KR20020017526A - A Principal Distance Based Error Diffusion Technique - Google Patents

Abstract

PURPOSE: An error diffusion method is provided to convert a continuous gradation image, having brightness values with a range of 0 to 155, into a half-toned image, corresponding to a principal distance being an ideal distance of white or black pixels, and to calculate a minor pixel distance by using an MPOA(Minor Pixel Offset Array) method so that it can generate a regular distribution of the continuous gradation image. CONSTITUTION: The method comprises steps of defining an ideal distance, between a few pixels for expressing a regular distribution, as a principal distance, converting a gradation value of an image into the principal distance, defining a length of a minor pixel distance and the principal distance as conditions for a regular distribution, half-toning the image converted into the principal distance, calculating the minor pixel distance and using the calculated minor pixel distance as a half-tone threshold value, using the minor pixel distance as the half-tone threshold value in a gradation range of larger than 128, using the minor pixel distance with a minus sign attached as the half-tone threshold value in a gradation range of smaller than 128, and defining the difference between a pixel value, converted into the principal distance, and the principal distance of a half-toned pixel, as an error.

Description

Principal Distance Based Error Diffusion Technique

The present invention relates to an error diffusion method based on principal distance, and more particularly, a continuous gray scale image having a value between 0 and 255 as a value corresponding to the principal distance in order to represent an image in a binary output device such as a digital printer. To create a uniform distribution of gradation images by defining the difference between the main distance of the converted pixel value and the binarized pixel as an error and calculating the minimum pixel distance using the Miner PixelOffset Array (MPOA) technique. The present invention relates to a main distance based error diffusion method.

Conventionally, in order to express a continuous gradation image capable of expressing 256 levels of contrast with a binary output device capable of expressing only black and white like a printer, it is necessary to convert it into a binary gradation image composed of only black and white. Furthermore, in order to represent an image in a binary output device such as a digital printer, a halftoning technique for converting a continuous grayscale image into a binary grayscale image is required.

At this time, when converting the continuous grayscale image into a binary grayscale image, a binarization error necessarily occurs. Among the half-toning techniques, the error diffusion method currently widely used is known to perform a low pass filtering process for binarization errors. This low-pass filtering process produces binary grayscale images that match the visual characteristics of people sensitive to low-frequency components.

Despite these advantages, the error diffusion method produces a visually detrimental pattern in which black or white points are arranged in a certain direction at a particular gray level, and especially bright and dark colors in which black or white points are sensitive to human vision. There is a problem in that it is not evenly distributed in grayscale. Such non-uniform distribution in light and dark gradations is a major factor in degrading the image quality of a binary gradation image.

In addition, in order to represent an image using a binary output device, a continuous grayscale image must be converted into a binary image, and the halftoning method of converting a continuous grayscale image into a binary image is divided into dithering, error diffusion, and optimization techniques. It can be divided into methods used. The performance of the binarization technique for generating a binary image depends on the reproducibility of the gradation representing the gradation of the original image, the degree of noise in the binary image, the reproducibility of the boundary line, and the distribution characteristics of the binary pixels suitable for human visual characteristics. Among them, the uniform distribution of the hydrophobic pixels, which is defined as black points in light gray and white points in dark gray, has a great influence on the quality of binary images.

Currently, the most widely used error diffusion method is to represent the gray level of the original image by minimizing the binarization error by taking the binarization error generated after binarizing the pixel into the binarization of the surrounding pixels. In addition, the error diffusion method generates a binary image suitable for human vision sensitive to low frequency components through a high pass filtering process for the binarization error. However, the error diffusion method has a limitation in generating a uniform distribution in light and dark gradations only by the propagation process of the binarization error. Therefore, a representative error diffusion method recently published for generating a uniform distribution is a method of obtaining a uniform dot distribution through an additional operation such as a binary threshold propagation method, a road map method, or a binary threshold modulation method using a periodic function. Have been announced.

The binary threshold propagation method is a method of changing a binary threshold by weighting a threshold imprint according to the gray level and the binarization result of the input pixel and propagating it to the surrounding pixels similarly to the process of propagating the binarization error to the surrounding pixels. .

In the binary threshold propagation method, the calculation amount increases due to the addition of the propagation process, and since the change in the binary threshold does not accurately reflect the distribution of the binarized surrounding pixels, an uneven distribution occurs at a specific gray level.

