Abstract:
A multi-gradation image having a plurality of colors is binary coded by processing halftones in a pseudo manner. After the binary coding, an undesirable overlaying of colors on the image is eliminated so that image quality can be improved and also process load can be alleviated. A detailed process is this: Colors at a target pixel are binary coded, and the results are retained as data. When a color following the color already binary coded is processed, the retained data of the preceding color is referred to, thereby avoiding an undesirable composite black due to an overlaying of three primary colors on the same pixel. When the colors of an input image include black (K), this K is firstly binary coded at the target pixel, and when K is output, the other colors are halted outputting or a threshold value is set so that the other colors are not output. When K is not output, the other colors are binary coded in the order of higher density or higher visual sensitivity so that a quality image can be output.

Description:
FIELD OF THE INVENTION 
     The present invention relates to an image binary coding method that is employed in printers, scanners, copying machines, facsimile machines and the like, and the method can reproduce a multi-gradation-image into a binary gradation image. 
     BACKGROUND OF THE INVENTION 
     The error-diffusion method is known as one of the methods converting a multi-gradation image into a binary-gradation image. 
     The principle of the error diffusion method is to display halftones of image in a pseudo manner into binary gradation depending on a number of dots per unit area. 
     FIG. 8 is a block diagram illustrating a circuit embodying a conventional error-diffusion-method. 
     In FIG. 8, multi-gradation data “D” of a target pixel that is to be binary coded is read out from image memory  1 . The data “D” undergoes γ(gamma) correction by referring to the correction data stored inγ(gamma) correction ROM  2 , and are corrected to multi-gradation data D′ responsive to printing characteristics of output devices such as printers and the like. Adder  3  of error diffusion device  8  adds an error data “E” of this target pixel to the corrected multi-gradation data D′, then adder  3  outputs the data “F” of target pixel, i.e. F=D′+E. 
     Data “F” including the error data of the target pixel is compared with a threshold value “Th” at the binary coding in comparator  5 . In a case of F  Th a binary signal B=“1” is tapped off, and in a case of F&lt;Th, a binary signal B=“0” is tapped off. Based on this output, error E produced in the binary coding process is calculated by subtracter  7  as E=F−B′. 
     When input data has 256 gradations (0-255), B′=B×255 is found. Therefore, e.g. in a case of error-weighted input multi-gradation data F=230 and threshold value Th=128, output data after binary coding is B=1, and thus the error is E=F−B×255=230−1×255=−25. 
     This error E is weighted by weighting-error-calculator  6  according to a given error matrix Mxy, then the weighted error is stored in error memory  4  for being diffused to pixels data that are to be processed subsequently. 
     The weighted error data are added to the multi-gradation data of a subsequent pixel by the adder  3 , whereby the error data can be diffused. 
     In this example, when input multi-gradation data is D=230, the output data after binary coding is “1”, i.e. “255” of the 256 gradations resulting from the comparison of the input multi-gradation data with threshold value Th=128. Thus, the error=25 is produced with regard to the input multi-gradation data D=230. As a result, the error=25 is an error of the input multi-gradation data D=230. This error is weighted by weighting-error-calculator  6  with an error matrix, then is stored in error memory  4  to be reflected to the subsequent binary coding for unprocessed pixels. 
     FIG. 9 shows an example of the error matrix Mxy employed in the conventional error diffusion method. In FIG. 9, a target pixel in present is marked with * symbol, and the binary coding is provided to this target pixel. The error produced in the binary coding of this target pixel is weighted by the weighting coefficients ( 7 , 1 , 5 , 3 ) shown in FIG. 9, then is diffused to the subsequent unprocessed pixel. The weighted error is stored in error memory  4  as an error distribution value. When the subsequent pixel is binary coded, the error distribution value stored in error memory  4  is read out, and the subsequent input value read out from the image memory  1  is corrected with this error distribution value. 
     As described above, according to the error diffusion method, a binary coded error, which is produced in a binary coding process provided to a pixel, is diffused (distributed) to the subsequent pixel data to be binary coded. This method tries to minimize an error between the image data after the binary coding and that before the binary coding. 
     This error diffusion method distributes a binary-coded-error in sequence to unprocessed pixels to be binary coded, so that the original image in multi-gradation can be displayed in binary gradation having dot-densities. 
     On the other hand, in the image displayed in binary gradation by the error diffusion method, the binary coding results in “1” or “0” depending on the error distribution. The result depends on a kind of probability, thus an undesirable binary-coded result can be output as follows. 
