Patent Publication Number: US-11394854-B2

Title: Image processing apparatus, image processing method, and storage medium for obtaining density characteristics to reduce density unevenness

Description:
BACKGROUND OF THE DISCLOSURE 
     Field of the Disclosure 
     The aspect of the embodiments relates to an image processing technique for obtaining density characteristics of each printing element to reduce density unevenness and streaks which occur when ink is discharged to form an image. 
     Description of the Related Art 
     In printheads used for an inkjet printer, variations in the amount of ink discharge may occur among a plurality of printing elements (nozzles) due to a production error or the like. If variations in the amount of ink discharge occur, density unevenness is more likely to occur in a formed image. A head shading (HS) technique is a known technique for reducing density unevenness. In the HS technique, image data is corrected based on information about the amount of ink discharge from each printing element (density characteristics of each printing element). This correction processing makes it possible to increase or decrease the number of ink dots to be discharged from each printing element to adjust the density of an image to be formed. 
     To obtain density characteristics of each printing element, a method of printing each patch (e.g., a uniform image for each gradation) on paper and measuring the patch by a scanner is known. In this case, unevenness may occur in a scanned image due to characteristics of a scanner, which may lead to deterioration in the accuracy of obtaining density characteristics of each printing element. Japanese Patent Laid-Open No. 2012-147126 discusses a technique in which, in a case where a non-discharge nozzle is present, filtering is performed after the measured value corresponding to the non-discharge nozzle is interpolated with a measured value near the measured value. 
     However, noise caused by the scanner is significant in a high-density region of a measurement target object, and thus it may be difficult to fully reduce the noise in the high-density region. 
     SUMMARY OF THE DISCLOSURE 
     According to one aspect of the embodiments, an apparatus that corrects a measured value obtained by measuring a measurement image formed using a printing element configured to discharge ink, the measured value being used to identify a density characteristic of the printing element, the image processing apparatus comprises: a first obtaining unit configured to obtain a measured value by measuring a measurement image; and a first correction unit configured to correct the measured value based on a density of the measurement image. 
     Further features of the disclosure will become apparent from the following description of exemplary embodiments with reference to the attached drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The accompanying drawings, which are incorporated in and constitute a part of the specification, illustrate embodiments of the disclosure and, together with the description, serve to explain the principles of the disclosure. 
         FIG. 1  schematically illustrates a configuration of an image forming apparatus according to a first exemplary embodiment. 
         FIG. 2  is a block diagram illustrating a configuration of an image forming system according to the first exemplary embodiment. 
         FIGS. 3A and 3B  are block diagrams each illustrating a functional configuration of an image processing apparatus according to the first exemplary embodiment. 
         FIG. 4  is a flowchart illustrating head shading (HS) processing. 
         FIG. 5  illustrates an example of a measurement image. 
         FIGS. 6A and 6B  are graphs each illustrating HS processing. 
         FIG. 7  is a graph illustrating an example of a measured value obtained by measuring a measurement image. 
         FIG. 8  is a flowchart illustrating processing for correcting a measured value. 
         FIGS. 9A and 9B  are graphs each illustrating a relationship between a filter size and a representative value. 
         FIG. 10  is a flowchart illustrating multi-color shading (MCS) processing. 
         FIG. 11  illustrates a three-dimensional color space for MCS processing. 
         FIGS. 12A and 12B  are flowcharts each illustrating processing executed by the image processing apparatus. 
         FIG. 13  is a block diagram illustrating a functional configuration of an HS processing unit. 
     
    
    
     DESCRIPTION OF THE EMBODIMENTS 
     Exemplary embodiments of the disclosure will be described in detail below with reference to the accompanying drawings. The following exemplary embodiments are not meant to limit the scope of the disclosure as encompassed by the appended claims. Not all features described in the exemplary embodiments are essential for the disclosure. The features may be arbitrarily combined. Further, in the accompanying drawings, the same or similar components are denoted by the same reference numerals, and redundant descriptions are omitted. 
     First Exemplary Embodiment 
     A first exemplary embodiment illustrates a method for obtaining density characteristics of each printing element of an image forming apparatus in an image forming system including the image forming apparatus that forms an image on a recording medium and a host apparatus that controls the image forming apparatus. In the image forming system, the density characteristics of each printing element are obtained based on control processing performed by the host apparatus. The first exemplary embodiment illustrates an example where an inkjet printer is used as the image forming apparatus and a personal computer (PC) is used as an example of the host apparatus. 