Further, in the road map method, first of all, the gray scales are divided into two kinds of intermediate gray scales to be binarized by error diffusion and the remaining gray scales sensitive to dot distribution. When binarizing pixels having light or dark gradations where dot distribution is important, the presence or absence of a minority pixel is searched for an area already binarized according to the gradation value. As a result, the pixel to be currently binarized is binarized to the minority pixel only when there is no minor pixel in the search range. On the other hand, for pixels of intermediate gray scale, the binary pixel is determined by the same process as the conventional error diffusion method.

As such, the roadmap method has a disadvantage in that all binary images corresponding to the maximum search range (16 line memory) must be stored.

In addition, the method using the periodic function is a method of changing the threshold value by defining the main distance of the minority pixels for uniform distribution according to the gray scale as the period of the periodic function. In the method using the periodic function, there is almost no increase in the amount of calculation because the binary threshold is determined only by the gray level value of the pixel to be binarized. Will occur.

In order to solve the problems caused by the error diffusion methods, an ideal distance of black or white points for uniform distribution of a continuous grayscale image having a value capable of expressing 256 levels of contrast between 0 and 255 can be solved. Converts to a binary gradation image corresponding to a principal distance, calculates a minimum pixel distance, which is the distance from the pixel where binarization is performed to the closest black or white point according to the gray scale, In order to adjust the binary threshold by weighting the difference between and the minimum pixel distance, and to calculate the minimum pixel distance with a small amount of calculation and a small amount of memory, a minor pixel offset array (MPOA) is used. Change the gradation value of the input continuous gradation image to a new main distance-based variable so that the distance and the minimum pixel distance are equal on average It is an object to provide a method for.

In addition, in the conventional error diffusion method, the difference in the gray value due to binarization is propagated to the surrounding pixels, whereas in the present invention, the difference in the main distance is propagated, and the main distance corrected by the error diffusion kernel is smaller than the minimum pixel distance. Another object of the present invention is to provide an error diffusion method based on a main distance for binarizing only a small number of pixels so that the distance between the minority pixels represents the main distance on average.

Also, in order to calculate the minimum pixel distance, the present invention stores the type of binary pixel and the position in two dimensions for all pixels of the upper 16 lines corresponding to the maximum main distance from the pixel which is currently binarized, as in the roadmap method. In order to effectively calculate the minimum pixel distance, the minimum pixel distance is stored in one-dimensional by diminishing the type and position of the fractional pixels in the already binarized region by the Minor Pixel Offset Array technique. Another object is to present a method of determining distance.

1 is a graph showing the main distance for each gray level;

2A and 2B illustrate a binarization process;

3A is a diagram illustrating a part of a binary image for an M × N image;

3B is a diagram showing po (k) values for the binarized region of FIG. 3A;

4A and 4B are views showing a minimum pixel distance calculation method as an example;

5 is a graph showing an average of the results calculated for each gray level;

6A to 6D show experimental results of a single grayscale 250;

7A to 7D are diagrams showing experimental results on a general image.

In order to achieve the above object, the present invention provides a method comprising: defining an ideal distance between minority pixels for a uniform distribution as a main distance, converting a gray level value of an image into a main distance, Defining the magnitude of the principal distance as a condition of a uniform distribution, binarizing the image converted to the principal distance, calculating a minimum pixel distance and using it as a binary threshold, and minimum pixels at gray scales greater than 128 Using distance as a binary threshold and taking a negative number at the minimum pixel distance for a gray scale smaller than 128 and using it as a binary threshold, and defining the difference between the pixel value converted to the main distance and the main distance of the binarized pixel as an error. It is characterized by performing the steps.

Hereinafter, the present invention will be described in detail with reference to the accompanying drawings.

In the present invention, first, the conventional error diffusion method will be described, and the main distance-based error diffusion method will be described in detail as an embodiment for achieving the object of the present invention. In addition, we describe the minor pixel offset array method, which is a method of calculating the minimum pixel distance with a small amount of calculation and a small amount of memory, and compares and evaluates the performance of the error diffusion method with the results of the conventional binarization methods.

First, to summarize the terms mainly used in the present invention, there is provided a binarization method for generating a uniform distribution by maintaining a constant distance of the number of pixels according to the gray level of the image, for this purpose is ideal The distance is defined as the principal distance, and the closest distance between the pixel to be binarized and the binarized decimal pixels is defined as the "minor pixel distance".

In addition, in the binary threshold modulation method using the main distance constraint, a minor pixel offset array (MPOA) is used to calculate the minimum pixel distance with a small amount of calculation and a small amount of memory.