     1. Composite black can be happened in a low density area of an image. The composite black indicates a phenomenon where a first color, a second color and a third color, which should not have been printed simultaneously, are printed at the same dot thereby producing black color. The composite black in a low density area increases substantially the granularity of the image, whereby the image undergone the binary coding is degraded. 
     2. In the case where an input image includes black (K) , black (K) that should not have been printed is overlaid on the dots illuminating colors other than black such as cyan, magenta, yellow. This phenomenon invites color overlay with ease. In other words, dots which should have illuminated colors other than black are concealed by black (K), so that the colors in original image cannot be reproduced exactly. As a result, the display undergone the binary coding is degraded. 
     Further, since the error diffusion method involves matrix calculation for error diffusion process in each pixel and color, the calculations impose a substantial load to the error diffusion device. 
     SUMMARY OF THE INVENTION 
     The present invention addresses the problems discussed above and aims to provide a method of binary coding which can avoid overlaying colors components on a dot. 
     In the following description, ON or OFF of a color indicates that a binary coded output of a color is “detective” or “non-detective” in an output image. Further, colors components displaying an image are converted from red (R), green (G), and blue (B) into cyan (C), magenta (M), yellow (Y) and black (K) before undergoing the binary coding. The respective colors are represented by (R), (G), (B), (C), (M), (Y) and (K) hereinafter. 
     The present invention is not limited to the binary coding of (C), (M), (Y) and (K), but can be applied to the binary coding of other three primary colors. 
     When a multi-gradation-image is binary coded by processing halftones in a pseudo manner, the image-binary-coding-method of the present invention can avoid overlaying the respective dots of first, second and third colors on a target pixel by retaining the binary-coded-results, i.e. ON or OFF, of the first and second colors. In other words, when the binary-coded-result of the first color is ON, the result of the second color is forced to be OFF. When either one of results of first and second colors is ON, the result of third color is forced to be OFF, of whereby overlaid printing of first, second and third colors can be restrained. 
     If the input image includes (K), (K) firstly undergoes binary coding in the target pixel. When the result is ON, the binary-coding-results of (C), (M) and (Y) are output as OFF. In this case, the colors other than (K) in the target pixel are forcibly output as OFF, which seems to lower the reproduced image quality; however, the error diffusion method distributes errors, whereby (C), (M) and (Y) are output as ON in other pixels. As a result, the image can be correctly reproduced. When the binary coding of (K) results in OFF, other colors are binary coded in the order of higher density by caring that (C), (M) and (Y) have little chances to overlie with each other on the target pixel. Further, the characteristics of human eyes are taken into consideration, and binary coding is provided accordingly to (M), (C) and (Y) in this order, i.e. the order of higher visual sensitivity by caring that (M), (C) and (Y) have little chances to overlie with each other on the target pixel. 
     When a color is output as OFF, the matrix calculation for error diffusion can be omitted, thereby shortening a process time. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a block diagram illustrating the structure of an error diffusion device in accordance with a first exemplary embodiment of the present invention. 
     FIG. 2 is a block diagram illustrating the structure of an error diffusion device in accordance with a second exemplary embodiment of the present invention. 
     FIG. 3 is a flowchart depicting a process in accordance with a second exemplary embodiment of the present invention. 
     FIG. 4 is a block diagram illustrating the structure of an error diffusion device in accordance with a third exemplary embodiment of the present invention. 
     FIG. 5 is a block diagram illustrating the structure of an error diffusion device in accordance with a fourth exemplary embodiment of the present invention. 
     FIG. 6 is a flowchart depicting the process in accordance with the third and fourth embodiments of the present invention. 
     FIG. 7 is a block diagram illustrating the structure of an error diffusion device in accordance with a fifth exemplary embodiment of the present invention. 
     FIG. 8 is a block diagram illustrating a binary coding process by a conventional error diffusion device. 
     FIG. 9 illustrates an error matrix used in the conventional error diffusion method. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
     The following embodiments describe the binary coding through an error diffusion method, where data comprising cyan (C), magenta (M), yellow (Y) and black (K) converted from red (R), green (G) and blue (B) are binary coded. 
     Exemplary Embodiment 1 
     The first embodiment is described with reference to FIG.  1 . This embodiment has an aim to eliminate overlaying the respective dots of a first and second colors. 
