Patent Publication Number: US-9421761-B2

Title: Image processing apparatus, image processing method, and image recording apparatus

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to an image processing apparatus, an image processing method, and an image recording apparatus. 
     2. Description of the Related Art 
     There have heretofore been available image recording apparatuses configured to eject ink onto a recording medium while causing a recording head having an ejection opening array in which a plurality of ejection openings for ejecting ink of the same color are arranged in a predetermined direction to scan in a cross direction crossing the predetermined direction to complete the formation of an image on the recording medium. Such image recording apparatuses adopt a method that uses multiple scans or passes across a unit area on a recording medium, called multi-pass recording method, to suppress or reduce degradation of image quality. 
     It is well known that the ejection of ink using the multi-pass recording method described above may cause a certain ejection opening to have a failure to eject ink, such as being unable to eject ink or ejecting ink in a reduced amount. If such an inoperative ejection opening that has a failure to eject ink is assigned recording data for ejecting ink, no ink will be ejected onto an area onto which ink normally would be ejected, resulting in the quality of the image being reduced. Japanese Patent Laid-Open No. 5-330082 describes the following technique to address the issue of the degradation of image quality described above. If a certain ejection opening which will eject ink during a certain scan has a failure to eject ink, the recording data for such an inoperative ejection opening that has a failure to eject ink is complementarily assigned to any other ejection opening capable of ejecting ink onto the same area as that of the inoperative ejection opening during a different scan to perform complementary recording. 
     It is also well known that a recent image recording apparatus of the type described above includes a recording head in which a plurality of ejection opening arrays for ink of the same color are arranged side-by-side in the cross direction described above, and performs control to eject ink onto a recording medium while conveying the recording medium with respect to the recording head in the cross direction. Such an image recording apparatus provides recording by using a single scan without adopting the multi-pass recording method while achieving the effect of suppressing or reducing degradation of image quality similar to that of the multi-pass recording method (hereinafter also referred to as the “multi-pass effect”). 
     The use of the recording head described above may result in the amount of conveyance of a recording medium periodically varying. Accordingly, the positions where ink drops ejected from different ejection opening arrays land in the cross direction may be periodically displaced, causing a reduction in image quality. The displacement of the landing positions of ink drops increases with the difference between the times at which ink drops land, or increases with the distance between the ejection opening arrays in the cross direction. To address this issue, Japanese Patent Laid-Open No. 2008-168629 discloses the following technique. Binary data indicating positions in which ink drops are ejected is distributed to each ejection opening array, and recording data used for the ejection of ink drops from each ejection opening array is generated by setting the proportion of a predetermined number of ejection opening arrays arranged in close proximity to each other (for example, two adjacent ejection opening arrays) to which the binary data is distributed among a plurality of (for example, four) ejection opening arrays to be higher than the proportion of the other ejection opening arrays to which the binary data is distributed. 
     If a recording operation is performed using certain ejection opening arrays located in close proximity to each other among a plurality of ejection opening arrays arranged on a recording head in order to suppress or reduce the periodic displacement of the landing positions of ink drops described above, a certain ejection opening arranged in the certain ejection opening arrays may also experience such a failure to eject ink as described above. 
     The degradation of image quality due to the failure in the ejection of ink may be reduced to some extent by the performance of complementary recording using an ejection opening in any other non-defective ejection opening array located at a position such that ink drops can be ejected onto the same area as that of the inoperative ejection opening which has experienced the failure in ejection of ink in the certain ejection opening arrays. However, depending on the substitute to which the recording data for the inoperative ejection opening is complementarily assigned, complementary recording may be performed using an ejection opening other than ejection openings located in close proximity to the inoperative ejection opening as described above. This may result in failure to suppress or even reduce the displacement of the landing positions of ink drops. 
     SUMMARY OF THE INVENTION 
     Accordingly, the present invention provides recording with suppressed or reduced displacement of the landing positions of ink drops even in a case where complementary recording is performed upon occurrence of a failure in the ejection of ink. 
