming / crosstalk errors so that the colors achieved on the display are closer to the predicted colors. Furthermore, the method stabilizes error diffusion when the desired color falls outside the achievable color gamut, because error diffusion would typically produce unbounded errors when dithering to colors outside the convex hull of the primaries.

[0026] In some embodiments, image replication may be performed using the error diffusion model illustrated in Figure 1 of the accompanying drawings. The method illustrated in Figure 1 begins with an input 102 and a color value x i,j is fed to the processor 104 and the color value x i,j is added to the output of the error filter 106 to obtain the modified input u i,j and the modified input u i,j may be referred to hereafter as "error corrected input color" or "EMIC". i,j is fed to the quantizer 108.

[0027] In some embodiments, processes that utilize model-based error diffusion can become unstable because the input image is assumed to lie within the (theoretical) convex hull (i.e., color gamut) of the primary colors, but the actual achievable color gamut is likely to be smaller due to gamut loss due to dot overlap. Thus, the error diffusion algorithm may attempt to achieve colors that are not actually achievable in practice, and the error continues to grow with each successive "correction." This problem can be prevented by clipping or otherwise limiting the error, but it has been suggested that this leads to other errors.

[0028] In practice, one solution would be to have a better non-convex estimate of the achievable color gamut so that the error diffusion algorithm can always achieve its target color when performing gamut mapping of the source image. It may be possible to approximate this from the model itself or to determine it empirically. In some embodiments, the quantizer 108 examines the primaries in terms of the effect that selecting each would have on the error, and the quantizer selects the primary with the least error (by some metric), if selected. However, the primaries fed to the quantizer 108 may be too close to the natural primaries of the system {P k} but the adjusted set of primary colors {P ~ k}, which allow the color of at least some neighboring pixels, and their influence on the pixel is quantized by blooming or other inter-pixel interactions.

[0029] One embodiment of the above method may use a standard Floyd-Steinberg error filter, processing pixels in raster order. Assuming a display is processed top-to-bottom and left-to-right, as is conventional, it seems logical to use the basic neighbors above and to the left of a pixel to calculate blooming or other inter-pixel effects, since these two neighboring pixels have already been determined. In this way, all modeled errors caused by neighboring pixels are accounted for, since right- and below-neighbor crosstalk is considered when those neighbors are accessed. If the model considers only the above- and left-neighbors, the adjusted set of primaries must be a function of the state of those neighbors and the primary color under consideration. The simplest approach is to assume that the blooming model is additive, i.e., the color shift due to the left-neighbor and the color shift due to the above-neighbor are independent and additive. In this case, only N-2 (equal to N × (N-1) / 2) model parameters (color shifts) need to be determined. For N=64 and below, these can be estimated from colorimetric measurements of checkerboard patterns of all these possible primary pairs by subtracting the ideal mixture values ​​from the measurements.

[0030] To take a specific example, consider the case of a display with 32 primaries. If only the top and left neighbors are considered, then with 32 primaries, there are 496 possible neighboring sets of primaries for a given pixel. Because the model is linear, only these 496 color shifts need to be stored, since the additive effect of both neighbors can be produced at run time without much overhead. So, for example, if the unadjusted set of primaries includes (P1...P32) and the current top and left neighbors are P4 and P7, then the modified primaries (P ~1···P ~ 32 ), i.e., the adjusted primaries fed to the quantizer are given by: P ~ 1=P1+dP (1,4) +dP (1,7) ; .... P ~ 32 =P 32 +dP (32,4) +dP (32,7) In the formula, dP (i,j) is an empirically determined value in a color shift table.

[0031] More complex pixel-to-pixel interaction models are, of course, possible, for example, nonlinear models, models that consider corner (diagonal) neighborhoods, or models that use non-causal neighborhoods in which the color shift at each pixel is updated as more of its neighborhood is learned.

[0032] The quantizer 108 receives the adjusted input u' i,j The adjusted primary colors {P ~ k}Compare and select the most appropriate primary color y i,k to the output. Any suitable method of selecting appropriate primaries may be used, for example a minimum Euclidean distance quantizer in linear RGB space, which has the advantage of requiring less computational power than some alternative methods.

[0033] y from the quantizer 108 i,k The output values ​​may be fed not only to the output but also to a neighborhood buffer 110 where they are stored for use in generating adjusted primary colors for subsequently processed pixels. i,j Value and output y i,j Both values ​​are fed to processor 112, which calculates the following: e i,j =u i,j -y i,j and passes this error signal to error filter 106 in the same manner as described above with reference to FIG.