     FIG. 1 is a block diagram illustrating the error diffusion device in accordance with a first exemplary embodiment of the present invention. Image memory  100  stores image data to be binary coded. This image data undergoes the conversion from R, G, B to C, M, Y, K, and then the data is fed into γ (gamma) correction ROM  101 , which includes a conversion table. This conversion table corrects characteristics of image data responsive to characteristics of an output device. The image data undergoesγcorrection according to this table, then the data is fed into error diffusion device  102 . 
     Error diffusion device  102  comprises the following elements: 
     ON/OFF determiner  103  for a first color; 
     error weighting calculator  104 ; 
     binary coding means  105 ; 
     error calculator  106 ; 
     error data memory  107 ; and 
     ON/OFF data memory  108  for the first color. 
     Determiner  103  refers to data stored in ON/OFF data memory  108 , and determines whether the first color is ON or not at a target pixel. Weighting error calculator  104  refers to the errors stored in memory  107  and generated at pixels, which have been binary coded and are around the target pixel, and then provides the image data of the target pixel with error weighting. 
     Binary coding means  105  refers to a threshold value at binary coding, and provides the weighted data supplied from calculator  104  with binary coding process. The binary coded data is output as a binary signal. 
     ON/OFF data memory  108  for the first color stores ON/OFF information of the binary coded data regarding the first color. ON/OFF determiner  103  refers to this information. 
     Error calculator  106  calculates the error of image data binary coded by coding means  105 . The error has been produced in this binary coding process. The calculated error data is stored in error data memory  107 , and is referred to when an error weighting is practiced in calculator  104 . 
     An operation of error diffusion device  102  constructed as discussed above is detailed hereinafter how to handle the first and second colors. 
     (1) First, provide the first color with the binary coding in the following procedure. During this process, a process by determiner  103  can be omitted. In the first place, the first color data of a target pixel undergoes error weighting. At this moment, error data of pixels around the target pixel are referred to. Those error data have been stored in error data memory  107  by error weighting calculator  104 . The weighted data then undergoes the binary coding through binary coding means  105  based on a given threshold value. Error calculator  106  calculates binary coding errors produced in this process. The calculated errors are stored in memory  107 . The result of binary coding of the first color is stored in memory  108  as ON/OFF data. 
     (2) Second, provide the second color with the binary coding. In the first place, determiner  103  refers to the ON/OFF data stored in memory  108  of the first color. When the first color is ON, the second color is assigned to OFF by error-diffusion-device  102  free from an error diffusion process. When the first color is OFF, the second color undergoes a usual error diffusion process as discussed above, i.e. error data weighting by calculator  104 , and binary coding by coding means  105  are provided, then the result is output as a binary signal. 
     (3) Regarding the third color, the usual error diffusion process is provided, and the result is output as a binary signal without referring to the ON/OFF data of the first color. 
     Exemplary Embodiment 2 
     An operation of error diffusion device  102  in accordance with the second embodiment of the present invention is described with reference to FIG.  2 . This second embodiment has an aim to eliminate overlaying the respective dots of a first, second and third colors. 
     In the meantime, the process, where data stored in image memory  100  undergoesγ(gamma) correction and is fed into error diffusion device  102 , is the same in every embodiment. 
     In FIG. 2, ON/OFF data memory  109  for the second color and ON/OFF determiner  110  for the second color are added to the structure shown in FIG.  1 . Other elements in FIG. 2 are the same ones used in FIG.  1 . 
     The second exemplary embodiment in the construction discussed above is detailed hereinafter. 
     (1) First, provide the first color with the binary coding in the following procedure. During this process, processes by determiners  103  and  110  can be omitted. In the first place, the first color data of a target pixel undergoes error weighting. At this moment, error data of pixels around the target pixel are referred to. Those error data have been stored in error data memory  107  by error weighting calculator  104 . The weighted data then undergoes the binary coding through binary coding means  105  based on a given threshold value. Error calculator  106  calculates binary coding errors produced in this process. The calculated errors are stored in memory  107 . The result of binary coding of the first color is stored in memory  108  as ON/OFF data. 
     (2) Second, provide the second color with the binary coding. In the first place, determiner  103  refers to the ON/OFF data stored in memory  108  of the first color. (a) When the first color is ON, error-diffusion-device  102  assigns the second color to OFF free from an error diffusion process, and outputs an OFF signal. Memory  109  stores this OFF information. (b) When the first color is OFF, the second color undergoes a usual error diffusion process as discussed above, i.e. error data weighting by calculator  104 , and binary coding by coding means  105  are provided, then the result is output as a binary signal. Memory  109  stores this result. 
