Dither matrix generation method

Abstract

To suppress the degradation of image quality due to patterns caused by lack of uniformity in an image in an area larger than the size of a smoothing filter, and graininess caused by lack of uniformity in an area smaller than the size of the smoothing filter.SOLUTION: A generation method of a dither matrix includes the steps of filtering the dot pattern with a predetermined number of dots using at least three smoothing filters with different filter sizes, calculating an evaluation value indicating the degree of density of each pixel in the dot pattern for each result of the filter processing, calculating a comprehensive evaluation value indicating the overall degree of density for each pixel on the basis of the evaluation value, specifying the position of at least one pixel determined to be sparse or dense in the dot pattern on the basis of the comprehensive evaluation value, and determining a threshold value of the dither matrix.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present invention relates to a method for generating a dither matrix. [Background technology]

[0002] The Void & Cluster method is known as a method for generating a dither matrix. In the Void & Cluster method, for example, a smoothing filter (averaging filter) such as a Gaussian filter is used to detect areas in a dot pattern where dots are concentrated and areas where dots are sparse, and based on the detection results, positions where dots should be added or removed are determined, and threshold values ​​for the dither matrix positions corresponding to those determined positions are determined.

[0003] For example, Patent Document 1 discloses a void and cluster method that uses two filters with different noise removal characteristics. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] Japanese Patent Application Publication No. 2019-126035 Summary of the Invention [Problem to be solved by the invention]

[0005] In Patent Document 1, two filters are used, but the size of each filter (in other words, the standard deviation) is fixed.

[0006] Therefore, it is not possible to detect a state (pattern) in which a region in the image lacks uniformity and is larger than the size of the larger filter (first filter).

[0007] Furthermore, it is not possible to detect a lack of uniformity (ie, poor graininess) in an area smaller than the size of the smaller filter (second filter).

[0008] In other words, it is difficult with conventional techniques to effectively address both density unevenness across the entire image and local graininess.

[0009] One object of the present invention is to provide a method for generating a dither matrix that can suppress deterioration in image quality due to patterns that occur when the image lacks uniformity in areas larger than the size of the smoothing filter, and deterioration in image quality due to poor graininess that occurs when the image lacks uniformity in areas smaller than the size of the smoothing filter.

[0010] Other objects of the present invention will become apparent to those skilled in the art by referring to the following exemplary aspects and best modes, as well as the accompanying drawings. [Means for solving the problem]

[0011] In order to facilitate an understanding of the outline of the present invention, the following examples are given of embodiments according to the present invention.

[0012] In an aspect according to the present invention, a method for generating a dither matrix includes the steps of filtering a dot pattern with a predetermined number of dots using at least three smoothing filters with different filter sizes; determining an evaluation value indicating the degree of sparseness or density of each pixel in the dot pattern for each result of the filtering; calculating an overall evaluation value indicating the overall degree of sparseness or density for each pixel based on the evaluation value of each pixel in the dot pattern obtained for each result of the filtering; identifying the position of at least one pixel in the dot pattern that is determined to be sparse or dense based on the overall evaluation value; and determining a threshold value at a position in the dither matrix that corresponds to the position of the identified pixel.

[0013] According to this aspect, by combining and using three or more smoothing filters of different sizes, it is possible to effectively address both density unevenness across the entire image and local graininess. Using multiple filters, for example, an extremely small filter of about the size of a dot, a filter slightly larger than that filter, or an even larger filter, can be appropriately combined to smooth the image, thereby making both repeating patterns across the entire image and local coarse grain texture less noticeable. An appropriate number (three or more) of smoothing filters may be selected from a larger number of smoothing filters.

[0014] By using the dither matrix generated in this manner, for example, for screening an input image, it is possible to reduce the overall density unevenness that occurs in response to the density (gradation) of the image, and also improve granularity.

[0015] Those skilled in the art will easily understand that the exemplified embodiments according to the present invention can be further modified without departing from the spirit of the present invention. [Brief explanation of the drawings]

[0016] [Figure 1] FIG. 1A is a diagram showing an example of a system for constructing a dither matrix generating device, and FIG. 1B is a diagram showing an example of the configuration of a dither matrix generating device. [Figure 2] Figure 2(A) is a diagram showing all the smoothing filters that are prepared, Figure 2(B) is a diagram showing examples of the minimum and maximum standard deviations, and Figures 2(C) to 2(F) are diagrams showing examples of smoothing filters that are used when selecting a smoothing filter to be used in accordance with the density of the dot pattern. [Figure 3] Figures 3(A) and 3(B) show the effect of suppressing density unevenness across the entire image, which occurs in response to the density (gradation) of the image, and Figures 3(C) and 3(D) show the effect of improving graininess. [Figure 4]FIG. 4 is a diagram showing examples of 17 smoothing filters (Gaussian filters) of different sizes. [Figure 5] FIG. 5(A) shows the dot pattern before filter processing, and FIGS. 5(B) to 5(E) show the dot patterns after processing by the first, fourth, eighth, and seventeenth smoothing filters. [Figure 6] FIG. 10 is a diagram showing an example of a dot array model for obtaining index values ​​required when selecting three or more smoothing filters to be used from among a plurality of smoothing filters. [Figure 7] 7(A) to 7(J) are diagrams showing the process of generating a dither matrix. [Figure 8] 8(A) to 8(I) are diagrams showing the process of generating a dither matrix following the process shown in FIGS. 7(A) to 7(J). [Figure 9] 9(A) to 9(G) are diagrams showing the process of generating a dither matrix in a modified example. [Figure 10] 10 is a flowchart illustrating an example of a procedure for generating a dither matrix using an improved void and cluster method. [Figure 11] FIG. 11A is a diagram showing the characteristics of a Gaussian filter, and FIG. 11B is a diagram showing an example of binarization of an image using a dither matrix. DETAILED DESCRIPTION OF THE INVENTION

[0017] The best mode described below is used to facilitate understanding of the present invention, and therefore, those skilled in the art should be aware that the present invention is not unduly limited by the embodiments described below.

[0018] (First embodiment) First, let us refer to Fig. 1. Fig. 1(A) is a diagram showing an example of a system for constructing a dither matrix generating device, and Fig. 1(B) is a diagram showing an example of the configuration of a dither matrix generating device.

[0019] 1A, a system for constructing a dither matrix generating device includes an image processing device 10, a control unit (processor) 30, and a memory 40. The image processing device 10 includes a dither matrix generating unit 20.