Next, prior to explaining the error diffusion method of the present invention to briefly summarize the existing error diffusion method to compare the difference with the existing error diffusion method, the error diffusion method has a continuous gradation of [0, 255] The binarization error generated after binarizing a pixel to 0 or 255 is propagated to surrounding pixels to be considered when binarizing the next pixel. Equations 1 to 3 show general error diffusion methods.

In Equations 1, 2, and 3, x (m, n) is a continuous gray value in the (m, n) th pixel, and w (k, l) is an error diffusion coefficient as an error value e (m, n) propagates to surrounding pixels defined in R at a constant rate. In Equation 3, T is a binary threshold for determining a binary pixel, and a constant value of 128 is generally used.

The error diffusion method is a method of minimizing the binarization error by spreading the error generated when binarizing the continuous gradation that changes linearly by a linear model as shown in Equation 2. The binary image obtained by the error diffusion method of Equations 1 to 3 expresses the gradation of the original image relatively accurately, whereas the dot distribution is not uniform in the bright or dark portions of the image, causing an unobtrusive pattern. This pattern is caused by the uneven distribution of the black points in the bright areas and the white points in the dark areas defined as hydrophobic pixels.

Accordingly, in the error diffusion method of the present invention, dwelling, which is an ideal distance between the decimal pixels for generating a binary image having a uniform dot distribution, is represented by the following equation (4).

FIG. 1 is a graph showing the main distance for each gray level shown in Equation 4, and dwelling shows only between 128 and 255 gray levels because it is symmetric with respect to gray level 128. In the case of binarizing a single grayscale image, ideally the distance between all the minor pixels in the binary image should match the main distance for the given grayscale.

When this condition is satisfied, the binary image forms a uniform dot distribution and reproduces a given gray scale. However, in the case of digital printers, dots are printed only at positions on the grid, so the distance between the minority pixels is 1, , 2, It will only have a limited value. Therefore, for all grayscales between 0 and 255, it is impossible for the distance between the minority pixels in the binary image to match the main distance shown in FIG.

Therefore, the present invention proposes a method in which a distance between minority pixels in a certain region of a binary image represents a main distance on an average through an error diffusion method. To this end, first, a new variable v _x (m, n) based on the main distance is defined as in Equation 5 below.

V _x (m, n) defined in Equation 5 has a form of a straight line passing through the origin. It has a positive value when x (m, n)> 128 and a negative value when x (m, n) ≤ 128, which is the opposite. The maximum value of v _x (m, n) represents the principal distance for gradation 255. The conventional error diffusion method shown in Equations 1 to 3 is defined for the gray value x (m, n), whereas the main distance-based error diffusion method proposed in the present invention is for v _x (m, n). Is defined. The proposed error diffusion method is represented by equations (6) to (10).

In the proposed method, the error due to binarization is defined as e _v (m, n) of Equation 6, which is represented by the value of v ' _x (m, n) of Equation 7 and It is calculated as the difference between v _b (m, n), which is the value of v _x (m, n) corresponding to the point.

The error defined in this way is propagated to surrounding pixels by Equation 7, and then, v _x (m, n) in the pixel to be binarized is corrected. In Equation 7, w (k, l) represents the error diffusion coefficient.

Of equation (9) and Denotes the minimum pixel distance when x (m, n)> 128 and x (m, n) ≤ 128, respectively. The minimum pixel distance represents the shortest distance among the distances between the pixel x (m, n) to be currently binarized and the already binarized decimal pixels. That is, if x (m, n)> 128, the fractional pixel is a black dot, Represents the distance from x (m, n) to the nearest black point among the points already binarized to black points. Conversely, if x (m, n) ≤ 128 Indicates the distance to the nearest white point.

A method for efficiently calculating the minimum pixel distance will be described in detail later. The binarization is performed by Equation 8, and the binarization process shown in Equation 8 will be described with reference to Figs. 2A and 2B.

In FIG. 2A and FIG. 2B, it is assumed that x (m, n) is 230. At this time, the minority pixel becomes a black point and the distance between the black points should represent the main distance on average. 2A is a minimum pixel distance Is less than the modified v ' _x (m, n) value. In this case, x (m, n) is binarized to a white point. In other words, it is assumed that the minimum pixel distance is smaller than the main distance and the printing of black dots is suspended. The error generated as a result of the binarization is propagated to the surrounding pixels by the equation (7).

