Abstract:
An image processor includes: memory storing data including pixel values; memory storing dither matrixes corresponding to dot size and having cells with individual threshold values; a generator generating quantized data including dots corresponding to cells by comparing the data with a dither matrix, and showing that a given sized dot is formed; a calculator calculating a duty ratio of first sized dots to second sized dots based on quantized data; a determining unit determining whether the duty ratio satisfies a predetermined condition; and a threshold updater updating the dither matrixes if the condition is satisfied, at least one update being based on duty ratio; the threshold values being to: form larger dots around the dither matrix center; decrease dot size as a distance between a cell and the dither matrix center increases; and decrease dot density as the distance between a cell and the dither matrix center increases.

Description:
The entire disclosure of Japanese Patent Application No. 2005-035647, filed on Feb. 14, 2005 is expressly incorporated by reference herein. 
   BACKGROUND 
   1. Technical Field 
   The present invention relates to image processing for binarization using a clustered dither. Specifically, the invention relates to image processing capable of improving granularity of an image formed on a print media. 
   2. Related Art 
   An image forming device having ink ejecting mechanism, such as an ink jet printer, has a plurality of nozzles for ejecting an ink dot in a droplet form, in order to perform high-speed printing. The nozzles are mounted on a printing head. An ink jet printer causes the printing heads to eject ink dots by moving a sheet of paper (or a print media) in a sheet feeding direction and moving the printing heads repeatedly in a direction orthogonal to the sheet feeding direction, thereby forms images on the paper. This kind of printer is referred to as a “multi-pass printer”. 
   The printing speed of a multi-pass printer is restricted since the multi-pass printer needs a two-directional scan. Therefore, an improvement in printing speed is required. 
   Reducing the scan dimension into a one-dimensional scan, for example, scanning only in a sheet feeding direction, referred to as single-pass printing, is one of the approaches to improve printing speed. It is necessary for single-pass printing to extend the size of a printing head greater than the width of the printing paper. This kind of printer, in other words, a printer having a printing head which is larger than the width of printing paper, is referred to as a “line head printer”. In a printing head of a line head printer, it is necessary to layout nozzles at a regular distance from each other on the printing head. However, it is difficult to fabricate a printing head in which the nozzles are laid out at exact intervals, because of fabrication errors. 
   The dispersion of a distance between two adjacent nozzles causes the actual position of an ink dot formed on printing paper to be different from an ideal position. Furthermore, a skew of a nozzle also causes the actual position of an ink dot formed on printing paper to be different from an ideal position. The phenomenon of causing a difference between the ideal position and the actual position, is called “splash bending”. In a single-pass printer such as a line head printer, the phenomenon of splash bending causes white bands or dark bands to appear on the print product. The white band appears where a distance between two adjacent nozzles is greater than the ideal distance, and the dark band appears where a distance between two adjacent nozzles is less than the ideal distance. This phenomenon is referred to as “banding”. 
   To prevent deterioration in image quality, some technologies have been developed. For example, JP-A-9-107473 discloses a “clustered dither” as a binarization algorithm. Furthermore, JP-A-2001-177722 discloses an image processing that is a combination of an error diffusion method and a dither method. According to JP-A-2001-177722, concentrated dots are formed in low and medium density, and dispersed dots are formed around the concentrated dots in high density. 
   Some ink jet printers can control a dot radius of an ink dot ejected by a nozzle, in other words, a dot size of an ink dot formed on the printing paper. In an ink jet printer capable of ejecting an ink dot whose size is either one of the sizes S, M, and L, the image quality is dependent on an algorithm for generating an ink dot having one of the three sizes, in other words, an algorithm for determining where a dot is to be formed and which size of dot is to be formed. JP-A-2001-177722 has a problem in that the granularity of the image deteriorates because the concentrated dots are generated in low and medium density. A further drawback in JP-A-2001-177722 is that, it discloses a method of image processing performed only with single-size ink dots, and not a multi-size ink dot. 
   SUMMARY 
   An advantage of some aspects of the invention is to improve the granularity of an image formed by an image forming device by using an image processing device. The image forming device has an ink dot ejecting system capable of controlling a dot size of an ink dot. The image processing device performs image processing using a clustered dither. 