[0020] The dither matrix generating unit 20 includes the units (described later) shown in Fig. 1(B). Also, a program PRG that causes a computer to operate as the units shown in Fig. 1(B) is installed in the memory 40.

[0021] The control unit 30 controls the operation of the dither matrix generation unit 20 provided in the image processing device 10 in accordance with the program PRG.

[0022] As shown in FIG. 1(B), dither matrix generation unit (or dither matrix generation device) 20 has a dot pattern acquisition unit 100 that acquires a dot pattern to be processed, a filter unit 102 that has m smoothing filters F1 to Fm (here, m is a natural number of 3 or more), a filter selection unit 104, a sparse / dense evaluation value calculation unit 106, a sparse / dense overall evaluation value calculation unit 108, a dot addition / removal position identification unit 110, a dot addition / removal unit 112, and a dither matrix threshold setting unit 113.

[0023] The uneven density across the entire image can be thought of as a bias over a wider area, while the deterioration of graininess can be thought of as a bias over a narrower area. By selecting an appropriate size of smoothing filter, both types of bias can be effectively suppressed.

[0024] In other words, by preparing multiple smoothing filters of different sizes so that there is a filter with an appropriate standard deviation for any size area of ​​the dot pattern, and determining the pixels (pixel positions) at which dots are added or deleted in each filter to improve the bias in the dot arrangement, and by taking the results into consideration overall, it is possible to select relatively preferable dot positions for any size dot pattern area. Thus, it is possible to construct a dither matrix with excellent uniformity.

[0025] Therefore, in this embodiment, multiple filters are prepared in the filter unit 102, including a relatively large filter that can appropriately smooth out density unevenness across the entire area, and a relatively small filter that can improve localized deterioration of graininess.

[0026] In a preferred example, the dot pattern acquisition unit 100 acquires a dot pattern of the same size as the dither matrix. The size of the dither matrix is, for example, 256 x 256, but is not particularly limited. In this embodiment, the size of the dither matrix is ​​smaller than the size of the input image.

[0027] The filter selection unit 104 selects a filter of an appropriate size according to the density of the dot pattern acquired by the dot pattern acquisition unit 100 (it is preferable to select three or more filters), and performs filtering using the selected filter.

[0028] The sparse / dense evaluation value calculation unit 106 calculates an evaluation value indicating the degree of sparseness or denseness for each pixel for each output based on the output of each filter.

[0029] The sparse / dense overall evaluation value calculation unit 108 calculates an overall evaluation value by, for example, adding (summing up) the evaluation values ​​obtained based on the outputs of the filters for the same pixel.

[0030] The overall evaluation value is considered to be a value that indicates whether the output of any filter can be judged as sparse (or dense). Therefore, by using the overall evaluation value, it is possible to make a highly reliable (in other words, effective) judgment of sparseness / denseness that comprehensively considers the output of each filter.

[0031] The dot addition / removal position specification unit 110 determines the dot addition (or removal) positions based on the overall evaluation value.

[0032] The dot addition / removal unit 112 adds / removes dots.

[0033] The dither matrix threshold setting unit 113 determines the threshold value of the position on the dither matrix that corresponds to the pixel position of the dot pattern where a dot has been added or removed. Thereafter, the dot pattern acquisition unit 100 acquires the dot pattern where the number of dots in the dot pattern has been updated, and repeats the same process to generate a dither matrix.

[0034] The detailed operation of each unit will be described later (FIGS. 7 to 9).

[0035] Furthermore, the filter selection unit 104 is provided as needed, and has the function of selecting a filter to be used (a filter whose output is enabled) from among m filters F1 to Fm according to the density (tone) of the dot pattern.

[0036] It is preferable to provide the filter selection unit 104 when, for example, the value of m is a fairly large value (for example, 10 or more). Also, it is preferable that the number of selected filters is 3 or more.

[0037] It should be noted that the "smoothing filter" is also called an averaging filter, a blurring filter, etc., and may be simply referred to as a "filter" in the following description. A smoothing filter is a filter that has the function of blurring and smoothing an image. As the smoothing filters F1 to Fm, for example, a Gaussian filter can be used (however, the smoothing filters are not limited to this).

[0038] A Gaussian filter uses a normal distribution GD as shown in Figure 11(A) to weight neighboring pixel values ​​according to their distance from a pixel of interest, thereby blurring the image. The size of the Gaussian filter (the extent of spread or height of the normal distribution) can be expressed by the standard deviation σ. In the normal distribution GD, the range from -σ to +σ corresponds to approximately 68% of the entire distribution.

[0039] A dither matrix is ​​a matrix in which threshold values ​​for generating binary data for printing are set corresponding to each pixel of an image.

[0040] As shown in FIG. 11(B), when an image 500 with 256 gradations (gradation values ​​0 to 255) is input to a binarization processing device, the gradation value of each pixel is compared with the threshold value of the dither matrix DM corresponding to that pixel, and the presence or absence of a dot in the binary image 600 is determined based on the comparison result.

[0041] 11(B), if the "tone level of the input image is equal to or greater than the threshold value of the dither matrix," it is determined that a dot should be placed (black area), and if not, it is determined that a dot should not be placed (white area). When the size of the dither matrix is ​​smaller than the input image, as in this embodiment, the dither matrix is ​​arranged vertically and horizontally to determine the positions where dots should be placed and the values ​​where dots should not be placed.

[0042] Next, reference will be made to Fig. 2. Fig. 2(A) is a diagram showing all smoothing filters that are prepared, Fig. 2(B) is a diagram showing examples of the minimum and maximum standard deviations, and Fig. 2(C) to Fig. 2(F) are diagrams showing examples of smoothing filters that are used when a smoothing filter to be used is selected according to the density of a dot pattern.

[0043] In the example of FIG. 2(A), the filter unit 102 is provided with ten smoothing filters F1 to F10 (m=10) that have different sizes (in other words, standard deviations σ).

[0044] FIG. 2B shows an example of the difference in size (standard deviation σ) between the minimum size filter F1 and the maximum size filter Fm.

[0045] If σ1 is too small, the brightness value of each pixel will remain the same after smoothing, making it impossible to determine the degree of density for each pixel, and no valid evaluation value can be obtained. If σm is too large, the brightness of each pixel will be over-smoothed, making it similarly impossible to obtain a valid evaluation value. Therefore, in this embodiment, σ1 is set to about the dot size, and σm is set to about 1 / 6 to 1 / 4 times the size of the dot pattern (size of the dither matrix). However, this is merely an example, and the present invention is not limited to this.