     Configuration of Image Forming Apparatus 
       FIG. 1  schematically illustrates a configuration of an image forming apparatus according to the present exemplary embodiment. The image forming apparatus according to the present exemplary embodiment is an inkjet printer. As illustrated in  FIG. 1 , an image forming apparatus  100  includes printheads  101 ,  102 ,  103 , and  104 . Each of the printheads  101  to  104  includes a plurality of nozzles for discharging ink. The plurality of nozzles is arranged along a predetermined direction within a range corresponding to the width of a recording sheet  106 . In other words, each of the printheads  101  to  104  according to the present exemplary embodiment is a full-line printhead. The printhead  101  is a printhead for discharging black (K) ink, and the printhead  102  is a printhead for discharging cyan (C) ink. The printhead  103  is a printhead for discharging magenta (M) ink, and the printhead  104  is a printhead for discharging yellow (Y) ink. An interval between the nozzles in each of the printheads  101  to  104  is set to have a resolution of 1200 dpi. 
     A conveyance roller  105  (and other rollers (not illustrated)) is rotated by a driving force from a motor (not illustrated), thereby conveying the recording sheet  106 , which is a recording medium, in a direction indicated by an arrow in  FIG. 1 . While the recording sheet  106  is conveyed, ink is discharged based on recording data from the plurality of nozzles of each of the printheads  101  to  104 . As a result, an image corresponding to one raster that corresponds to a nozzle row of each of the printheads  101  to  104  is sequentially formed. In addition, a scanner  107  including scanning elements arranged at a predetermined pitch in a state where the scanning elements are arranged in parallel with the printheads  101  to  104  is disposed at a position downstream of the printheads  101  to  104  in a y-direction. The scanner  107  can scan images formed using the printheads  101  to  104  and can output the scanned images as multivalued data having a color signal value. For example, an image corresponding to one page can be formed by repeatedly performing an ink discharge operation of discharging ink from each of the printheads  101  to  104  on the conveyed recording sheet as described above. 
     A full-line type image forming apparatus is used as the image forming apparatus in the present exemplary embodiment. However, the present exemplary embodiment can also be applied to a serial type image forming apparatus that performs recording by scanning each of the printheads  101  to  104  in a direction crossing a recording sheet conveyance direction. 
     Configuration of Image Forming System 
       FIG. 2  is a block diagram illustrating the configuration of the image forming system according to the present exemplary embodiment. As illustrated in  FIG. 2 , the image forming system according to the present exemplary embodiment includes the image forming apparatus  100  illustrated in  FIG. 1  and a PC  200  serving as the host apparatus that controls the image forming apparatus  100 . 
     The PC  200  includes a central processing unit (CPU)  201 , a random access memory (RAM)  202 , a hard disk drive (HDD)  203 , a data transfer interface (I/F)  204 , a keyboard/mouse I/F  205 , and a display I/F  206 . The CPU  201  executes various processes based on programs held in the HDD  203  and the RAM  202 . In particular, the CPU  201  executes programs to execute processing for an image processing apparatus  300  according to an exemplary embodiment to be described below. The RAM  202  is a volatile storage and temporarily holds programs and data. The HDD  203  is a nonvolatile storage and can hold programs and table data generated by processing according to each exemplary embodiment to be described below. The data transfer I/F  204  controls transmission and reception of data to and from the image forming apparatus  100 . As a connection method for transmitting and receiving data, a universal serial bus (USB), Institute of Electrical and Electronics Engineers (IEEE) 1394, a local area network (LAN), and the like can be used. The keyboard/mouse I/F  205  is an I/F for controlling a human interface device (HID) such as a keyboard or a mouse. A user inputs data via the keyboard/mouse I/F  205 . The display I/F  206  controls display on a display (not illustrated). 
     The image forming apparatus  100  includes a CPU  211 , a RAM  212 , a read-only memory (ROM)  213 , a data transfer I/F  214 , a head controller  215 , an image processing accelerator  216 , and a scanner controller  217 . The CPU  211  executes processing based on programs held in the ROM  213  and the RAM  212 . The RAM  212  is a volatile storage and temporarily holds programs and data. The ROM  213  is a nonvolatile storage and holds data and programs. The data transfer I/F  214  controls transmission and reception of data to and from the PC  200 . The head controller  215  supplies recording data to each of the printheads  101  to  104  illustrated in  FIG. 1  and controls the printhead discharge operation. Specifically, the head controller  215  can be configured to read a control parameter and recording data from a predetermined address in the RAM  212 . When the CPU  211  writes the control parameter and recording data at the predetermined address in the RAM  212 , processing is started by the head controller  215  and ink is discharged from each of the printheads  101  to  104 . The CPU  211  also functions as a formation control unit for forming a measurement image to be described below. The image processing accelerator  216  executes image processing at a higher speed than the CPU  211 . Specifically, the image processing accelerator  216  can be configured to load a parameter and data for image processing from a predetermined address in the RAM  212 . When the CPU  211  writes the parameter and data at the predetermined address in the RAM  212 , the image processing accelerator  216  is started to perform predetermined image processing. Note that the image processing accelerator  216  need not necessarily be provided. The processing may be executed by the CPU  211  alone depending on, for example, the specifications of the image forming apparatus  100 . The scanner controller  217  controls each scanning element of the scanner  107  illustrated in  FIG. 1  and outputs data obtained by scanning to the CPU  211 . 