   According to an aspect of the invention, an image processing device comprises: an image memory that is adapted to store image data, the image data including a plurality of pixels, the image data including a pixel value of each pixel; a threshold memory that is adapted to store a plurality of dither matrixes, each of the plurality of dither matrix having a plurality of cells, each of the plurality of cells having a threshold value, each of the dither matrix corresponding to a dot size; a first generator that is adapted to generate quantized data by comparing the image data with one of a plurality of dither matrixes, the quantized data including a plurality of dots, each of the plurality of dots corresponding to one of a plurality of cells, each of the plurality of dots showing a dot having one of a plurality of dot sizes is formed; a calculator that is adapted to calculate a duty ratio on the basis of the quantized data, the duty ratio showing a ratio of a number of formed dots having a dot size to formed dots having another dot size; a determining unit that is adapted to determine whether the duty ratio satisfies a predetermined condition; and a threshold updater that is adapted to update at least one of a plurality of the dither matrixes in a case that the determining unit determines that the duty ratio satisfies the predetermined condition, at least one of the plurality of the dither matrixes being updated on the basis of the duty ratio; wherein the plurality of dither matrixes include threshold values to form dots under the following conditions: (1) around the center of the dither matrix, dots having larger dot size are formed; (2) the longer a distance between a cell and the center of the dither matrix is, the smaller a dot size is; and (3) the longer a distance between a cell and the center of the dither matrix is, the smaller a density of a dot to be formed is. 
   It is preferable that the image processing device further comprises an image reduction unit that is adapted to reduce the size of the image data; the first generator generates a quantized data for the image data whose size is reduced by the image reduction unit; and the image processing device further comprises a second generator that is adapted to generate quantized data by comparing the image data with the dither matrix updated by the threshold updater, the quantized data including a plurality of dots, each of the plurality of dots corresponding to one of a plurality of cells, each of the plurality of dots showing a dot having one of a plurality of dot sizes. 
   It is preferable that the predetermined condition is a condition where the greater the dot size is, the greater the duty ratio is. 
   It is preferable that the dither matrix is an m×m dot matrix or an m×n dot matrix, either of m and n being a positive integer. 
   According to another aspect of the invention, an ink jet printer comprises the above described image forming device. 
   According to a further aspect of the invention, an image processing method comprises: storing image data, the image data including a plurality of pixels, the image data including a pixel value of each pixel; storing a plurality of dither matrixes, each of the plurality of dither matrix having a plurality of cells, each of the plurality of cells having a threshold value, each of the dither matrix corresponding to a dot size; generating quantized data by comparing the image data with one of a plurality of dither matrixes, the quantized data including a plurality of dots, each of the plurality of dots corresponding to one of a plurality of cells, each of the plurality of dots showing a dot having one of a plurality of dot sizes is formed; calculating a duty ratio on the basis of the quantized data, the duty ratio showing a ratio of a number of formed dots having a dot size to formed dots having another dot size; determining whether the duty ratio satisfies a predetermined condition; and updating at least one of a plurality of the dither matrixes in a case that the determining unit determines that the duty ratio satisfies the predetermined condition, at least one of the plurality of the dither matrixes being updated on the basis of the duty ratio; wherein the plurality of dither matrixes include threshold values to form dots under the following conditions: (1) around the center of the dither matrix, dots having larger dot size are formed; (2) the longer a distance between a cell and the center of the dither matrix is, the smaller a dot size is; and (3) the longer a distance between a cell and the center of the dither matrix is, the smaller a density of a dot to be formed is. 
   According to a still further aspect of the invention, an computer program product causes a computer device to execute the above described image processing method. 
   According to a still further aspect of the invention, A print product, comprising: a plurality of dot matrixes, each of the plurality of the dot matrixes having a plurality of dots, each of the plurality of dots having a dot size; wherein the plurality of dots satisfy the following conditions: (1) the longer a distance between a dot and the center of the dot matrix is, the smaller a dot size is; and (2) the longer a distance between a dot and the center of the dot matrix is, the smaller a density of a dot to be formed is. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The invention will be described with reference to the accompanying drawings, wherein like numbers reference like elements. 