[0046] Thus, the standard deviation σ1 of the minimum size filter F1 is minute, for example, 1 to 3 times the dot size, while the standard deviation σm of the maximum size filter Fm is considerably large, for example, 1 / 6 to 1 / 4 times the size of the dot pattern (size of the dither matrix).

[0047] When the difference in size between the standard deviations σ1 and σm is this large, it is preferable to select an appropriate smoothing filter to actually use depending on the density (tone) of the dot pattern.

[0048] For example, when the density of a dot pattern is low and there are few pixels with dots, even if filtering is performed using a small filter (e.g., a local filter with a standard deviation of about the dot size), there is little effect in blurring the dot pattern.

[0049] In other words, the brightness values ​​of pixels without dots before filtering remain almost unchanged after filtering. If a density evaluation is performed in this state, most of the many pixels without dots will be determined to be the most sparse, and no valid evaluation value will be obtained. Calculating an overall evaluation value using many ineffective evaluation values ​​as is will not produce a highly reliable result.

[0050] Therefore, in the example of Figure 2(C), when the density (gradation) of the dot pattern is low, filtering is performed selectively using relatively large filters of a certain size or more, and as the density of the dot pattern increases, relatively small filters are also used, and the number of filters is increased little by little (for example, stepwise or continuously).

[0051] In FIG. 2C, when the density (gradation) of the dot pattern is "low density," filters F8 to F10 with relatively large sizes are used.

[0052] In other words, when the density of the dot pattern is low, the average distance between dots is large and the dot pattern has many gaps, so a large filter that can "blur" a wide area is used, and relatively small filters that cannot be expected to produce a blurring effect are excluded from actual use.

[0053] When the dot pattern density is "medium density (low)," filters F4 to F10 are used. The number of filters used is four more than when the density is low.

[0054] When the dot pattern density is "medium density (high)," filters F2 to F10 are used. The number of filters used is two more than when the dot pattern density is "medium density (low)."

[0055] When the dot pattern density is "high density," all available filters F1 to F10 are used. The number of filters used is one more than when the dot pattern density is "medium density (high)."

[0056] In this way, by selecting an appropriate size filter (preferably three or more filters) from among a plurality of filters according to the density (tone) of the dot pattern and using them in combination, appropriate blurring processing can be achieved. This makes it possible to calculate highly reliable evaluation values ​​and overall evaluation values. Details of the calculation of evaluation values ​​and overall evaluation values ​​will be described later.

[0057] Next, let us refer to Fig. 3. Fig. 3(A) and Fig. 3(B) are diagrams showing the effect of suppressing density unevenness across the entire image, which occurs in response to the density (tone) of the image, and Fig. 3(C) and Fig. 3(D) are diagrams showing the effect of improving graininess.

[0058] "Global density unevenness" is a pattern that occurs when the dot arrangement in an image is not uniform in an area the size of the dither matrix. If the size of the dither matrix is ​​smaller than the size of the input image, the repeated pattern becomes noticeable across the entire image.

[0059] "Granularity" is a term that describes the uniformity of dot arrangement in a local region of an image (for example, a region that is much smaller than the size of the dither matrix). A local region in which the dot arrangement is uniform is said to have "good granularity," while a local region in which the dot arrangement is not uniform and a coarse granular appearance (coarse granular texture) is noticeable is said to have "poor granularity." Good granularity also means that the dot arrangement in the local region has a certain degree of randomness. When viewing something with good granularity, one gets the impression of a smooth texture, while when viewing something with poor granularity, one gets the impression of a rough texture.

[0060] As shown in Figure 3(A), when binarization is performed using a dither matrix generated by the conventional void and cluster method, a repeating pattern that appears across the entire image may become noticeable depending on the image density. In Figure 3(A), one unit of the repeating pattern that appears in the binary image 200 is circled with a dashed line and assigned the reference number 201.

[0061] As shown in Figure 3(B), when an image is binarized using a dither matrix according to the present invention (a method for generating a dither matrix using an improved void and cluster method), the uniformity of the binary image 202 is improved, and repeated patterns over a wide area become less noticeable.

[0062] As explained above, by selecting and combining filters of appropriate size (preferably 3 or more) corresponding to the density of the dot pattern, it is possible to effectively prevent repetitive patterns from occurring across the entire image, thereby improving density unevenness across the entire image.

[0063] In addition, in the binary image 200 produced by the conventional method shown in Fig. 3(C), the dot arrangement in the local region is not uniform, resulting in a noticeable coarse grain texture 203. Note that on the right side of Fig. 3(C), a circle indicated by a dashed line is drawn, and the coarse grain texture 203 is depicted within the circle; this is an enlarged view of the local region Z1 of the binary image 200. This is also true for Fig. 3(D).

[0064] As shown in Figure 3(D), when the present invention is applied, the dot arrangement in local areas of the binary image 202 is more uniform than in Figure 3(C), so the coarse grainy texture is less noticeable and the image has a smooth texture. In this way, the present invention also improves the graininess of binary images.

[0065] As explained above, the present invention can smooth an image by appropriately combining extremely small filters, for example, about the size of a dot, filters slightly larger than those filters, and even larger filters, thereby making localized coarse granular texture less noticeable and suppressing deterioration of graininess.

[0066] Next, reference will be made to Fig. 4. Fig. 4 is a diagram showing an example of 17 smoothing filters (Gaussian filters) of different sizes. Filter F1 is the filter with the smallest size, and filter F17 is the filter with the largest size. In the following description, filters F1 to F17 may be referred to as the first to seventeenth filters.

[0067] In Figure 4, 17 filters F1 to F17 are spaced apart so that their sizes can be compared. To clearly show the size differences, a high-brightness area is provided in the center of each square, which corresponds to the filter size. The larger the filter size, the larger the high-brightness area, resulting in an overall increase in brightness. Comparing the smallest filter F1 with the largest filter F17, the difference is clear.

[0068] Furthermore, in the example of Figure 4, in order to ensure that a smoothing filter of an appropriate size exists for any size area in the dot pattern, the sizes of each filter F1 to F17 are not determined randomly but are correlated with each other at a certain magnification.