     (3) Finally the third color is processed. ON/OFF determiner  103  for the first color refers to the ON/OFF data of the first color at the target pixel, the data has been stored in memory  108 . Then ON/OFF determiner  110  for the second color refers to the ON/OFF data of the second color at the target pixel, this data has been stored in memory  109 . (a) When either one of the first color or second color is ON, error diffusion device  102  assigns the third color to OFF free from the diffusion process, and outputs an OFF signal. (b) When both the first and second colors are OFF, the third color undergoes a usual error diffusion process, i.e. error data weighting by calculator  104 , and binary coding by coding means  105  are provided, then the result is output as a binary signal. 
     The process in the second embodiment is further detailed with reference to the flowchart shown in FIG.  3 . 
     In FIG. 3, an image data of the target pixel undergoes color conversion from R, G, B to C, M, Y, K. (Step s 200 ) 
     Then, the converted image data undergoes γ(gamma) correction so that the data is corrected to be responsive to color reproducibility of an output device. (Step s 210 ) 
     The corrected data undergoes binary coding in the order of C, M, Y and K. The processes of first, second and third colors, i.e. C, M, Y, are described hereinafter. 
     (1) First, the First Color is Processed. (Step s 220 ) 
     Based on error data of the pixels around the target pixel, error data weighting is provided to the target pixel, and then binary coding is provided by comparing with a threshold value. (Step s 230 ) 
     Determine whether the binary coding results in ON or OFF. (Step s 240 ) 
     When the result is ON, assign data  1 , i.e. ON/OFF data of the first color, to ON. When the result is OFF, assign data  1  to OFF. 
     Next, calculate errors produced at the binary coding process (Step s 380 ), then, store the error data. (Step s 400 ) 
     (2) Next, the Second Color is Processed. (Step s 270 ) Refer to the binary coded result of the first color. (Step s 280 ) When data  1  is ON, assign data  2 , i.e. ON/OFF data of the second color, to OFF, and output data  2  as OFF data. When data  1  is OFF, provide data  2  with error-data weighting, and then provide data  2  with the binary coding by comparing with the threshold value. Then, calculate binary coding errors. (Step s 380 ), and store the error data. (Step s 390 ) 
     (3) Finally the Third Color is Processed. (Step s 340 ) 
     Refer to the binary coded results of the first and second colors using data  1  and data  2  of respective ON/OFF data. (Step s 350 ) 
     When either one of results is ON, outputs OFF as the binary coded result of the third color. (Step s 360 ) When both the results of first and second colors are OFF (Step s 350 ), provide the third color with the error-data-weighting, and then provide it with the binary coding by comparing with the threshold value. Then, calculate binary coding errors (Step s 380 ), and store the error data (Step 
     Exemplary Embodiment 3 
     The third embodiment describes the case where an input image includes black (K) in addition to C, M, Y. 
     The third embodiment takes an example where binary coding results in K to be ON at a pixel, and C, M, Y are output as OFF at the pixel. 
     FIG. 4 is a block diagram where the third embodiment is practiced. 
     In error diffusion device  102 , ON/OFF determiner  111  for the binary- coded K and memory  112  for storing binary-coded result of K are added to the elements shown in FIG.  1 . 
     Determiner  111  refers to the data stored in memory  112 , and determines whether a binary-coded result of K is ON or not at a target pixel. 
     An error diffusion process in the construction discussed above is detailed hereinafter. 
     (1) First, color K at the target pixel is binary coded in the following manner. First, provide K with the binary coding in the following procedure. During this process, processes by determiners  111  can be omitted. In the first place, K data of a target pixel undergoes error weighting. At this moment, error data of pixels around the target pixel are referred to. Those error data have been stored in error data memory  107  by error weighting calculator  104 . The weighted data then undergoes the binary coding through binary coding means  105  based on a given threshold value. Error calculator  106  calculates binary coding errors produced in this process. The calculated errors are stored in memory  107 . The result of binary coding of K is stored in memory  112  as ON/OFF data. 
     (2) Next, C, M, Y are binary coded in the following manner. Determiner  111  refers to the ON/OFF data of K stored in memory  112 . When K is ON, error data of pixels around the target pixel are referred to. Those error data have been stored in error data memory  107  by error weighting calculator  104 . The error-data-weighting is provided to C,M,Y data of the target pixel. Binary coding means  105  outputs OFF without comparing the weighted data with the threshold value and free from the binary coding process. Error calculator  106  calculates the errors of OFF output. Error memory  107  stores the calculated errors. 