       FIG. 1  shows a block diagram illustrating a functional configuration of image forming device  1 . 
       FIG. 2  shows a block diagram illustrating a hardware configuration of image forming device  1 . 
       FIG. 3  shows a flow chart illustrating an operation of image forming device  1 . 
       FIG. 4  illustrates an outline of the binarization with dither matrix method. 
       FIG. 5  shows a flow chart illustrating binarization in step S 130 . 
       FIG. 6  shows examples of unit images, images after binarization. 
       FIG. 7  shows a flow chart illustrating an ON/OFF determination in step S 400 . 
       FIG. 8  shows a flow chart illustrating the update of the dither matrix in step S 440 . 
       FIG. 9  shows a flow chart illustrating binarization in accordance with the second embodiment. 
       FIG. 10  shows an example of image forming system  100  in accordance with another embodiment. 
       FIG. 11  illustrates an outline of the binarization with dither matrix method using a rectangular dot matrix. 
   

   DESCRIPTION OF EXEMPLARY EMBODIMENTS 
   1. First Embodiment 
     FIG. 1  shows a block diagram illustrating a functional configuration of image forming device  1  in accordance with the first embodiment. Image forming device  1  is a device that converts input image data into print control data, and prints an image in accordance with the print control data. In the present embodiment, the image data includes multilevel data in RGB (Red, Green, and Blue) system. Furthermore, the print control data corresponds to binary data in CMYK (Cyan, Magenta, Yellow, and Black) system. Resolution converter  11  converts a resolution of input image data into a resolution conforming with that of image forming device  1 . Colorimetric system converter  12  converts RGB image data into CMYK image data. Quantization unit  13  converts multi-level CMYK image data into binary CMYK image data. Print control data generator  14  generates print control data on the basis of binary CMYK data. The print control data is data for controlling ejection of an ink dot from a nozzle. Image forming unit  15  performs print operation in accordance with the print control data. 
     FIG. 2  shows a block diagram illustrating a hardware configuration of image forming device  1 . In the present embodiment, image forming device  1  is a line head type ink jet printer. CPU (Central Processing Unit)  21  reads and executes a printing program stored in ROM (Read Only Memory)  22 . RAM (Random Access Memory)  23  functions as a work area for CPU  21  in executing a program. I/F  24  is an interface for communicating data or a control signal with another device. For example, image forming device  1  can receive image data from an electronic device such as a personal computer (hereinafter referred to as “PC”) or a digital camera, via I/F  24 . RAM  23  also stores data received via I/F  24 . Image forming unit  25  has a plurality of nozzles, a nozzle driver circuit, and a sheet feeding system (not shown in the figures). Image forming unit  25  prints an image in accordance with print control data under the control of CPU  21 . The above described elements are mutually connected via bus  26 . By CPU  21  executing a printing program, image forming device  1  has functions shown in  FIG. 1 . 
     FIG. 3  shows a flow chart illustrating an operation of image forming device  1 . When power is supplied to image forming device  1  by a power supply (not shown in the figures), CPU  21  reads and executes a printing program stored in ROM  22 . By executing the printing program, CPU  21  is in standby state for inputting image data. When receiving image data via I/F  24 , CPU  21  stores in RAM  23  the input image data in step S 100 . In the present embodiment, input image data is RGB multi-level image data. Image forming device  1  is an ink jet printer printing an image with a four color ink, CMYK. Image forming device  1  needs to convert a colorimetric system of input image data from an RGB system into a CMYK system. Furthermore, a nozzle of image forming device  1  can eject an ink dot whose size is one of S, M, or L. In other words, image forming device  1  can represent a four-level gradation of an ink dot, namely, no-dot, S/M/L size dot. In image forming device  1 , a pixel of input image corresponds to an m×m dot matrix. The dot matrix is referred to as “unit image”. Gradation of a pixel is represented by a number and size of dots formed in the dot matrix. Input image data needs to be converted into data indicating an ON/OFF state of a dot for each dot size. As will be described later, a resolution of input image data needs to be converted into a resolution corresponding to the number of the nozzles. Furthermore, the input image data needs to be converted from multi-level data into binary (or quantized) data indicating an ON/OFF state of a dot. It is to be noted that, in this specification, an “ON state of a dot” means ejecting an ink dot from a nozzle. Similarly, an “OFF state of a dot” means not ejecting an ink dot from a nozzle. For example, the phrase “data indicating an ON/OFF state of a dot” means data indicating whether a nozzle ejects an ink dot. Furthermore, the terms, “dot” or “ink dot” also mean an image formed on printing paper by an ink droplet, and further mean a unit of data for ejecting an ink dot. 