[0069] That is, the size of the second filter F2 is set to a predetermined multiple (e.g., 1.3 times) the size of the first filter F1, the size of the third filter F3 is set to a predetermined multiple (e.g., 1.3 times) the size of the second filter F2, and so on, with the filter sizes being enlarged by a constant factor (however, this is a preferred example and is not limiting). In other words, the sizes of the multiple filters (at least three smoothing filters) are different by the same factor.

[0070] By using such a filter of the same size, it is possible to obtain a filter of a regularly varying size. This makes it possible to reliably prepare a filter of a size (standard deviation) appropriate for the size of the dot pattern area, regardless of the size of the dot pattern area. This makes it possible to prevent a decrease in the accuracy of the calculated evaluation value and overall evaluation value.

[0071] Next, reference will be made to Fig. 5. Fig. 5(A) shows the dot pattern before filter processing, and Fig. 5(B) to Fig. 5(E) show the dot patterns after processing by the first, fourth, eighth, and seventeenth smoothing filters.

[0072] Comparing the dot patterns after filter processing (Figs. 5(B) to 5(E)) reveals that the degree of smoothing varies considerably. For example, comparing the dot pattern after smoothing using the minimum-sized filter F1 (Fig. 5(B)) with the dot pattern after smoothing using the maximum-sized filter F17 (Fig. 5(E)), it is clear that the levels of smoothing (averaging) are extremely different.

[0073] In this invention, a combination of multiple filters with different smoothing effects is used. As explained above, in a preferred embodiment, filters of inappropriate sizes are excluded to prevent a decrease in the reliability of the evaluation values ​​related to sparseness / denseness and the overall evaluation value based on those evaluation values, and uniform dot arrangements are achieved both globally and locally, thereby improving image quality.

[0074] In Patent Document 1 mentioned above, two filters are used, but only one filter can handle repeating patterns across the entire image, and only one filter can handle localized coarse grained textures, and the size (standard deviation) of each filter is fixed, so it is not possible to perform the diverse and flexible smoothing processing of the present invention.

[0075] In this way, by appropriately selecting and using multiple filters of various sizes, it is possible to improve both the density unevenness and graininess across the entire binary image, thereby significantly improving the image quality of the binary image.

[0076] Next, reference is made to Fig. 6, which is a diagram showing an example of a dot array model for obtaining index values ​​required when selecting three or more smoothing filters to use from among a plurality of smoothing filters.

[0077] As explained above with reference to Figure 2, it is preferable to exclude filters that are too small in size depending on the density value of the dot pattern. In order to objectively determine which size of filter to exclude, some objective index is required.

[0078] As the density of the dot pattern increases, the dots become denser, and the distance between the dots (dot spacing) becomes shorter. Conversely, as the density decreases, the dots become sparser, and the dot spacing becomes longer.

[0079] Therefore, if the average value of the dot interval, which changes in response to density, can be identified objectively in some way, it is possible to identify the size of the filter to be excluded based on this index value.

[0080] However, since the actual dot arrangement is irregular and there are many gaps (white areas) between the dots, it is actually difficult to measure the dot spacing at a certain density.

[0081] Therefore, the following model is used to objectively identify the dot spacing when the dot pattern has a certain density and use it as an index value. Then, a reference value based on this index value is used to determine the "size (magnitude of standard deviation)" or "range of size (magnitude of standard deviation)" of the filter to be excluded. The above-mentioned "reference value" may be the index value itself, or it may be a value obtained by multiplying the index value by a predetermined coefficient (such as a coefficient representing a magnification).

[0082] A specific explanation will be given below. As shown in Figure 6, a dot pattern of a certain density is assumed, and the number of dots corresponding to that density is considered to be ideally densely arranged. In Figure 6, each dot is considered to be a circle 300.

[0083] Then, it is assumed that the circles are circles 300 of the same radius, and that the radius is as large as possible (in other words, the maximum), and furthermore, a model is imagined in which the circles are arranged so that they do not overlap and are as densely packed as possible within the dot pattern.

[0084] This model can be said to be an arrangement that realizes a plane tessellation (honeycomb structure) using circles.

[0085] 6 shows seven circles 300, with a virtual regular hexagon with diagonal lines overlapping the central circle. If we consider each circle as a regular hexagon, we can treat one dot pattern as a collection of regular hexagons arranged without any gaps.

[0086] In this case, the average area S of one dot is calculated. If the number of horizontal pixels of the dither matrix (equivalent to the size of the dot pattern) is W (pixels), the number of vertical pixels is H (pixels), the horizontal resolution is WR (pixels / inch), the vertical resolution is HR (pixels / inch), and the current density is D (expressed in the range of 0.0 to 1.0), then Dither matrix area = W × H ÷ (WR × HR) Number of dots in current density = D x W x H Average area per dot S = area of ​​dither matrix ÷ number of dots of current density =1.0 ÷ (WR × HR × D) This becomes:

[0087] That is, the area of ​​the hatched regular hexagon shown in Fig. 6 is the above S. In the following description, a non-negative square root will be written as "sqrt".

[0088] Here, if the radius of one circle is r, the length of one side of the regular hexagon is expressed as 2×r / sqrt3.

[0089] The area of ​​the triangle obtained by dividing area S into six equal parts is (2×r / sqrt3)×r×1 / 2. Therefore, S×(1 / 6)=(2×r / sqrt3)×r×(1 / 2). The radius of the circle, r, is given by: r=sqrt(sqrt(3.0)×S÷6)

[0090] As described above, the radius r of the circle increases or decreases in accordance with the increase or decrease in density of the dot pattern, and can be used as an index value corresponding to the average value of the dot interval for a certain density.

[0091] Then, by setting the size of the filter to be excluded to a predetermined magnification of this index value (i.e., the radius r of the circle) or less, or by specifying a size range using this index value, it becomes possible to clearly specify the filter to be excluded. Here, the magnification is preferably set to, for example, about "0.5 to 1.5".

[0092] For example, if density values ​​are classified into multiple levels and the appropriate magnification for each level is measured experimentally, once the density of the dot pattern is determined, the radius r of the circle representing the dot and the magnification to be used can be determined, and therefore the filter to be excluded can be uniquely determined.

[0093] In this way, by using the index values ​​obtained by the above model, it becomes possible to quickly select an appropriate number of filters to actually use from among a plurality of filters.