     Functional Configuration of Image Processing Apparatus 
       FIG. 3A  is a block diagram illustrating the functional configuration of the image processing apparatus  300  included in the PC  200 . The image processing apparatus  300  includes an input unit  301 , an image processing unit  302 , and an output unit  308 . 
     As illustrated in  FIG. 3A , the input unit  301  receives image data and outputs the image data to the image processing unit  302 . The image processing unit  302  includes an input color conversion processing unit  303 , an ink color conversion processing unit  304 , and a head shading (HS) processing unit  305 . The image processing unit  302  further includes a tone reproduction curve (TRC) processing unit  306  and a quantization processing unit  307 . 
     The input color conversion processing unit  303  converts the input image data obtained from the input unit  301  into image data corresponding to a color reproduction range of a printer. The input image data used in the present exemplary embodiment is data representing coordinates (R, G, B) in a standard red, green, and blue (sRGB) color space, which is a color space corresponding to a display. The sRGB color space is a space in which “R”, “G”, and “B” are each set as an axis, and each coordinate is represented by eight bits. Accordingly, the input image data is image data in which R, G, and B values are each represented by eight bits. The input color conversion processing unit  303  converts an input color signal value for each of the R, G, and B values in the input image data into a printer color signal value for each of R′, G′, and B′ values corresponding to the color reproduction range of the printer. The color signal value for each of the R, G, and B values is hereinafter expressed as a color signal value (R, G, B). In the conversion processing, a known method, such as matrix operation processing or processing using a three-dimensional lookup table (LUT), is used. In the present exemplary embodiment, the conversion processing is performed using the three-dimensional LUT and an interpolation operation. The resolution of 8-bit image data that is treated in the image processing unit  302  is 1200 dpi. 
     The ink color conversion processing unit  304  performs conversion processing for converting the color signal values in the image data converted by the input color conversion processing unit  303  into color signal values corresponding to a plurality of types of ink. The image forming apparatus  100  uses black (K) ink, cyan (C) ink, magenta (M) ink, and yellow (Y) ink. Accordingly, a printer color signal value (R′, G′, B′) is converted into an ink color signal value (K, C, M, Y). The K, C, M, and Y values are also represented by eight bits, like the R, G, and B values. Like the input color conversion processing unit  303 , the ink color conversion processing unit  304  also performs the conversion processing using the three-dimensional LUT and the interpolation operation. 
     The HS processing unit  305  performs correction processing based on the density characteristics of the nozzles constituting each of the printheads  101  to  104  on the image data having the ink color signal value (K, C, M, Y).  FIG. 13  is a block diagram illustrating the detailed functional configuration of the HS processing unit  305 . The HS processing unit  305  includes an image data obtaining unit  1301 , a measured value obtaining unit  1302 , a measured value correction unit  1303 , a target obtaining unit  1307 , and a color signal value correction unit  1308 . The measured value correction unit  1303  includes a representative value obtaining unit  1304 , a filter size determination unit  1305 , and a filtering unit  1306 . The HS processing unit  305  according to the present exemplary embodiment calculates density characteristics of each nozzle using data obtained by reading the measurement image, and executes correction processing on the image data using the calculated density characteristics of each nozzle. HS processing performed by the HS processing unit  305  will be described in detail below. 
     The TRC processing unit  306  adjusts, for each color of ink, the number of ink dots to be recorded by the image forming apparatus  100  on image data having an HS color signal value (K′, C′, M′, Y′) obtained by the HS processing. Specifically, the image data is corrected such that the relationship between the number of dots to be recorded on a recording medium and the brightness achieved by the dots becomes linear. This correction processing enables adjustment of the number of dots to be recorded on a recording medium. 
     The quantization processing unit  307  performs quantization processing (halftone processing) on image data having a TRC color signal value (K″, C″, M″, Y″) obtained by TRC processing, and generates binary data in which each pixel value is represented by one bit. The binary data that is used as recording data represents an arrangement of ink dots to be discharged. In the present exemplary embodiment, a known dithering method is used as a method for quantization processing, but instead, a known error diffusion method or the like may be used. 
     The output unit  308  outputs the binary data obtained by the quantization processing to the image forming apparatus  100 . The image forming apparatus  100  drives each of the printheads  101  to  104  based on the received binary data and discharges ink of each color onto a recording medium to form an image on the recording medium. 