   Next, CPU  21  obtains the resolution of the input image data. In a case that the resolution of the input image data is different from that of image forming device  1 , CPU  21  converts in step S 110  the resolution of the input image data into a resolution conforming to image forming device  1 . CPU  21  stores the resolution-converted image data in RAM  23 . Next, in step S 120 , CPU  21  converts the colorimetric system of the image data from an RGB-system into a CMYK-system, in order to conform to the colorimetric system of image forming device  1 . Next, in step S 130 , CPU  21  performs binarization (or quantization) of the colorimetric-system-converted image data. Details of the binarization will be described later. 
     FIG. 4  illustrates an outline of the binarization with dither matrix method. RAM  23  or ROM  22  stores a dither matrix having a predetermined size of 4×4 cells as shown in  FIG. 4 . Here, a dither matrix includes a plurality of cells; each of the cells having a threshold value. CPU  21  divides the multi-level image data into a plurality of divided images. A divided image comprises a plurality of pixels. Each divided image, in this case, has the same size of pixels as the 4×4 cells of a dither matrix. In the present embodiment, a divided area corresponds to a unit image of a printed image (or binarized image data). A printed image comprises a plurality of unit images. In other words, a unit image of a printed image is formed by m×m dots (m=4 in this case). For each of the divided images, CPU  21  compares a pixel value of a target pixel of the divided image with a threshold value of a corresponding cell of the dither matrix. In other words, a pixel value of the target pixel is compared with a threshold value. Here, a target pixel is a pixel to be processed. In a case that the pixel value is greater than the threshold value, a target dot is determined as “ON”. Here, a target dot is a dot to be processed. A target dot corresponds to a target pixel. In this specification, a “pixel” means a smallest unit of image data before binarization, and a “dot” means a smallest unit of image data after binarization. On the contrary, in a case that the pixel value is smaller than the threshold value, the target dot is determined as “OFF”. For example, in  FIG. 4 , a pixel value of the left-top pixel is “180”, and the corresponding threshold value in the dither matrix is “44”. In this case, the pixel value is greater than the corresponding threshold value. Therefore, the binarized pixel value (in other words, a dot value of a target dot) is determined as “ON”. In binarized image data shown in  FIG. 4 , “1” shows an ON dot, and “0” shows an OFF dot. In the present embodiment, image forming device  1  has three dither matrixes, each of which corresponds to one of dot sizes S, M, and L. This is because image forming device  1  can eject three sizes of ink dots. Furthermore, image forming device  1  performs binarization for each of the four color components, CMYK. 
     FIG. 5  shows a flow chart illustrating binarization in step S 130 . In step S 400 , CPU  21  initializes a dither matrix. Detail of the initialization is as follows. ROM  22  stores in advance a plurality of initial dither matrixes, each of which corresponds to both: one of four color components and one of dot sizes. CPU  21  reads from ROM  22  an initial dither matrix corresponding to a color component that is a target color of the operation. Then, CPU  21  stores in RAM  23  the initial dither matrix. 
   Here, an initial dither matrix includes threshold values to form dots under the following conditions.
     (1) Around the center of a unit image, larger sized dots are formed.   (2) The longer a distance between a target dot and the center of a unit image is, the smaller a dot size of the target dot is.   (3) The longer a distance between a target dot and the center of a unit image is, the smaller a density (or a number) of an ON dot is.   

     FIG. 6  shows examples of unit images, images after binarization. Each of (a)-(c) in  FIG. 6  shows a unit image having a size of 8×8 dots. As shown in  FIG. 6 , the larger dots are formed near the center of the unit image. Furthermore, a dot size gets correspondingly smaller as a distance between a dot and the center of the unit image becomes longer. According to the binarization with the dither matrix of the present embodiment, two adjacent unit images are connected by dots whose density is gradually increased or decreased. Therefore, dot concentration which results in granularity of an image is not conspicuous compared to methods of related art. Thus, the present embodiment provides a high quality image in view of granularity. 