2b is a minimum pixel distance Is the same as or greater than the modified v ' _x (m, n) value. In this case, x (m, n) is binarized to black dots and the difference is propagated by Equation 7 as well.

In the error diffusion method described above, the distance between the minority pixels shows the main distance on the average through the process of error propagation, thereby generating a uniform dot distribution in the bright and dark areas of the image.

Next, a method of efficiently calculating the minimum pixel distance will be described in detail.

The method proposed in the present invention requires the calculation of the minimum pixel distance for every pixel. In order to calculate the minimum pixel distance, it is necessary to store the type and two-dimensional position of the already binarized pixel for the region corresponding to the upper 16 lines, which is the maximum main distance. The actual minimum pixel distance is determined by searching for the fractional pixels in the stored area, calculating the Euclidean distances between the fractional pixels and the current position, and selecting the smallest distance among the calculated distances. do.

This process requires a lot of memory, 16 lines, and requires a lot of computation because it calculates Euclidean distances for every fractional pixel in a two-dimensional region.

In the present invention, by using the Minor Pixel Offset Array (MPOA) method of reducing the amount of memory and the amount of calculation required for calculating the minimum pixel distance by converting and storing the types and positions of the fractional pixels in the binarized region in one dimension.

Next, referring to FIG. 3, a minor pixel offset array (MPOA) method will be described. FIG. 3A shows a part of a binary image of an M × N size image, and the pixel to be currently binarized is the (m, n) th pixel. to be. In FIG. 3A, the black area represents the number of pixels having gray level 0 and the white area gray level 255. Two-dimensional positional information of the minority pixels is encoded into a one-dimensional array called po (k). po (k) consists of (N + 1) elements. The first N numbers represent positions of the decimal pixels in the 1 to Nth columns, and po (N + 1) represents position information of the decimal pixels in the same row as the pixel to be processed. The first N po (k) (where k = 1, 2, ..., N) is determined as follows. If the element of the (m-1) th row, which is the previous row, is a white point, the number of consecutive white points located in the upward direction becomes po (k). On the contrary, when the element of the (m-1) th row, which is the previous row, is a black point, the value of the negative number of consecutive black points located in the upward direction becomes a po (k) value. The last element po (N + 1) is the number of white points continuously present in the left direction when the previous element b (m, n-1) is a white point. In the case where b (m, n-1) is a black point, a value obtained by taking the negative number of black points continuously present in the left direction is a po (N + 1) value.

FIG. 3B shows the po (k) value for the binarized region of FIG. 3A. For example, in the case of po (n-4), when b (m-1, n-4) is a white point and meets the black point b (m-3, n-4) in the upward direction as shown in FIG. 3A Since two white dots exist in succession, the value is +2.

In the case of po (n-1), b (m-1, n-1) is a black point and b (m-2, n-2) immediately above is a white point, so the value of po (3) is -1. to be.

Determining the minimum pixel distance consists of calculating the distance of the closest minority pixel for each po (k) and then selecting the smallest value among them. At this time, in order to calculate the distance of the minority pixels, the deviation x _{ind in} the x-axis direction from the pixel x (m, n) to be binarized to the minority pixel and the deviation y _ind in the y-axis direction must be determined first. This process can be seen with reference to FIG.

In FIG. 4, it is assumed that the gradation value of the pixel to be binarized is 230, and the residential value corresponding to the gradation value 230 is 3.19. After po (k) values are determined for a given pixel x (m, n), a search range in po (k) is determined according to the main distance corresponding to x (m, n). That is, only (2 [λ _x ] +2) po (k) values centered on the pixel to be binarized are search targets. This represents the part indicated by the bold line in FIG. 4A. FIG. 4B shows x _ind and y _ind which are deviations in the x-axis and y-axis directions with respect to the search target shown in FIG. 4A.

Table 1 below shows the rules for calculating x _ind and y _ind from po (k). In FIG. 4B, the dark portion of the last row represents the Euclidean distance within the search region. Among the calculated distances, the shortest distance 1 is the minimum pixel distance for x (m, n). The Euclidean distance of FIG. 4B may store in advance a distance calculated from possible x _ind and y _ind values in a LUT (Look-Up Table) without having to calculate each time. Therefore, the minimum pixel distance is determined only by comparison and calculation. Also, the po (k) values for the next pixel are obtained by correcting only the changed portions without recalculating.