     Processing Executed by Image Processing Apparatus 
       FIG. 12A  is a flowchart illustrating processing executed by the image processing apparatus  300 . The processing executed by the image processing apparatus  300  will be described in detail below with reference to  FIG. 12A . In the following description, each step is denoted by “S” followed by a number. 
     In step S 1201 , the input unit  301  receives input image data and outputs the received image data to the image processing unit  302 . In step S 1202 , the input color conversion processing unit  303  converts the input color signal value (R, G, B) of the input image data into the printer color signal value (R′, G′, B′) corresponding to the color reproduction range of the printer. In step S 1203 , the ink color conversion processing unit  304  coverts the printer color signal value (R′, G′, B′) into the ink color signal value (K, C, M, Y) corresponding to a plurality of types of ink. In step S 1204 , the HS processing unit  305  performs HS processing on the image data having the ink color signal value (K, C, M, Y). In step S 1205 , the TRC processing unit  306  performs TRC processing on the image data having the HS color signal value (K′, C′, M′, Y′) obtained by the HS processing. In step S 1206 , the quantization processing unit  307  performs quantization processing on the image data having the TRC color signal value (K″, C″, M″, Y″) obtained by the TRC processing. In step S 1207 , the output unit  308  outputs the binary data generated by the quantization processing to the image forming apparatus  100 . 
     HS Processing 
       FIG. 4  is a flowchart illustrating the HS processing performed by the HS processing unit  305 . The HS processing will be described in detail below with reference to  FIG. 4 . 
     In step S 401 , the image data obtaining unit  1301  obtains image data having the ink color signal value (K, C, M, Y) output from the ink color conversion processing unit  304 . In step S 402 , the measured value obtaining unit  1302  obtains a measured value for identifying density characteristics of each nozzle. The measured value is obtained as image data in advance by preliminarily measuring the measurement image by the scanner  107 , and the image data is held in the HDD  203  or the like. 
     A method for generating image data including a measured value will be described below. First, a measurement image for obtaining density characteristics of each nozzle is formed on the recording sheet  106 .  FIG. 5  illustrates an example of the measurement image. Patches corresponding to nine gradations of  501 ,  502 ,  503 ,  504 ,  505 ,  506 ,  507 ,  508 , and  509 , respectively, are formed on the recording sheet  106 . Each patch is formed using only ink of a single color. An example where a patch is formed using only the printhead  101  (K ink) will be described below. In the present exemplary embodiment, processing for forming the measurement image uses only ink of a single color, and thus the processing is performed through a bypass path  309  indicated by a dashed line in  FIG. 3A . With this configuration, the input image data can be directly input to the TRC processing unit  306  without passing through the input color conversion processing unit  303 , the ink color conversion processing unit  304 , and the HS processing unit  305 . 
     Next, the measurement image is scanned by the scanner  107  and a scanned image is obtained by scanning. Each pixel value of the scanned image is obtained using three channels of (R, G, B). Next, the scanned image is converted into a scanned image in which a pixel value corresponding to one channel is included in each pixel by using a color conversion table, which is prepared in advance, according to the color characteristics of the scanner  107 . In the present exemplary embodiment, the scanned image is converted into a 16-bit value that is linear to “Y” in a CIE XYZ color space. Any color space can be used to represent each pixel value of the scanned image obtained after color conversion. For example, “L*” in a CIEL*a*b* color space, or a density may be used. In a case where the measurement image is formed using color ink of C, M, Y, or the like, a value corresponding to chroma can also be used instead of a value corresponding to brightness. For example, R, G, and B values may be used as values corresponding to complementary colors of C, M, and Y, respectively. The resolution of the scanned image in the present exemplary embodiment is 1200 dpi. The above-described processing makes it possible to generate image data having each pixel value of the scanned image as the measured value and to obtain the image data in step S 402 . 
     In step S 403 , the measured value correction unit  1303  corrects the measured value obtained in step S 402 . Processing for correcting the measured value will be described in detail below. In step S 404 , the target obtaining unit  1307  obtains target characteristic data representing a target characteristic based on a measurement curve generated based on the corrected measured value. The term “target characteristic” used herein refers to a predetermined target density characteristic based on a measurement curve for each nozzle. As illustrated in  FIG. 6A , a horizontal axis represents a gradation and a vertical axis represents a measured value. Referring to  FIG. 6A , a straight line that is linear to a gradation represents a target characteristic  604 . A dashed line  601  indicates an upper limit of the horizontal axis. Since the input signal value is represented by an 8-bit value, the upper limit in the present exemplary embodiment is 255. A measurement curve  602  is a curve generated by plotting the measured value in the scanned image of each of the patches  501  to  509  and performing an interpolation operation. A known piecewise linear interpolation is used for the interpolation operation in the present exemplary embodiment. A known spline curve or the like may be used as the measurement curve. The measurement curve  602  represents the density characteristic of a nozzle corresponding to a pixel position “x”, and a number of curves corresponding to the number of nozzles used for forming the measurement image are obtained. Different measurement curves for the density characteristics of each nozzle are obtained. For example, the measurement curve for the nozzle that discharges a small amount of ink is shifted upward (in a direction in which the brightness increases). In each gradation, a number of measured values corresponding to the width of each patch in the y-direction are obtained. Accordingly, average values of the measured values obtained in the y-direction in each gradation are used as nine measured values to generate the measurement curve. 