[0034] However, in practice, error diffusion-based methods can be slow for some applications because they are not easily parallelizable: in this case, the next pixel output cannot be completed until the previous pixel's output is available. Alternatively, mask-based methods can be employed due to their simplicity; the output at each pixel depends only on that pixel's input and values ​​from a look-up table (LUT), which means that each output can be calculated completely independently of the others.

[0035] Referring now to Figure 2, an exemplary black and white dithering method is illustrated. As shown, an input grayscale image with normalized darkness values ​​between 0 (white) and 1 (black) is dithered at each output location by comparing the corresponding input darkness with a dither threshold. For example, if the darkness u(x) of the input image is higher than the dither threshold T(x), the output location is marked as black (i.e., 1); otherwise, it is marked as white (i.e., 0). Figure 3 illustrates several mask designs according to the subject matter disclosed herein.

[0036] In practice, when implementing multicolor dithering, it is assumed that the input colors to the dithering algorithm can be represented as a linear combination of multiple primary colors. This can be achieved by dithering in source space using the corners of the gamut, or by gamut mapping the input to the gamut of device space. Figure 4 illustrates one way to generate color separations using a set of weights Px. In this case, each color C is defined as follows:

number

[0037] where the partial sum of these weights is called the separated accumulation Λ(C):

number

[0038] In practice, dithering for multiple colors consists in intersecting the relative cumulative amounts of the colors with a dither function (e.g., the threshold array T(x) in FIG. 5). Referring now to FIG. 5, a method for printing with four different colored inks, C1, C2, C3, and C4, is illustrated here by way of example. In each pixel of the output pixmap, the color separation gives the relative proportions of each of the base colors, e.g., d1 for color C1, d2 for color C2, d3 for color C3, and d4 for color C4. In this case, one of the colors, e.g., C4, may be white.

[0039] The step of extending dithering to multiple colors consists in intersecting the relative cumulative amounts of colors Λ1(x)=d1, Λ2(x)=d1+d2, Λ3(x)=d1+d2+d3, and Λ4(x)=d1+d2+d3+d4 with a threshold array T(x), as shown in Figure 5. A dithering example for purposes of illustrating the subject matter presented herein is illustrated in Figure 5. In the interval where Λ1(x)>T(x), the output location or pixel region will be printed using the base color C1, in the interval where Λ2(x)>T(x), the output location or pixel region will display color C2, in the interval where Λ3(x)>T(x), the output location or pixel region will display color C3, and in the remaining interval where Λ4(x)>T(x) and Λ3(x)≦T(x), the output location or pixel region will display color C4. Thus, multi-color dithering as presented herein converts the relative amounts of d1, d2, d3, d4 of colors C1, C2, C3, and C4 into relative coverage ratios, which by definition ensures that the contributing colors are printed side by side.

[0040] In some embodiments, a multi-color rendering algorithm such as that illustrated in Figure 6 may be utilized in accordance with the subject matter disclosed herein. As shown, image data im i,jmay first be fed through a sharpening filter 702, which may be optional in some embodiments. This sharpening filter 702 may be useful in some cases where the threshold array T(x) or filter is less sharp than an error diffusion system. This sharpening filter 702 may be a simple FIR filter, e.g., 3x3, which may be easily calculated. Subsequently, the color data may be mapped and color separations may be generated using the methods illustrated in Figures 2-5. This color data may be used to index a CSC_LUT lookup table, which may have N entries per index, providing the desired separation information in a form directly required by the mask-based dithering step. In some embodiments, this CSC_LUT lookup table may be constructed by combining both the desired color enhancement and / or gamut mapping and the selected separation algorithm. Finally, the separation accumulation data is used in conjunction with a threshold array 710 to generate the output y to generate multiple colors. i,j The dithering results using various mask designs are illustrated in Figures 7-10.

[0041] In some embodiments, the threshold array T(x) or the mask used can be optimized to minimize the so-called blooming effect. Blooming occurs when dithering is used in an electrophoretic display, where the output at each pixel can spill over or invade neighboring pixels, affecting their optical state. This is very similar to "dot gain" in printing systems. In some cases, the blooming effect can cause the average color of the dithering pattern to differ significantly from the desired color predicted by averaging the colors in the pattern in a linear color space. In particular, the resulting color is often worse, which means that the total gamut of colors achievable on the display will be much smaller than the ideal gamut volume.