[0094] Next, reference will be made to Fig. 7. Fig. 7(A) to Fig. 7(J) are diagrams showing the process of generating a dither matrix. An example of a method of generating a dither matrix of the present invention using the void and cluster method will be specifically described below.

[0095] In Figure 7(A), an initial dot pattern is read. In Figure 7(A), an initial dot pattern is used in which two dots are placed at "arbitrary asymmetric positions." In other words, it starts with a low density. This is because low density makes density unevenness and graininess across the entire area more noticeable. However, it is also possible to start with a dot rate of 50%, as in the general void and cluster method.

[0096] Furthermore, the above expression "initial dot pattern at any asymmetric position" can be rephrased as "a pattern in which at least two dots are arranged in asymmetric positions with respect to a virtual point or line within the dither matrix."

[0097] If an initial dot pattern in which only one dot is arranged is used, depending on the position of the next dot, it may result in a symmetrical arrangement with respect to a virtual point or line (point symmetry or line symmetry), in which case regularity will occur in the dot arrangement. Therefore, to prevent this, it is preferable to arrange at least two dots in asymmetric positions and use this as the initial pattern. This reduces the possibility of regularity occurring in the dot arrangement.

[0098] 7B, 0 and 1 are set at positions in the dither matrix DM that correspond to two dot positions in the dot pattern. It should be noted that which of the two dot positions will be 0 (or 1) can be determined arbitrarily.

[0099] Next, as shown in Figures 7(C) to 7(E), the dot pattern is smoothed using three smoothing filters (low-pass filters for spatial frequency) a to c with different smoothness (sizes), resulting in smoothed dot patterns 410a to 410c. The brightness level at each dot position in the smoothed dot pattern is a value indicating the degree of sparseness / denseness at each dot position (void value or cluster value). In practice, it is preferable to use more filters, as shown in Figures 2 and 4, but for convenience of explanation, three filters are used. The filter to be used is selected by filter selection unit 104 shown in Figure 1(B).

[0100] Also, as shown in FIG. 7(F), in this state, the contents of the dither matrix DM do not change, and the state of FIG. 7(B) is maintained.

[0101] Next, as shown in FIGS. 7(G) to 7(I), an evaluation value of sparseness / denseness at each dot position of the dot pattern is calculated based on the smoothed outputs (i.e., void values ​​or cluster values) of the three filters. For example, a sparse / dense determination is made according to the degree of brightness at each dot position after filter processing, and here, ranking is performed according to the degree of sparseness (note that ranking according to the degree of denseness is similar to the following, and explanation of this case will be omitted). For example, the ranking is performed so that the higher the degree of sparseness, the lower the ranking. Because the range of values ​​that can be taken by the smoothed output of a filter varies depending on the size of the filter, the smoothed output of the filter can be normalized by ranking.

[0102] The ranking (a numerical value indicating the ranking) thus assigned is used as an evaluation value for sparseness / denseness. As a result, the first evaluation value matrices 420a-420c shown in Figures 7(G)-7(I) are obtained. This process is performed by the sparseness / denseness evaluation value calculation unit 106 shown in Figure 1(B).

[0103] In this embodiment, the sparse / dense evaluation value is calculated as a ranking indicating the degree of sparseness / denseness based on the smoothed output (void value or cluster value) of the filter. However, for example, the sparse / dense evaluation value may be calculated by weighting the smoothed output of the filter according to the size of the filter. By weighting, the smoothed output of the filter can be normalized. In other words, the sparse / dense evaluation value can be calculated as a value that does not depend on the size of the filter.

[0104] Also, as shown in FIG. 7(J), in this state, the contents of the dither matrix DM do not change, and the state of FIG. 7(F) is maintained.

[0105] Next, reference will be made to Fig. 8. Fig. 8(A) to Fig. 8(I) are diagrams showing the process of generating a dither matrix following the generation process shown in Fig. 7.

[0106] In FIGS. 8(A) and 8(B), the overall evaluation value calculation process is carried out following the processes in FIGS. 7(G) to 7(I) described above.

[0107] In other words, the evaluation values ​​for the same pixel in each evaluation value matrix are added (summed) for each pixel to calculate an overall evaluation value for sparseness / denseness. For example, if the evaluation values ​​are rankings, the sum of the rankings is calculated. The sum of the rankings indicates the overall evaluation value for sparseness / denseness. As a result, a matrix 430 is obtained in which an overall evaluation value is set for each pixel. This process is performed by the sparse / dense overall evaluation value calculation unit 108 in FIG. 1(B). If the evaluation value is a weighted value of the smoothed output of the filter, the weighted sum of the evaluation values ​​is calculated as the overall evaluation value for sparseness / denseness.

[0108] As shown in FIG. 8A, in matrix 430, in which the overall evaluation values ​​(in this embodiment, the sum of the rankings) of each pixel are set, the value in row 6, column 3 is "3 (shown enclosed in a thick line)," which is the smallest value, and therefore this pixel is determined to be the sparsest pixel. As a result, the positions at which dots are added (or removed) are identified. This process is performed by dot addition / removal position identification unit 110 in FIG. 1B.

[0109] Then, as shown in Figure 8(B), a dot is added to the pixel determined to be the sparsest in dot pattern 400, in other words, the top pixel (pixel position). When a pixel position determined to be the densest is identified, a dot is removed from that position. This process is performed by dot addition / removal unit 112 in Figure 1(B).

[0110] Next, as shown in Fig. 8(C), a dither threshold is set at a position in the dither matrix DM that corresponds to the position where a dot is added in the dot pattern. Here, a gradation value of "2" in the gradation range of 0 to 63 is set as the dither threshold. This process is performed by the dither matrix threshold setting unit 113 in Fig. 1(B).

[0111] Next, as shown in Figures 8(D) to 8(F), filtering is performed again. This results in smoothed (averaged) dot patterns 410a' to 410c'. In this state, the dither matrix DM remains unchanged as shown in Figure 8(G), and the state of Figure 8(C) is maintained.

[0112] As shown in FIG. 8(H), the same process is repeated until dots are set in all pixels of the dot pattern (in other words, until the dot pattern becomes all black).

[0113] This completes the dither matrix DM as shown in Fig. 8(I) In this way, a dither matrix is ​​generated that can suppress uneven density and deterioration of graininess across the entire area of ​​a binary image.

[0114] (Second embodiment) In the second embodiment, a modified example will be described in which multiple candidates for dot addition / removal are set when dots are added / removed based on a comprehensive evaluation value. See Fig. 9. Figs. 9(A) to 9(G) are diagrams showing the process of generating a dither matrix in this modified example.