     In step S 405 , the color signal value correction unit  1308  corrects the ink color signal value (K, C, M, Y) of the image data obtained in step S 401  based on the measured value calculated in step S 403 , and obtains the HS color signal value (K′, C′, M′, Y′). A method for obtaining the HS color signal value (K′, C′, M′, Y′) will be described with reference to  FIG. 6B . Referring to  FIG. 6B , an input value  605  represents the ink color signal value (K, C, M, Y). The color signal value correction unit  1308  obtains the value of the target characteristic  604  corresponding to the input value  605 , and uses the obtained value as a target value  606 . Further, a signal value  607  of a measurement curve  603  corresponding to the target value  606  is obtained as the corrected HS color signal value (K′, C′, M′, Y′). The measurement curve  603  used herein is a measurement curve obtained by performing a piecewise linear interpolation on the measured value corrected in step S 403 . 
     Processing for Correcting Measured Value 
     Processing for correcting the measured value will be described in detail below.  FIG. 7  is a graph illustrating an example of the measured value obtained by measuring the measurement image illustrated in  FIG. 5 . In the graph illustrated in  FIG. 7 , a horizontal axis represents a nozzle number, which corresponds to the number of nozzles included in the printhead  101 . In the graph illustrated in  FIG. 7 , a vertical axis represents a measured value. Measured values  701 ,  702 ,  703 ,  704 ,  705 ,  706 ,  707 ,  708 , and  709  are measured values respectively corresponding to the patches  501  to  509  illustrated in  FIG. 5 . As described above, in each gradation, a number of measured values corresponding to the width of each patch in the y-direction are obtained. The present exemplary embodiment illustrates an average value of the measured values obtained in the y-direction in each gradation. As illustrated in  FIG. 7 , high-frequency noise occurs in the measured values  707  to  709  corresponding to the high-density patches  507  to  509 , respectively. This high-frequency noise is noise that is caused due to a dark current in the scanner  107  and is significant in a high-density region in which the measured value is small. The high-frequency noise can be reduced by filtering on the measured value. On the other hand, it may be desirable to prevent unnecessary filtering from being performed on the measured values  701  to  703  corresponding to the low-density patches  501  to  503 , respectively, in which no high-frequency noise occurs, so as to prevent blur in the measured value. Therefore, the HS processing unit  305  according to the present exemplary embodiment corrects the measured value by filtering based on the density of the measurement image. 
       FIG. 8  is a flowchart illustrating processing for correcting the measured value in the HS processing unit  305 . In step S 801 , the representative value obtaining unit  1304  obtains a representative value of the measured values for each gradation (for each density). In the present exemplary embodiment, the average value is calculated as the representative value for each of the measured values  701  to  709  illustrated in  FIG. 7 . In step S 802 , the filter size determination unit  1305  determines the size of a filter used for filtering based on the representative value. The filter used in the present exemplary embodiment is a one-dimensional average value filter with a variable size in an x-direction. For example, when the filter size is “3”, the filter has a configuration in which the average value of the measured values corresponding to a pixel of interest and two pixels adjacent to the pixel of interest in the x-direction is set as the measured value of the pixel of interest.  FIG. 9A  is a graph illustrating an example of the relationship between the representative value and the filter size. The filter size increases as the representative value decreases (as the density increases). For example, when the total number of nozzles is 15000, the filter size is set such that a minimum filter size is “0” and a maximum filter size is “15000”. The representative value is calculated for each of the measured values  701  to  709 . Similarly, the filter size is determined for each of the measured values  701  to  709 . 
     In step S 803 , the filtering unit  1306  corrects the measured values. Specifically, filtering is performed on each of the measured values  701  to  709  by the average value filter with the size determined in step S 802 . Each of the measured values  701  to  709  to which filtering is applied corresponds to the average value of the measured values obtained in the y-direction in each gradation. When the filter size is “0”, filtering is not performed. Further, when a pixel corresponding to an end of a patch is set as a pixel of interest, the measured value corresponding to a paper white region which is a region other than the patch may be included in a filter application range. Accordingly, in the present exemplary embodiment, when the measured value corresponding to the paper white region is included in the filter application range, filtering is performed on the measured values other than the measured value corresponding to the paper white region. This leads to an improvement in the filtering accuracy. 