[0042] In practice, for the same amount of physical blooming, the problem can be more severe with higher-resolution backplanes (fewer pixels) because the total edge length per unit area is longer. One way to alleviate this problem is to double-up the pixels at the output so that the effective resolution is lower. In extreme cases, even larger groupings (i.e., superpixels) can be used until the edge artifact area becomes such a small percentage of the total area that the ideal color gamut is restored. This can be achieved by first downsampling the source image to half the display resolution, applying a nominal rendering system, and then upsampling by replication to the display resolution.

[0043] Alternatively, this problem can be solved in the dithering algorithm itself. In some embodiments, if pixels are allowed to be grouped in smooth areas with little detail, but not in areas with fine detail, this trade-off with resolution will be less severe. This can be achieved using a mask-based dithering system by clustering thresholds in a mask (instead of clustering output pixels). For example, if there is a sharp input image transition that occurs halfway between threshold clusters, it will be reflected in the output because some of the sharp change will be below the threshold and some above. In particular, bi-level text will always pass directly through the mask unchanged, without loss of detail.

[0044] In practice, a mask with blooming-reducing clustering can be achieved in several ways. One approach is to employ a non-clustered scattered-dot or blue-noise mask, defined on a rectilinear tile of pixels, creating a new mask twice as large, with each threshold element replicated to a 2x2 pixel area. Furthermore, this approach can be extended to any MxN, possibly rectangular, replication size. Alternatively, due to the strong human visual system sensitivity to horizontal and vertical spatial frequencies, it may be advantageous to create clusters using other periodic tiles rather than rectangular ones. For example, the same threshold cluster of five pixels total can be used to tile a mask with a spatial frequency of approximately 26.6 degrees (arctan(1 / 2)).

[0045] For further details of color display systems to which the present invention may be applied, the reader is directed to the aforementioned EPD patent (which also provides a detailed discussion of electrophoretic displays) and the following patents and publications: U.S. Patent Nos. 6,017,584, 6,545,797, 6,664,944, 6,788,452, 6,864,875, 6,914,714, 6,972,893, 7,038,656, 7,038,670, 7,046,228, 7,052,571, 7,075,502, 7,167,155, 7,385,751, 7,492,505, 7,667,684, 7,684,1 No. 08, No. 7,791,789, No. 7,800,813, No. 7,821,702, No. 7,839,564, No. 7,910,175, No. 7,952,790, No. 7,956,841, No. 7,982,941, No. 8 ,040,594, No. 8,054,526, No. 8,098,418, No. 8,159,636, No. 8,213,076, No. 8,363,299, No. 8,422,116, No. 8,441,714, No. 8,441,71 No. 6, No. 8,466,852, No. 8,503,063, No. 8,576,470, No. 8,576,475, No. 8,593,721, No. 8,605,354, No. 8,649,084, No. 8,670,174, No. 8, No. 704,756, No. 8,717,664, No. 8,786,935, No. 8,797,634, No. 8,810,899, No. 8,830,559, No. 8,873,129, No. 8,902,153, No. 8,902,49 Nos. 1, 8,917,439, 8,964,282, 9,013,783, 9,116,412, 9,146,439, 9,164,207, 9,170,467, 9,182,646, 9,195,111, 9,199,441, 9,268,191, 9,285,649, 9,293,511, 9,341,916, 9,360,733, 9,361,836, and 9,423,666, and U.S. Patent Application Publication Nos. 2008 / 0043318, 2008 / 0048970, 2009 / 0225398, 2010 / 0156780, 2011 / 0043543, 2012 / 0326957, 2013 / 0242378, 2013 / 0278995, 2014 / 0055840, 2014 / 0078576, 2014 / 0340736, 2014 / 0362213, Nos. 2015 / 0103394, 2015 / 0118390, 2015 / 0124345, 2015 / 0198858, 2015 / 0234250, 2015 / 0268531, 2015 / 0301246, 2016 / 0011484, 2016 / 0026062, 2016 / 0048054, 2016 / 0116816, 2016 / 0116818, and 2016 / 0140909.

[0046] It will be apparent to those skilled in the art that numerous changes and modifications can be made in the specific embodiments of the invention described above without departing from the scope of the invention. Accordingly, the entire foregoing description should be interpreted in an illustrative and not a limiting sense.

Claims

[Claim 1] The invention described in this specification.

Images