     Exemplary Embodiment 4 
     The fourth embodiment of the present invention is described hereinafter with reference to FIG.  5 . 
     This embodiment describes the case where an input image includes color K in addition to C, M, Y, and binary coded result of K at a target pixel is OFF. FIG. 5 differs from FIG. 4 in the following points. 
     i) the following two elements are added, i.e. density comparator  113  for comparing the densities of C, M, Y and determining the density order, and threshold value determiner  115  for determining threshold values for binary coding C, M, Y. 
     ii) Memory  112  for storing binary coded result of K is replaced with memory  114  for storing binary coded results of C, M, Y and K at a target pixel. 
     The error diffusion process in the structure discussed above in accordance with the fourth embodiment is detailed hereinafter. 
     (1) First, provide color K with the binary coding in the following procedure. During this process, processes by determiners  111  and comparator  113  can be omitted. In the first place, K data of a target pixel undergoes error weighting. At this moment, error data of pixels around the target pixel are referred to. Those error data have been stored in error data memory  107  by error weighting calculator  104 . The weighted data then undergoes the binary coding through binary coding means  105  based on a given threshold value. Error calculator  106  calculates binary coding errors produced in this process. The calculated errors are stored in memory  107 . Then the result of binary coding of K is stored in memory  114  as ON/OFF data. 
     (2) Next, C, M, Y are binary coded in the following manner. In the first place, determiner  111  refers to the ON/OFF data of K at the target pixel stored in memory  108 . Since the binary coded result of K is set OFF in this case, comparator  113  compares the densities of C, M, Y, and the binary coding through error diffusion is provided to the highest density color and the followers in this order. The highest density color is referred to as a first color, the color next to the highest is referred to as a second color, and the lowest density color is referred to as a third color hereinafter. 
     First, error weighting calculator  104  refers to error data of the pixels around the target pixel, and provides the first color with the error weighting. The error data have been stored in memory  107 . Binary coding means  105  refers to a threshold value determined by determiner  115 , and provides the first color with the weighted binary coding. 
     Threshold determiner  115  refers to respective ON/OFF information of C, M, Y, and determines a threshold value so that there are little chances for dots to be overlaid. The respective ON/OFF information have been stored in memory  114 . 
     Based on the information of binary coded output, error calculator  106  calculates error data. Error memory  107  stores the calculated error data. Memory  114  stores the binary coded result of the first color as ON/OFF information of the dot. 
     (3) Error diffusion device  102  provides the second color and the third color with the binary coding in this order with the same manner as it did for the first color. First, error weighting calculator  104  refers to error data of the pixels around the target pixel, and provides the second and third colors with the error weighting. The error data have been stored in memory  107 . Binary coding means  105  refers to a threshold value determined by determiner  115 , and provides the second and third colors with the weighted binary coding. 
     Threshold determiner  115  refers to ON/OFF information of the first color, and determines a threshold value so that there are little chances for dots to be overlaid. When the first color has resulted in ON, the threshold value is determined so that the second color can have a lot of chances to be OFF. 
     Based on the information of binary coded output, error calculator  106  calculates error data. Error memory  107  stores the calculated error data. Memory  114  stores the binary coded results of the second and third colors as ON/OFF information of the dot. 
     Threshold value determiner  115  determines threshold values so that respective colors can avoid overlaying with each other at ON status. The flowchart shown in FIG. 7 details how to determine the threshold values by determiner  115 . 
     The process by error diffusion device  102  in accordance with the third and fourth embodiments is further detailed with reference to the flowchart shown in FIG.  6 . 
     First, provide the error-weighting to K by referring to error data of the binary coded pixel in an error matrix (Step s 500 ). 
     Next, provide the binary coding to K based on a default threshold value, and obtain ON/OFF data of K (Step s 510 ). 
     When K is ON (Step s 520 ), output the binary coded C, M, Y at OFF status (Step s 530 ). Calculate respective error data from the binary coded results of C, M, Y and K (Step s 630 ). 
     Then, store the calculated error data into error memory (Step s 640 ). 
     When K is OFF (Step s 520 ), compare the densities of C, M, Y with each other, and name each density C 1 , C 2  and C 3  in this order from the highest density to the lowest (Step s 540 ). 
     Next, the color C 1  is provided with error-weighting, and then the weighted color is binary coded by comparing with the default threshold value (Step s 550 ). 