   Referring to  FIG. 5  again, in step S 410 , CPU  21  determines an ON/OFF state of a dot. On determining the ON/OFF state of a dot, CPU  21  compares a divided image with a corresponding dither matrix. CPU  21  reserves in RAM  23  a storage area of a unit image of a dot matrix for each dot size. Hereinafter, the dot matrix is also referred to as “dot ejection data”. RAM  23  stores a plurality of dot ejection data. Each of the dot ejection data corresponds to a dot size. Initially, all dots included in dot ejection data are set as “0”, showing that no dot is formed. 
     FIG. 7  shows a flow chart illustrating an ON/OFF determination in step S 400 . In step S 500 , CPU  21  reserves in RAM  23  a storage area for parameter DS. The value of parameter DS is set to “1” as an initial value. Here, parameter DS is a parameter showing a dot size. In the present embodiment, a smaller value of DS represents a larger dot size. Furthermore, MAX DS  shows a number of dot sizes that image forming device  1  can eject. In the present embodiment, MAX DS  =3 because image forming device  1  can eject dots of S, M, and L sizes. 
   Next, in step S 510 , CPU  21  compares a dot value of a target dot with a corresponding threshold value of a dither matrix. In a case that the dot value of the target pixel is greater than the corresponding threshold value (in step S 510 : YES), CPU  21  generates in step S 550  data which shows that a dot having a dot size of DS is formed at the target pixel. In other words, CPU  21  updates a pixel value of a target pixel as “1” showing an ON state of a dot. On the contrary, in a case that the dot value of the target pixel is greater than the corresponding threshold value (in step S 510 : NO), CPU  21  updates in step S 520  the parameter DS in accordance with a predetermined equation, DS=DS+1 in the present embodiment. Next, in step S 530 , CPU  21  determines whether parameter DS satisfies a predetermined condition, DS&gt;MAX DS . In a case that parameter DS satisfies DS&gt;MAX DS  (in step S 530 : YES), CPU  21  determines in step S 540  that the target dot is an OFF dot. In other words, the pixel value of the target dot remains “0”. In a case that parameter DS does not satisfy the equation DS&gt;MAX DS  (in step S 530 : NO), CPU  21  repeats the operations of steps S 510 -S 520 . 
   Next, in step S 560 , CPU  21  determines whether the ON/OFF determination is completed for all pixels of the multi-level image data. In a case that the ON/OFF determination is not completed for all pixels (in step S 560 : NO), CPU  21  repeats the operations of steps S 500 -S 560  until the ON/OFF determination is completed for all pixels. In a case that the ON/OFF determination is not completed for all pixels (in step S 560 : NO), CPU  21  terminates the ON/OFF determination and proceeds to the operation in step S 420  of  FIG. 5 . 
   Operations of image forming device  1  are described with reference to  FIG. 5 . In step S 420 , CPU  21  calculates a duty ratio of dots. Here, “duty ratio” of dots means a ratio of a number of dots having a particular dot size. Image forming device  1  can form dots of three sizes, S, M, and L. In the present embodiment, duty ratio DUTY DS  is determined as DUTY DS =(number of dots having a dot size DS)/(number of dots having a dot size DS+1). For example, in a case of DS=1, DUTY DS =(number of L size dots)/(number of M size dots). CPU  21  calculates a duty ratio for all dot sizes, DS=1 through (MAXS DS −1). CPU  21  stores in RAM  23  the calculated duty ratios. 
   Next, in step S 430 , CPU  21  determines whether the duty ratios are within a predetermined range. ROM  22  stores in advance a reference value of the duty ratio. For example, ROM  22  stores a minimum value DUTY DS   MIN  and a maximum value DUTY DS   MIN . CPU  21  compares for each dot size DS the calculated duty ratio DUTY DS  with DUTY DS   MIN  and DUTY DS   MAX , thereby determining whether each of duty ratios DUTY DS  satisfies the equation DUTY DS   MIN ≦DUTY DS ≦DUTY DS   MAX . In a case that duty ratio DUTY DS  satisfies the predetermined condition (in step S 430 : YES), CPU  21  terminates the binarization and proceeds to the operation in step S 140  of  FIG. 3 . In a case that duty ratio does not satisfy the predetermined condition (in step S 430 : NO), CPU  21  updates in step S 440  the corresponding dither matrix(es). Detail of the update is as follows. 