     Advantageous Effects of First Exemplary Embodiment 
     As described above, the image processing apparatus according to the present exemplary embodiment obtains a measured value by measuring a measurement image and corrects the measured value based on the density of the measurement image. This configuration makes it possible to reduce noise which is included in the measured value for identifying the density characteristics of each printing element and which depends on the density of the measurement image. Consequently, the density characteristics of each printing element can be obtained with high accuracy. In addition, the HS processing using the obtained density characteristics of each printing element can reduce density unevenness and streaks in an image to be formed on a recording medium. 
     Modified Examples 
     In step S 803  according to the exemplary embodiment described above, filtering is performed on the measured values by the average value filter. However, processing other than filtering may be used, as long as values in different frequency ranges can be corrected in each of the low-density region and the high-density region of the measurement image. For example, known filtering using a Gaussian filter or a median filter, or known noise reduction processing using frequency transform, such as Fourier transform or wavelet transform, may also be used. 
     In step S 801  according to the exemplary embodiment described above, the average value of the measured values for each gradation is used as the representative value. However, the representative value is not limited to the average value, as long as a macro density can be obtained for each gradation. For example, a median may be used as the representative value. Further, in the case of calculating the representative value, the measured value in a region corresponding to a non-discharge nozzle can be excluded from being used. 
     In the exemplary embodiment described above, the scanning resolution for the measurement image is 1200 dpi, which is equal to the resolution for the arrangement of the nozzles of each of the printheads  101  to  104 . However, the scanning resolution may be higher or lower than the resolution for the arrangement of the nozzles of each of the printheads  101  to  104 . If the scanning resolution is increased, the density for each nozzle can be obtained more accurately. On the other hand, if the scanning resolution is decreased, it is difficult to detect high-frequency unevenness. In this case, however, the amount of data to be read decreases, which leads to a reduction in the cost of the system. Further, the measurement curve may be generated using the average value of measured values for a plurality of nozzles. This leads to a reduction in storage capacity for holding information about the measurement curve. 
     In the exemplary embodiment described above,  FIG. 9A  illustrates an example of the relationship between the representative value and the filter size. However, the relationship can be arbitrarily set based on the characteristics of the filter. During the setting, a scanned image is obtained, for example, in a dark environment in which there is no lighting, and signal values related to the scanned image are averaged in a sheet conveyance direction, so that characteristics related to a dark current can be obtained. Further, a sufficiently uniform gradation chart for calibration may be obtained to thereby obtain scanner noise characteristics for each gradation. 
     In the exemplary embodiment described above, the representative value of the measured values obtained by the scanner  107  is used as the value for determining the filter size. However, the measured values obtained by the scanner  107  need not necessarily be used, as long as the macro density for each gradation can be associated with the filter size. For example, a representative value of color signal values obtained by measuring the measurement image using a colorimeter, which is different from the scanner  107 , may also be used. 
     The exemplary embodiment described above illustrates the method of reducing more high-frequency components of the measured values in a higher-density region as a method for reducing the influence of noise due to a dark current. However, the characteristics that vary depending on the density are not limited to the characteristics of the scanner  107 . Noise does not always increase as the density increases. For example, a flaw on a surface of a print product due to abrasion is more likely to occur in a higher-density region with a larger amount of ink, and the influence of unevenness on the surface of the recording sheet itself becomes more significant than that in a lower-density region. Accordingly, as illustrated in  FIG. 9B , the filter size may be determined such that the filter size in each of the high-density region and the low-density region is larger than the filter size in a medium-density region. This configuration makes it possible to reduce the influence of noise due to a dark current in the scanner  107  and also reduce the influence of noise due to unevenness on the surface of the recording sheet itself. 
     In the exemplary embodiment described above, filtering is applied to the measured values for all the density regions from the low-density region to the high-density region. However, filtering may be applied only to the high-density region, as long as noise in the measured value corresponding to the high-density region can be reduced. 
     While the exemplary embodiment described above illustrates an example where the measured values are corrected by filtering every time an image is formed on a recording medium, the measured values may be corrected in advance using a filter with a size based on the density. In this case, the processes of steps S 402  and S 403  are performed in advance by the measured value obtaining unit  1302  and the measured value correction unit  1303 , respectively, and the corrected measured values are held in the HDD  203  or the like. This eliminates the need for performing correction processing every time image data is input, which leads to a reduction in processing cost and a reduction in density unevenness in an image. 
     Second Exemplary Embodiment 
     In the exemplary embodiment described above, each patch of the measurement image is formed using only ink of a single color and HS processing is performed on each color of ink. However, even after the HS processing is performed on each color of ink, color unevenness may occur when a multi-order color is represented by superimposing two or more colors of ink. To deal with such color unevenness, a technique called multi-color shading (MCS) processing is known. Accordingly, a second exemplary embodiment illustrates processing for reducing density unevenness and streaks in an image with high accuracy even when the characteristics of the measured value used in MCS processing vary depending on the density of the measurement image. 