Calculation rules for x _ind and y _ind from po (k) po (k), k = 1, 2, ..., N + 1 x _ind y _ind x (m, n) ≥128 │n-k│ 1, if po (k) <0 po (k) +1, if po (k) ≥ 0 x (m, n) <128 │n-k│ Po (k) +1, if po (k) <0 1, if po (k) ≥0

According to the present invention, in order to analyze the performance of the main distance-based error diffusion method, a comparison experiment was performed with the three methods proposed to obtain a uniform dot distribution.

First, we tested how the distance between the minority pixels and the main distance in the binary image obtained by the proposed method. The purpose of this experiment is to numerically evaluate the degree of uniform dot distribution. A single grayscale image with a size of 256 × 256 was generated for each of the grayscales from 128 to 255. Each single grayscale image is presented and binarized by three conventional methods.

In other words, 128 binary images from 128 to 255 were created for each of the four methods. When applying Marku's method, binarization was performed based on the search area and order of the top 9 lines defined in Marku's method. D _x defined in Equation 11 was calculated for all images (128 images 4 methods = 512 images). D _x is the average of the squares of the difference between the minimum distance and the main distance between all the minor pixels in the binary image. It is a measure of how the distance between the minority pixels matches the main distance in the binary image.

Here, N _x represents the number of decimal pixels in a binary image representing a single gray scale of x. Denotes the minimum pixel distance for the kth minor pixel in the binary image. That is, it means the distance between a given minority pixel and the nearest minority pixel. Ideally, the minimum distance between minority pixels should satisfy the main distance. Therefore, in Equation 11 The difference between and the principal distance x is squared and averaged. D _x of Equation 11 was calculated for each of grayscales between 128 and 255, and the same process was performed for the four methods.

5 shows D _x values for each of the four methods. Note that the D _x values from 0 to 127 are symmetric about 128. The degree of uniform distribution of dots is perceived sensitive to human vision in bright or dark shades. As shown in FIG. 5, it can be seen that the three conventional methods (Eschbaja, Marku, and Steel) show a relatively large D _x value compared to the method proposed by the present invention in bright gradation. A large value of D _x means that there is a void or cluster area of the minor pixels in the binary image.

Table 2 shows values obtained by averaging the results calculated for each gray level in FIG. 5. As shown in Table 2, in the method proposed by the present invention, it can be seen that the distance between the minority pixels best represents the main distance.

Mean of D _x value by gradation for four methods Way Eschbach Kang Marcu Method of the invention Average D _x 0.5940 0.3347 0.7476 0.2439

Next, the gray scale reproducibility, one of the important performance indicators of the binarization method, was evaluated. The ideal number of decimal pixels in a single grayscale binary image is calculated by the given grayscale value given the size of the image. For example, when the size of the image is 256 × 256, the ideal number Nx _{, ideal} of the number of pixels for the gray value x (128 ≦ x ≦ 255) is expressed by Equation 12.

Therefore, the number of ideal minority pixels and the number of actual minority pixels are defined as a measure of gradation reproducibility. This is calculated as in Equation 13 below.

Here, N _x represents the actual number of decimal pixels in a binary image representing a single gray scale as in Equation 11. I _x of Equation 13 was calculated for all binary images used to evaluate the uniformity of the dot distribution.

Table 3 shows the result of averaging I _x calculated for each of the four binarization methods. As shown in Table 3, the proposed method reproduces the gradation most accurately. Marku's method used for comparison uses the search area and order of the 9-line memory proposed in Marku's method, as already explained. Therefore, it can be confirmed that gradation is not accurately represented.

Average of I _x for Gradation 128 to 254 Way Eschbach Kang Marcu Method of the invention Average I _x 110.920 33.706 181.079 26.761

FIG. 6 shows the result of applying the existing three methods and the method of the present invention to a 256 × 256 single grayscale image of grayscale 250 to evaluate dot distribution in bright grayscale. The method proposed in Eschbach's method and lecture method generates voids in the upper part of the binary image as shown in FIGS. 6A and 6B. The reason for this is that Eschbach's method and the lecture method do not adjust the binary threshold by accurately considering the position of the fractional pixel. In Fig. 6C, which is the result of the Marku method, the hydrophobic pixels are distributed with a certain rule. This regular pattern appears because Marku's method binarizes the relative positions of the minor pixels in advance. On the other hand, as shown in Figure 6d it can be seen that the method proposed in the present invention is uniformly distributed without a specific pattern.