     FIG. 8  shows a flow chart illustrating the update of the dither matrix in step S 440 . In step S 600 , CPU  21  reads from RAM  23  duty ratios DUTY DS , each of which corresponds to a value of DS. Next, in step S 610 , CPU  21  initializes parameter DS as DS=1. Next, in step S 620 , CPU  21  determines whether DUTY DS  is within a predetermined range, similar to the operation in step S 430 . In a case that DUTY DS  is within the predetermined range (in step S 620 : YES), CPU  21  updates in step S 630  parameter DS in accordance with a predetermined equation, DS=DS+1 in this case. In step S 640 , CPU  21  determines that the operations are completed for all values of parameter DS. In other words, CPU  21  determines whether parameter DS satisfies a predetermined condition, DS&gt;MAX DS . In a case that the operations are not completed for all values of parameter DS (in step S 640 : NO), CPU  21  repeats the operations of steps S 620 -S 630 . In a case that the operations are completed for all values of parameter DS (in step S 640 : YES), CPU  21  proceeds to an operation in step S 680 . 
   In a case that CPU  21  determines duty ratio DUTY DS  is not within the predetermined range (in step S 620 : NO), CPU  21  determines in step S 650  whether duty ratio DUTY DS  is greater than a corresponding reference value. For example, an average DUTY DS   AVE , which is defined as DUTY DS   AVE =(DUTY DS   MIN +DUTY DS   MAX )/2, is employed as a reference value. Therefore, CPU  21  determines whether duty ratio DUTY DS  satisfies DUTY DS &gt;DUTY DS   AVE . In a case that duty ratio DUTY DS  satisfies the condition (in step S 650 : YES), CPU  21  updates in step S 660  threshold values in the dither matrix to be increased. On the contrary, in a case that duty ratio DUTY DS  does not satisfy the condition (in step S 650 : NO), CPU  21  updates in step S 670  threshold values in the dither matrix to be decreased. To increase the threshold value, CPU  21  can add a predetermined value to the threshold value. Alternatively, CPU  21  can multiply a predetermined value (the predetermined value is greater than 1) to the threshold value. Similarly, to decrease the threshold value, CPU  21  can subtract a predetermined value from the threshold value. Alternatively, CPU  21  can multiply a predetermined value (the predetermined value is less than 1) to the threshold value. It is to be noted that CPU  21  can employ in step S 650  a reference value other than DUTY DS . For example, CPU  21  may employ DUTY DS   MIN  or DUTY DS   MAX  as a reference value. Alternatively, CPU  21  may employ as a reference value another constant that is independent of DUTY DS   MIN  and DUTY DS   MAX . 
   Thus, the dither matrix is updated (or optimized) on the basis of the duty ratio. The reason for updating the dither matrix is as follows. It is known that increasing number of smaller sized dots provide a high quality image that satisfies human visual sense. However, for a single-pass printer such as a line head printer, increasing number of smaller sized dots causes banding to appear in a printed image. To prevent banding, it is preferable to form bigger sized dots around the center of a pixel of a printed image. Furthermore, to prevent deterioration in granularity of a printed image, it is preferable to form dots to satisfy the following conditions. (1) The longer a distance between a dot and the center is, the smaller a dot size of the dot is. (2) The longer a distance is between a dot and the center is, the smaller a density (or a number) of an ON dot is. Therefore, it is preferable to update a dither matrix so that the duty ratio of a larger sized dot becomes higher than the smaller one. 
   CPU  21  proceeds to an operation in steps S 630  and S 640 , after the operation in step S 660  and S 670 , respectively. In a case that the operations are completed for all values of parameter DS (in step S 640 : YES), CPU  21  performs clipping threshold values in a dither matrix to conform with the gradation range (0 through 255 in a case of 8 bit image data) of image forming device  1 . For example, a threshold value below zero is updated as zero, and a threshold value above 255 is updated as 255. When the operation in step S 680  is completed, CPU  21  proceeds to an operation in step S 410  of  FIG. 4 . 