     Functional Configuration of Image Processing Apparatus 
       FIG. 3B  is a block diagram illustrating the functional configuration of the image processing apparatus  300  according to the second exemplary embodiment. Image data output from the input color conversion processing unit  303  is input to an MCS processing unit  310 . The MCS processing unit  310  performs correction processing based on the density characteristics of the nozzles constituting each of the printheads  101  to  104  on the printer color signal value (R′, G′, B′) in the input image data. The MCS processing will be described in detail below. The image data having a corrected MCS color signal value (R″, G″, B″) is output to the ink color conversion processing unit  304 . Like the HS processing unit  305 , the MCS processing unit  310  obtains the measured value by measuring each patch in advance. The MCS processing unit  310  has a functional configuration similar to the functional configuration of the HS processing unit  305  illustrated in  FIG. 13 . 
     A measurement image for MCS processing includes a plurality of patches obtained by changing the input signal values R, G, and B independently. In the present exemplary embodiment, five gradations of 0, 64, 128, 192, and 25 are set for each of the R, G, and B values and 53 combinations (=125) of multi-order color patches are formed. The combinations of the patches are not limited to this example. In the present exemplary embodiment, processing for forming the measurement image for MCS processing is performed through a bypass path  311  indicated by a dashed line in  FIG. 3B . Thus, the image obtained after correction processing is performed by the HS processing unit  305  can be used as the measurement image. The measurement image is scanned by the scanner  107  and a scanned image is obtained. Unlike in the first exemplary embodiment, each pixel value of the scanned image is not converted into a value corresponding to one channel, but instead is held in the HDD  203  as an image having pixel values each corresponding to three channels of (R, G, B). 
     Processing Executed by Image Processing Apparatus 
       FIG. 12B  is a flowchart illustrating processing executed by the image processing apparatus  300 . The processing executed by the image processing apparatus  300  will be described in detail below with reference to  FIG. 12B . 
     In step S 1211 , the input unit  301  receives input image data and outputs the received image data to the image processing unit  302 . In step S 1212 , the input color conversion processing unit  303  converts the input color signal value (R, G, B) in the input image data into the printer color signal value (R′, G′, B′) corresponding to the color reproduction range of the printer. In step S 1213 , the MCS processing unit  310  performs MCS processing on the image data having the printer color signal value (R′, G′, B′). In step S 1214 , the ink color conversion processing unit  304  converts the MCS color signal value (R″, G″, B″) into the ink color signal value (K, C, M, Y) corresponding to a plurality of types of ink. In step S 1215 , the HS processing unit  305  performs HS processing on the image data having the ink color signal value (K, C, M, Y). In step S 1216 , the TRC processing unit  306  performs TRC processing on the image data having the HS color signal value (K′, C′, M′, Y′) obtained by the HS processing. In step S 1217 , the quantization processing unit  307  performs quantization processing on the image data having the TRC color signal value (K″, C″, M″, Y″) obtained by the TRC processing. In step S 1218 , the output unit  308  outputs the binary data generated by the quantization processing to the image forming apparatus  100 . 
     MCS Processing 
     The MCS processing will be described below with reference to a flowchart illustrated in  FIG. 10 . The MCS processing mainly differs from the HS processing in that the measurement image illustrated in  FIG. 5  is a multi-order color image and the measured value corresponds to three channels of (R, G, B). 
     In step S 1001 , the MCS processing unit  313  obtains image data having the printer color signal value (R′, G′, B′) output from the input color conversion processing unit  303 . In step S 1002 , the MCS processing unit  313  obtains, from the scanned image, the measured value at a nozzle position corresponding to a pixel of interest. In the present exemplary embodiment, 125 color signal values (R, G, B) are obtained as measured values for 125 patches. The measured values are obtained as image data by measuring the measurement image in advance by the scanner  107 , and the image data is held in the HDD  203  or the like. 
     In step S 1003 , the MCS processing unit  313  corrects the measured value. The correction processing is performed by the processing illustrated in  FIG. 8  in the same manner as in the first exemplary embodiment. The second exemplary embodiment differs from the first exemplary embodiment in that the representative value and the filter size are determined for each of the three channels of (R, G, B) and then filtering is performed. In step S 1004 , the MCS processing unit  313  obtains the target value (R, G, B). In the present exemplary embodiment, the target value (R, G, B) is obtained with reference to the LUT (not illustrated) in which the correspondence relation between the printer color signal value (R′, G′, B′) in the image data obtained in step S 1001  and the target value (R, G, B) of the scanned image is held. 