[0115] Fig. 9A is a diagram corresponding to Fig. 8A described above. In Fig. 8A, a pixel in the sixth row and third column of a matrix in which numbers indicating comprehensive evaluation values ​​(total values ​​of rankings in the second embodiment) are set is determined to be the sparsest pixel.

[0116] In contrast to this, in FIG. 9A, a plurality of pixels (four in this example) that are considered to have the highest overall evaluation value (in other words, top candidate pixels) are selected.

[0117] In FIG. 9A, for example, first, a pixel (this pixel is designated as G1) having the lowest number indicating the overall evaluation value (the sum of the rankings in the second embodiment) of "3" is selected.

[0118] If multiple pixels with the next smallest number, "4," are selected, the dot positions will be concentrated, creating a pattern. Therefore, pixels are selected so that this concentration of dot positions does not occur.

[0119] For example, the numerical values ​​representing the overall evaluation values ​​of the pixels surrounding the pixel G1 are temporarily increased to prevent them from being selected as top candidates. Then, a pixel (let's say G2) with a lower numerical value that is located at a moderate distance and dispersed from pixel G1 is selected. Similarly, the numerical values ​​representing the overall evaluation values ​​of the pixels surrounding pixel G2 are temporarily increased, and a pixel (let's say G3) with a lower numerical value that is located at a moderate distance and dispersed from pixel G2 is selected. The same process is repeated again to select a pixel (let's say G4) that will be a top candidate.

[0120] Also, as shown in FIG. 9B, in this state, the contents of the dither matrix DM do not change, and the state previously shown in FIG. 7J is maintained.

[0121] Next, the four pixels selected as candidates are ranked, as shown in Fig. 9(C). The ranking can be done in ascending order of overall evaluation value (the sum of the rankings in the second embodiment), but since there may be no or only a small difference in the numerical values ​​of the selected candidate pixels, the rankings are randomly assigned to the four pixels.

[0122] In FIG. 9C, pixel G3 is ranked first, pixel G1 is ranked second, pixel G2 is ranked third, and pixel G4 is ranked fourth.

[0123] Next, as shown in Fig. 9(D), dots are added to the positions of pixels G1 to G4. Also, as shown in Fig. 9(E), threshold values ​​(tone values) are set in the dither matrix DM at positions corresponding to the positions where the dots have been added, according to the candidate ranking.

[0124] In the example of FIG. 9(E), threshold values ​​(tone values) of "2", "3", "4", and "5" are set at the positions of the dither matrix DM corresponding to the pixels G3, G1, G2, and G4.

[0125] In the second embodiment, a modified example was described in which four candidates were set as candidates for adding / removing dots, but the number of candidates set is not limited to 4. Also, similar processing can be performed even if the overall evaluation value is the weighted sum of the smoothed output of the filter.

[0126] In this way, in the modified example of FIG. 9, multiple thresholds can be determined at once, so the speed of the dither matrix generation process can be increased, and the generation time can be shortened.

[0127] Thereafter, as shown in FIG. 9(F), the same process is repeated until dots are set in all pixels of the dot pattern (in other words, until the dot pattern becomes all black).

[0128] This completes the dither matrix DM as shown in Fig. 9(G) In this way, a dither matrix is ​​generated that can suppress uneven density and deterioration of graininess across the entire binary image.

[0129] The processing procedure of the embodiment of the present invention has been described above using the first and second embodiments. An outline of this processing procedure is shown in Fig. 10. Fig. 10 is a flowchart showing an example of the procedure for generating a dither matrix using the improved void and cluster method.

[0130] In step S1, a plurality of smoothing filters (here, Gaussian filters) having different values ​​of standard deviation σ (in other words, different sizes) are prepared.

[0131] In step S2, an initial dot (initial dot pattern) is input.

[0132] In step S3, for example, Gaussian filters whose size is too small for the (average value of) dot intervals of the current density (tone) are excluded (in other words, deselected).

[0133] In step S4, the input dot pattern is filtered using the active Gaussian filter (in other words, the selected Gaussian filter).

[0134] In step S5, an evaluation value indicating the degree of dot sparseness / denseness is calculated for each filter based on the filter processing result (void value or cluster value) of each filter (evaluation value calculation process).

[0135] In step S6, the evaluation values ​​for each filter for each pixel are summed (added) to calculate a comprehensive evaluation value that indicates the overall degree of sparseness / denseness (comprehensive evaluation value calculation process).

[0136] In step S7, one or more positions (pixels) that are determined to be the most sparse / dense are determined, and these positions are set as positions for adding / removing dots, and dots are added to or removed from the input dot pattern.

[0137] In step S8, a threshold value is set (determined) for the position in the dither matrix corresponding to the added / removed dot position.

[0138] In step S9, it is determined whether threshold values ​​for all densities (all gradations) have been determined. If the answer is No, the process moves to step S10, and if the answer is Yes, the process ends.

[0139] In step S10, a dot pattern with a density for which a threshold has not been determined is input, and then the process proceeds to step S3.

[0140] As described above, one embodiment of the dither matrix generation method of the present invention includes the steps of filtering a dot pattern with a predetermined number of dots using at least three smoothing filters with different filter sizes; calculating an evaluation value indicating the degree of sparseness or density of each pixel in the dot pattern for each result of the filtering; determining an overall evaluation value indicating the overall degree of sparseness or density for each pixel based on the evaluation value of each pixel in the dot pattern obtained for each result of the filtering; identifying the position of at least one pixel in the dot pattern that is determined to be sparse or dense based on the overall evaluation value; and determining a threshold value at a position in the dither matrix that corresponds to the position of the identified pixel.

[0141] By combining three or more smoothing filters of different sizes, it is possible to effectively address both density unevenness across the entire image and localized graininess. By using multiple filters, it is possible to appropriately combine extremely small filters, for example, those about the size of dots, filters slightly larger than those filters, and even larger filters, to smooth the image, making both repeating patterns across the entire image and localized coarse grain textures less noticeable.

[0142] By using a dither matrix generated by this method, for example, for screening an input image, it is possible to reduce the overall density unevenness that occurs in response to the density (gradation) of the image, and also improve granularity.