   Referring to  FIG. 3  again, in step S 140 , CPU  21  outputs the binary image data to image forming unit  25  as nozzle control data. Image forming unit  25  controls a nozzle in accordance with the binary image data, thereby forming an image on a print media. It is to be noted that the binary image data may be converted into another kind of data, and the converted data may be output as nozzle control data. Image forming device  1  performs the operations described above. 
   2. Second Embodiment 
   Next, the second embodiment of the invention will be described in this section. In the first embodiment, the ON/OFF determination and the calculation of a duty ratio are performed for all of the input image data. Thus, the duty ratio is determined to be in a predetermined range. However, image forming device  1  in accordance with the first embodiment needs to perform an ON/OFF determination every time a dither matrix is updated. Therefore, image forming device  1  in accordance with the first embodiment has heavy load. The present embodiment relates to a image processing device capable of updating a dither matrix with light load. 
     FIG. 9  shows a flow chart illustrating binarization in accordance with the second embodiment of the invention. In the second embodiment, most of the elements are the same as those of the first embodiment, except for binarization. Binarization shown in  FIG. 9  is employed instead of binarization shown in  FIG. 5 . The same elements as the first embodiment are not described in the following description. 
   In step S 700 , CPU  21  generates a reduction image. A reduction image is an image generated by scaling an input image down. In other words, CPU  21  converts a resolution of the input image data into a predetermined resolution. The resolution after the conversion may be a predetermined number less than the input image data, for example, ¼ or 1/16 of the resolution of the input image. Alternatively, the image data after the conversion may have a predetermined size. 
   Next, CPU  21  performs operations same as the operations in steps S 400 -S 440  of  FIG. 5 . Thus, a duty ratio is optimized for the reduction image. Although the reduction image is not the same as the input image, but the reduction image has the similar characteristics to the original input image. Therefore, the obtained duty ratio optimized for the reduction image is also optimized for the input image. CPU  21  performs in step S 710  an ON/OFF determination by using the updated dither matrix, after completing the operations in steps S 400 -S 440 . Details of the ON/OFF determination are the same as the first embodiment, shown in  FIG. 7 . 
   3. Further Embodiments 
   The invention is not restricted to the above described embodiments. Various modification can be applied to the embodiments. For example, in the above embodiments, a single apparatus, image forming device  1 , performs the operations in steps S 100 -S 140 . In another embodiment, a plurality of apparatus or a system may perform the operations. 
     FIG. 10  shows an example of image forming system  100  in accordance with another embodiment. Image forming device  1  is connected to PC  2  via wired or wireless network. Digital camera  3  is an image capturing device that stores an image in memory card MC. PC  2  has an interface for reading data from memory card MC. In image forming system  100 , for example, PC  2  may function as image processing device  200  that performs all or a part of operations in steps S 100 -S 140 . Alternatively, image forming device  1  may read data from memory card MC, and may perform all or a part of operations in steps S 100 -S 140 . 
   In the present embodiments, image processing is performed in an order of resolution conversion, calorimetric system conversion, quantization, and rasterization. The order of the operation is not restrict to the embodiments. Image processing may be performed, for example, in an order of colorimetric system conversion, resolution conversion, quantization, and rasterization. 
   In another embodiment, calorimetric system conversion is not restricted to that from an RGB system into a CMYK system. For example, RGB image data may be converted into a seven-color system, black, cyan, magenta, yellow, light-cyan, light-magenta, and dark-yellow. 
   Yet in another embodiment, the embodiments may be applied to not only a line head printer but also to a multi-pass printer. 
   In the above embodiment, each of the shape of the divided image data, the dither matrix, and the unit image are a square having a size of m×m. The shape of the divided image data, the dither matrix, and the unit image may be, for example, a rectangle having a size of m×n. 
     FIG. 11  shows an example of the divided image data, the dither matrix, and the unit image having a size of m×n. In the example shown in  FIG. 11 , the size is 3×4.