     In step S 1005 , the printer color signal value (R′, G′, B′) in the image data obtained in step S 1001  is corrected based on the corrected measured value, and the MCS color signal value (R″, G″, B″) is obtained. A specific method for correction processing will be described with reference to  FIG. 11 .  FIG. 11  illustrates a three-dimensional color space having “R”, “G”, and “B” of the color signal value (R, G, B) in the scanned image as each axis. A target value  1101  represents the target value obtained in step S 1004 . Values  1102 ,  1103 ,  1104 , and  1105  are four corrected measured values selected to form a minimum tetrahedron including the target value  1001  from among the 125 corrected measured values obtained in step S 1003 . The distance between the target value  1101  and each of the four corrected measured values  1102  to  1105  is calculated and an interpolation operation using the four corrected measured values is performed based on the ratio of the distance. The value obtained by the interpolation operation is obtained as the MCS color signal value (R″, G″, B″) corresponding to the pixel of interest. 
     Advantageous Effects of Second Exemplary Embodiment 
     As described above, the image processing apparatus according to the present exemplary embodiment performs correction processing based on the density of the measurement image on the measured value, and the color signal value in the image data is corrected by MCS processing using the corrected measured value. This configuration makes it possible to reduce noise which is included in the measured value for identifying the density characteristics of each printing element and which depends on the density of the measurement image. Consequently, the density characteristics of each printing element can be obtained with high accuracy. In addition, color unevenness in an image to be formed on a recording medium can be reduced by MCS processing using the obtained density characteristics of each printing element. 
     Modified Examples 
     The exemplary embodiment described above illustrates an example where the PC  200  functions as the image processing apparatus  300  in accordance with software installed in the PC  200 . Alternatively, the image forming apparatus  100  may include the image processing apparatus  300 . In a case where the image processing apparatus  300  is mounted in the image forming apparatus  100 , a dedicated image processing circuit that can achieve each functional configuration of the image processing apparatus  300  may be implemented. The functions of the image processing apparatus  300  may be executed by a server that can communicate with the image forming apparatus  100 . More alternatively, a part of the image processing apparatus  300  may be configured in the PC  200 , and the other part of the image processing apparatus  300  may be configured in the image forming apparatus  100 . 
     In the exemplary embodiments described above, an RGB color space is used as the color space representing each signal value of the measurement image, but any color space can be used. For example, a CIE XYZ color space or a CIEL*a*b* color space may be used. 
     In the exemplary embodiments described above, an image is formed using ink of four colors of K, C, M, and Y, but an image may be formed using other types of ink. For example, the above-described exemplary embodiments can also be applied to an image forming apparatus that forms an image using low-density ink of colors, such as light cyan, light magenta, and gray, or using ink of specific colors, such as red, green, blue, orange, and violet. 
     The exemplary embodiments described above illustrate an example where the image processing unit  302  performs processing on image data input in an RGB format represented by color signal values corresponding to three primary colors, but image data in a KCMY format may be directly input to the image processing unit  302 . In this case, the processing performed by the input color conversion processing unit  303  and the processing performed by the ink color conversion processing unit  304  can be omitted in the image processing unit  302 . 
     Other Embodiments 
     Embodiment(s) of the disclosure can also be realized by a computer of a system or apparatus that reads out and executes computer executable instructions (e.g., one or more programs) recorded on a storage medium (which may also be referred to more fully as a ‘non-transitory computer-readable storage medium’) to perform the functions of one or more of the above-described embodiment(s) and/or that includes one or more circuits (e.g., application specific integrated circuit (ASIC)) for performing the functions of one or more of the above-described embodiment(s), and by a method performed by the computer of the system or apparatus by, for example, reading out and executing the computer executable instructions from the storage medium to perform the functions of one or more of the above-described embodiment(s) and/or controlling the one or more circuits to perform the functions of one or more of the above-described embodiment(s). The computer may comprise one or more processors (e.g., central processing unit (CPU), micro processing unit (MPU)) and may include a network of separate computers or separate processors to read out and execute the computer executable instructions. The computer executable instructions may be provided to the computer, for example, from a network or the storage medium. The storage medium may include, for example, one or more of a hard disk, a random-access memory (RAM), a read only memory (ROM), a storage of distributed computing systems, an optical disk (such as a compact disc (CD), digital versatile disc (DVD), or Blu-ray Disc (BD)™), a flash memory device, a memory card, and the like. 
     While the disclosure has been described with reference to exemplary embodiments, it is to be understood that the disclosure is not limited to the disclosed exemplary embodiments. The scope of the following claims is to be accorded the broadest interpretation so as to encompass all such modifications and equivalent structures and functions. 
     This application claims the benefit of Japanese Patent Application No. 2019-180962, filed Sep. 30, 2019 which is hereby incorporated by reference herein in its entirety.