[0143] In another embodiment of the present invention, in the step of obtaining an evaluation value for each pixel, the results of the filtering process may be ranked according to the degree of density, and the evaluation value may be obtained as a ranking. For example, the ranking may be such that the higher the degree of sparseness, the lower the ranking. Because the range of values ​​that the smoothed output of a filter can take varies depending on the size of the filter, the ranking can normalize the smoothed output of the filter.

[0144] In another embodiment of the present invention, in the step of calculating an evaluation value for each pixel, the evaluation value may be calculated by normalizing the results of the filtering process using weighting according to the filter size of each filter. By weighting, the smoothed output of the filter can be normalized, i.e., the sparse / dense evaluation value can be calculated as a value independent of the filter size.

[0145] In another embodiment of the present invention, in the step of calculating an overall evaluation value for each pixel, the evaluation values ​​of each pixel in the dot pattern obtained for each result of the filter processing may be added, and in the step of identifying the position of at least one pixel, the position of the topmost pixel that is determined to be sparse or dense may be identified based on the result of adding the evaluation values ​​of each pixel.

[0146] The evaluation values ​​obtained from each of the multiple filter processes are added (summed), and a pixel that is determined to be sparse or dense based on the sum (overall evaluation value) is a pixel that is determined to be sparse or dense regardless of the sparse / dense determination based on any of the filter process results. In other words, a pixel that is determined to be sparse or dense based on the overall evaluation value can be said to be a pixel that is suitable for being determined to be sparse or dense, taking into consideration the outputs of each filter overall. Therefore, a highly reliable (in other words, effective) sparse / dense determination is possible.

[0147] In another embodiment of the present invention, in the step of calculating an overall evaluation value for each pixel, the evaluation values ​​of each pixel in the dot pattern obtained for each result of the filter processing may be added, and in the step of identifying the position of at least one pixel, the positions of multiple pixels that are top candidates for being judged to be sparse or dense may be identified based on the overall evaluation value of each pixel.

[0148] In this embodiment, when dots are added or removed based on the overall evaluation value, multiple pixels that are considered to be sparse or dense based on the overall evaluation value (in other words, multiple pixels that are top candidates for being determined to be sparse or dense) are selected. This allows multiple dither matrix thresholds to be determined at once, which increases the speed of the dither matrix generation process and shortens the generation time.

[0149] In another embodiment of the present invention, once the threshold values ​​for a portion of the dither matrix have been determined, the dot pattern may be updated, and the steps of filtering, determining the evaluation value, calculating the overall evaluation value, identifying the position of at least one pixel, and determining the threshold values ​​for the dither matrix may be repeated until all threshold values ​​for the dither matrix have been determined.

[0150] This completes a dither matrix that can suppress uneven density and graininess across the entire area of ​​a binary image.

[0151] In another embodiment of the present invention, the initial dot pattern used when the step of filtering the dot pattern first begins may be a pattern in which at least two dots are arranged in asymmetric positions with respect to a virtual point or line within the dither matrix.

[0152] In this embodiment, a dot pattern with two dots arranged at arbitrary asymmetric positions is used as the initial dot pattern that is read when the dither matrix generation process begins. In other words, it starts with a low density. This is because low density makes density unevenness and graininess across the entire area more noticeable.

[0153] Furthermore, if an initial dot pattern in which only one dot is arranged is used, depending on the position of the next dot, it may result in a symmetrical arrangement with respect to a virtual point or line (point symmetry or line symmetry), in which case regularity will occur in the dot arrangement. Therefore, to prevent this, at least two dots are arranged in asymmetric positions, and this is used as the initial pattern. This reduces the possibility of regularity occurring in the dot arrangement.

[0154] Furthermore, in an embodiment of the present invention, when the at least three smoothing filters are m smoothing filters (m is a natural number greater than or equal to 3) and all the prepared smoothing filters are n smoothing filters (n is a natural number satisfying n>m), m smoothing filters to be used for filtering may be selected from the n smoothing filters prepared according to the density of the dot pattern.

[0155] When the density of the dot pattern is low and there are few pixels with dots, even if filtering is performed using a small filter (for example, a local filter with a standard deviation of about the dot size), there is little effect in blurring the dot pattern.

[0156] In other words, the brightness values ​​of pixels without dots before filtering remain almost unchanged after filtering. If a density evaluation is performed in this state, most of the many pixels without dots will be determined to be the most sparse, and no valid evaluation value will be obtained. Calculating an overall evaluation value using many ineffective evaluation values ​​as is will not produce a highly reliable result.

[0157] Therefore, in a preferred example, when the density (gradation) of the dot pattern is low, filtering is performed selectively using relatively large filters of a certain size or more, and as the density of the dot pattern increases, relatively small filters are also used, gradually increasing the number of filters (for example, in stages).

[0158] In this way, by selecting filters of appropriate size (preferably three or more filters) from among multiple filters according to the density (tone) of the dot pattern and using them in combination, appropriate blurring processing can be achieved, which makes it possible to calculate highly reliable evaluation values ​​and overall evaluation values.

[0159] In addition, in another embodiment of the present invention, when selecting a smoothing filter, an index value corresponding to the average value of the spacing between dots in the density of the dot pattern is obtained, and that index value itself or a value obtained by multiplying that index value by a coefficient is used as a reference value.The reference value is then compared with the size of each of the n smoothing filters, and smoothing filters with sizes smaller than the reference value are excluded, thereby selecting m smoothing filters.

[0160] In order to objectively determine which size of filter to exclude, some objective indicator is required.

[0161] As the density of the dot pattern increases, the dots become denser, and the distance between the dots (dot spacing) becomes shorter. Conversely, as the density decreases, the dots become sparser, and the dot spacing becomes longer.

[0162] Therefore, if the average value of the dot interval, which changes in response to density, can be identified objectively in some way, it is possible to identify the size of the filter to be excluded based on this index value.

[0163] However, since the actual dot arrangement is irregular and there are many gaps (white areas) between the dots, it is actually difficult to measure the dot spacing at a certain density.

[0164] Therefore, for example, the dot arrangement is modeled, and the dot spacing when the dot pattern has a certain density is objectively identified as an index value. Then, a reference value based on this index value is used to determine the "size (standard deviation)" or "range of size (standard deviation)" of the filters to be excluded. This makes it possible to objectively and unambiguously identify which filters to exclude.

[0165] In addition, in another embodiment of the present invention, when calculating an index value for the density of a dot pattern, the radius of a circle representing each dot, when assumed to be filled in a plane within the dot pattern with the same radius and maximum area, can be found, and that radius can be used as the index value.