7 shows the result of applying the existing methods and the method proposed by the present invention to a general image having a size of 410 × 500. In FIG. 7A, the hydrophobic pixels are not uniformly distributed in the bright part of the onion and the cutting board behind the onion, and FIG. 7B shows that the hydrophobic pixels are aligned in a certain direction at the upper boundary of the mortar and the black background behind the cutting board. Able to know. In Fig. 7c, which is the result of Marku's method, the hydrophobic pixels are uniformly distributed as compared to the method of Eschbach. However, due to the reduced search area to check for the presence of minor pixels, more white spots appear near the background than the other three methods. This phenomenon is because, as discussed in Table 3, Marku's method does not accurately represent the gradation of the original image. It can be seen that FIG. 7D obtained by the method proposed by the present invention shows excellent image quality.

Finally, the calculation amount and memory usage required in applying the existing methods and the method proposed by the present invention are compared in Table 4. In other words, Eschbach's method increases the computational amount due to the propagation of the threshold imprint, and the lecture method compares the binary threshold with the grayscale value of the pixel to be binarized. Use less computation and memory.

The proposed method saves the position of binary pixels using the Minor Pixel Offset Array (MPOA) technique, which greatly reduces the amount of memory compared to Marku's method, and calculates the distance calculation using a look-up table (LUT) table. Since there is little increase in the amount of calculation, the calculation is performed using

Calculation and memory +,- ×, ÷ <, ＞ Line memory Eschbach 21 13 2 2 Kang 7 8 One One Marcu 4 4 148 10 Method of the invention 4 4 33 2

As described above, the present invention proposes an error diffusion method based on the principal distance to realize a uniform dot distribution, and the method of the present invention defines an error diffusion method by defining a new variable v _x (m, n) based on the principal distance. The binarization is performed using the binary threshold as the minimum pixel distance so that the minimum distance between the minority pixels on average is equal to the ideal main distance. By converting and storing these types and two-dimensional positions into one-dimensional, a minor pixel offset array (MPOA) technique is proposed, which calculates the minimum pixel distance with a small amount of computation and a small amount of memory. Experimental results show that the method of the present invention generates an improved dot distribution and accurately reproduces a given gradation compared to the conventionally proposed methods for uniform dot distribution, thereby minimizing the amount of computation and memory. As a result, the image quality of the binary image gradation is improved more clearly.

Claims (9)

Defining an ideal distance between the minority pixels to represent a uniform distribution as the main distance, Converting the grayscale value of the image into a main distance, Defining the magnitude of the minimum pixel distance and the principal distance as conditions of the uniform distribution, Binarizing the image converted into the main distance, Calculating a minimum pixel distance and using it as a binary threshold; Using a minimum pixel distance as a binary threshold in grayscales greater than 128 and taking a negative number at the minimum pixel distance in grayscales less than 128 to use a binary threshold; And a step of defining a difference between the pixel value converted into the main distance and the main distance of the binarized pixel as an error. The method of claim 1, wherein the converting the grayscale value of the image into a main distance comprises: Main distance-based error diffusion method characterized by expressing the main distance of the light gray scale with a positive number, and the main distance of the dark gray scale with a negative number. According to claim 1, In order to define the principal distance that is the ideal distance, Error distance diffusion method based on the main distance, characterized in that using. According to claim 1, In order to convert the gray value of the image to the main distance, Error distance diffusion method based on the main distance, characterized in that using. The method of claim 1, wherein the magnitude of the minimum pixel distance and the main distance are defined as a condition of a uniform distribution. Minimum pixel distance under uniform distribution If x is less than the modified v ' _x (m, n) value, x (m, n) is binarized to a white point, and the minimum pixel distance If _x is equal to or larger than the modified v ' _x (m, n) value, x (m, n) is binarized to a white point. According to claim 1, In order to binarize the image converted into the main distance, Equation , Equation , Equation , Equation And Equation Main distance-based error diffusion method characterized in that the applied. The method of claim 1, wherein the minimum pixel distance is calculated and used as a binary threshold. Equation And Equation Main distance-based error diffusion method characterized in that the applied. The method of claim 1, wherein in order to use the minimum pixel distance as a binary threshold at gray scales greater than 128 and to take a negative number at the minimum pixel distance in gray scales less than 128, Equation Main distance-based error diffusion method characterized in that the applied. The method of claim 1, wherein the difference between the pixel value converted into the main distance and the main distance of the binarized pixel is defined as an error. Equation And Equation Main distance-based error diffusion method characterized in that the applied.