     Store the binary coded result of C 1  as ON/OFF information (Step s 560 ). 
     Then, color C 2  undergoes the binary coding process. Set a threshold value for C 2  responsive to the binary coded result of C 1  (Step s 570 ). 
     The threshold value is set as follows: When C 1  is ON after binary coding, the threshold value is set so that C 2  can have a lot of chances to be OFF by the binary coding. When C 1  is OFF, the threshold value is set so that C 2  can have a lot of chances to be ON. 
     The error weighted C 2  undergoes the binary coding by using the threshold values set as discussed above (Step s 580 ). 
     Store the binary coded result of C 2  as ON/OFF information (Step s 590 ). 
     Finally, provide the binary coding to C 3 , the lowest density color. First, set a threshold value responsive to the binary coded results of C 1  and C 2  (Step s 600 ). The threshold value is set as follows: When C 1  is ON after binary coding, the threshold value is set so that C 3  can have a lot of chances to be OFF by the binary coding. When C 1  is OFF, the threshold value is set so that C 3  can have a lot of chances to be ON. 
     Further, when C 2  is ON after binary coding, the threshold value is set so that C 3  can have the more chances to be OFF by the binary coding. When C 2  is OFF, the threshold value is set so that C 3  can have the more chances to be ON. 
     The error weighted C 3  undergoes the binary coding by using the threshold values set as discussed above (Step s 610 ). 
     After the processes discussed above, calculate binary-coding-errors of respective colors at the target pixel based on ON/OFF information of the binary coded C, M, Y, and K (Step s 620 ). 
     Store the resultant error data of respective colors in the error memory (Step s 630 ). Refer to these error data for error weighting when the next pixel undergoes the binary coding. 
     All the processes discussed above are provided to every pixel, thereby producing a binary-coded-image (Step s 640 ). 
     Exemplary Embodiment 5 
     The fifth embodiment of the present invention is described hereinafter with reference to FIG.  7 . This embodiment provides binary coding to K, M, C, Y respectively in this order at a target pixel. 
     FIG. 7 differs from FIG. 5 in the following points. 
     i) Density comparator  113  for C, M, Y is removed. 
     ii) ON/OFF determiner  111  for K is directly connected to error weighting calculator  104 . 
     Error diffusion device  102  provides color K with the same process as it did in the third and fourth embodiments. 
     (1) When color K (black) results in OFF by the binary coding, the same process as in the fourth embodiment are provided to M, C, Y in this order, namely, the order of higher to lower visual sensitivity. 
     (2) When K results in ON, respective colors M, C, Y successively undergo the binary coding in this order. At this time, threshold-value-determiner  115  sets threshold values so that M, C, Y can have a lot of chances to result in OFF. 
     Exemplary Embodiment 6 
     The sixth embodiment of the present invention is described hereinafter with reference to FIG.  7 . 
     This embodiment provides binary coding to K, M, C, Y respectively in this order at a target pixel. Error diffusion device  102  provides color K with the same process as it did in the third and fourth embodiments. 
     (1) When color K (black) results in OFF by the binary coding, the same process as in the fourth embodiment are provided to M, C, Y in this order, namely, the order of higher to lower visual sensitivity. 
     (2) When K results in ON, respective colors M, C, Y in this order undergo the binary coding in the same manner as provided in the third embodiment, and they result in OFF. 
     The all six embodiments discussed above described the binary coding method using the error diffusion method. Other binary coding methods, such as screening and which display halftones in a pseudo manner, can employ the methods described in the first, second and third embodiments. Regarding the fourth and fifth embodiments, if a binary coding table in which threshold values are set is added so that a plurality of colors are prevented from being output as the same coordinates, the screening or dithering method could be employed. 
     The present invention can thus improve quality and granularity of an image. The embodiments 1, 2, 3, 4 and 6 proves that intermediate processes in a pseudo manner, such as error-weighting and binary coding, can be eliminated in the case where a color firstly binary coded results in ON and the following colors are processed to result in OFF. The present invention thus alleviates the load on process and reduces the process time. 
     The third embodiment proves that the present invention can prevent color overlay, i.e. dots of C, M, Y are overlaid by K, thereby canceling respective colors and encountering color overlay. As a result, the present invention can produce a quality binary gradation image where color overlay is restrained. 
     The fifth and sixth embodiments prove that the present invention can produce a higher quality binary-gradation-image by providing the binary coding to K, M, C, Y in this order, i.e. the order of higher to lower visual sensitivity.