[0166] In this embodiment, we assume that each dot is a circle of the same radius, and that the radius is as large as possible (in other words, the maximum), and further assume a model in which the circles are arranged so that they do not overlap and are as densely packed as possible within the dot pattern. This model can be said to be an arrangement that realizes a plane tessellation (honeycomb structure) with circles.

[0167] The radius of the circle increases or decreases depending on the density of the dot pattern, and can be used as an index value corresponding to the average dot spacing for a certain density. Filters to be excluded can be clearly specified by, for example, setting the size of the filters to be excluded to a predetermined multiple of this index value (i.e., the radius of the circle) or by specifying a size range using this index value.

[0168] In another embodiment of the present invention, the sizes of at least three smoothing filters may be different but equal in size.

[0169] By using such a filter of the same size, it is possible to obtain a filter of a regularly varying size. This makes it possible to reliably prepare a filter of a size (standard deviation) appropriate for the size of the dot pattern area, regardless of the size of the dot pattern area. This makes it possible to prevent a decrease in the accuracy of the calculated evaluation value and overall evaluation value.

[0170] As described above, according to the present invention, it is possible to realize a dither matrix that can suppress deterioration in image quality due to uneven density across the entire image caused by a lack of uniformity in an image in an area larger than the size of the smoothing filter, and deterioration in image quality due to poor graininess caused by a lack of uniformity in an image in an area smaller than the size of the smoothing filter.

[0171] The present invention is not limited to the above-described exemplary embodiments, and those skilled in the art will be able to easily modify the above-described exemplary embodiments to the extent that they fall within the scope of the claims. [Explanation of symbols]

[0172] 10...image processing device, 20...dither matrix generation unit (dither matrix generation device), 30...control unit (processor), 40...memory, 100...dot pattern acquisition unit, 102...filter unit, 104...filter selection unit, 106...sparse / dense evaluation value calculation unit, 108...sparse / dense overall evaluation value calculation unit, 110...dot addition / removal position identification unit, 112...dot addition / removal unit, 113...dither matrix threshold setting unit, 200...binary image (image with noticeable density unevenness or graininess across the entire image), 202...binary image (image with noticeable density unevenness across the entire image) an image with minimal unevenness or graininess), 300··· a circle modeled with dots, 302··· an equilateral triangle formed by dividing a regular hexagon into six equal parts, 400··· dot pattern, 410a to 410c (410a' to 410c')··· smoothed (averaged) dot pattern, 420a to 420c··· evaluation value matrix, 430··· a matrix (overall evaluation value matrix) in which the overall evaluation value (a number indicating the overall ranking) of each pixel is set, DM··· dither matrix, F1 to Fm··· smoothing filters of different sizes, G1 to G4··· top candidate pixels (pixel positions), PRG··· program.

Claims

1. filtering the dot pattern with a predetermined number of dots using at least three smoothing filters with different filter sizes; a step of calculating an evaluation value indicating the degree of density of each pixel in the dot pattern for each result of the filtering process; calculating a comprehensive evaluation value indicating the overall degree of density for each pixel based on the evaluation value for each pixel in the dot pattern obtained for each result of the filtering process; identifying a position of at least one pixel in the dot pattern that is determined to be sparse or dense based on the comprehensive evaluation value; determining a threshold value at a position in the dither matrix corresponding to the identified pixel location; Including, The dither matrix generation method.

2. In the step of obtaining an evaluation value for each pixel, The results of the filtering process are ranked according to the degree of density, and the ranking is obtained as the evaluation value. The method for generating a dither matrix according to claim 1 .

3. In the step of obtaining an evaluation value for each pixel, The filter processing results are normalized by weighting according to the filter size of each filter to obtain the evaluation value. The method for generating a dither matrix according to claim 1 .

4. In the step of calculating a comprehensive evaluation value for each pixel, Adding the evaluation values ​​of each pixel in the dot pattern obtained for each filter processing result; The step of identifying the location of the at least one pixel includes: Identifying the position of the topmost pixel that is determined to be sparse or dense based on the result of adding the evaluation values ​​of each pixel; The method for generating a dither matrix according to any one of claims 1 to 3.

5. In the step of calculating a comprehensive evaluation value for each pixel, Adding the evaluation values ​​of each pixel in the dot pattern obtained for each filter processing result; The step of identifying the location of the at least one pixel includes: Identifying the positions of a plurality of pixels that are top candidates for being determined to be sparse or dense based on the result of adding up the evaluation values ​​of each pixel; The method for generating a dither matrix according to any one of claims 1 to 3.

6. When the threshold values ​​for a portion of the dither matrix are determined, the dot pattern is updated thereafter, and the filtering step, the step of obtaining the evaluation value, the step of calculating the comprehensive evaluation value, the step of specifying the position of the at least one pixel, and the step of determining the threshold values ​​for the dither matrix are repeatedly performed until all threshold values ​​for the dither matrix are determined. The method for generating a dither matrix according to any one of claims 1 to 5.

7. As an initial dot pattern to be used when the step of filtering the dot pattern is first started, A pattern is used in which at least two dots are arranged in asymmetric positions with respect to a virtual point or line within the dither matrix.

7. A method for generating a dither matrix according to claim 1.

8. The at least three smoothing filters are m smoothing filters (m is a natural number equal to or greater than 3), When all the prepared smoothing filters are n smoothing filters (n is a natural number satisfying n>m), selecting the m smoothing filters to be used in the filtering process from the n smoothing filters that are prepared according to the density of the dot pattern; A method for generating a dither matrix according to any one of claims 1 to 7.

9. When selecting the smoothing filter, obtaining an index value corresponding to the average value of the intervals between dots in the density of the dot pattern; The index value itself or a value obtained by multiplying the index value by a coefficient is used as a reference value, and the reference value is compared with the size of each of the n smoothing filters; selecting the m smoothing filters by excluding smoothing filters having sizes smaller than the reference value; The method for generating a dither matrix according to claim 8.

10. When calculating the index value for the density of the dot pattern, When circles of the same radius representing each dot are assumed to be filled in the plane of the dot pattern with the maximum area and maximum density, the radius of the circle is calculated, and the radius is set as the index value. The method for generating a dither matrix according to claim 9.

11. The sizes of the at least three smoothing filters are different by the same factor. A method for generating a dither matrix according to any one of claims 1 to 10.

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