     An embodiment of the present invention provides an image processing apparatus for processing image data corresponding to an image to be recorded on a recording medium to record an image on the recording medium by ejecting ink onto the recording medium in accordance with recording data while causing a recording head and the recording medium to move with respect to each other in a cross direction crossing a predetermined direction. The recording head includes N ejection opening arrays each having, arranged in the predetermined direction, a plurality of ejection openings at least including a designated ejection opening, each of the plurality of ejection openings being configured to eject ink of a predetermined color. The N ejection opening arrays are arranged side by side in the cross direction so that N designated ejection openings respectively included in the N ejection opening arrays are capable of ejecting ink onto identical positions on the recording medium in the predetermined direction. The recording data defines ejection or non-ejection of ink onto each pixel area corresponding to a plurality of pixels on the recording medium for each of the N ejection opening arrays. The image processing apparatus includes a first obtaining unit configured to obtain dot recording data that defines dots to be recorded on the recording medium in accordance with the image data; a distribution unit configured to distribute the dot recording data obtained by the first obtaining unit to a first ejection opening array group including M ejection opening arrays among the N ejection opening arrays, where M&lt;N, to generate distribution data; a second obtaining unit configured to obtain information indicating whether or not each of the plurality of ejection openings arranged in each of the N ejection opening arrays has a failure to eject ink; a selection unit configured to select, in a case where the information obtained by the second obtaining unit indicates that K designated ejection openings in a first ejection opening group including M designated ejection openings arranged in the first ejection opening array group among the N designated ejection openings have a failure to eject ink, where K≦M, K substitute designated ejection openings from among (N−M) designated ejection openings other than the M designated ejection openings in the first ejection opening group; a complementary assignment unit configured to complementarily assign the distribution data distributed to the K designated ejection openings in the first ejection opening group to the K substitute designated ejection openings selected by the selection unit to generate complementary data; and a generation unit configured to generate the recording data in accordance with the distribution data distributed by the distribution unit and the complementary data complementarily assigned by the complementary assignment unit. The selection unit selects the K substitute designated ejection openings from among the (N−M) ejection openings so that a distance between designated ejection openings at opposite ends of a second ejection opening group in the cross direction is shortest, the second ejection opening group including (M−K) designated ejection openings, which are determined not to have a failure to eject ink by the information obtained by the second obtaining unit, and the K substitute designated ejection openings selected by the selection unit. 
     Further features of the present invention will become apparent from the following description of exemplary embodiments with reference to the attached drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic diagram illustrating an internal configuration of an image recording apparatus according to embodiments. 
         FIGS. 2A and 2B  are schematic diagrams of ejection opening array groups according to the embodiments. 
         FIG. 3  is a diagram illustrating a recording system according to the embodiments. 
         FIGS. 4A to 4C  are diagrams illustrating periodic shifts in the amount of conveyance of a recording medium. 
         FIG. 5  is a block diagram illustrating steps of image processing according to the embodiments. 
         FIG. 6  is a flowchart illustrating a process for the image processing according to the embodiments. 
         FIG. 7  is a diagram illustrating dot patterns according to the embodiments. 
         FIGS. 8A to 8C  are diagrams illustrating a distribution process according to the embodiments. 
         FIG. 9  is a flowchart illustrating a complementary assignment process according to the embodiments. 
         FIG. 10  is a flowchart illustrating an inoperative nozzle detection process according to the embodiments. 
         FIG. 11  is a diagram schematically illustrating detection patterns recorded in the embodiments. 
         FIG. 12  is a diagram schematically illustrating a read image of detection patterns to be recorded in the embodiments. 
         FIG. 13  is a flowchart illustrating a complementary nozzle determination method according to a first embodiment. 
         FIG. 14  is a diagram illustrating the steps of determining complementary nozzles according to the first embodiment. 
         FIG. 15  is a flowchart illustrating a complementary nozzle determination method according to a second embodiment. 
         FIG. 16  is a diagram illustrating the steps of determining complementary nozzles according to the second embodiment. 
     
    
    
     DESCRIPTION OF THE EMBODIMENTS 
     A first embodiment of the present invention will be described in detail hereinafter with reference to the drawings. 
     First Embodiment 
       FIG. 1  is a schematic diagram partially illustrating an internal configuration of an inkjet recording apparatus  100  according to this embodiment. 
     The inkjet recording apparatus (hereinafter also referred to as the “printer” or “image recording apparatus”)  100  according to this embodiment includes a recording head group  107  having recording heads  101  to  104 . The recording heads  101  to  104  are configured to eject black (K) ink, cyan (C) ink, magenta (M) ink, and yellow (Y) ink, respectively. The recording heads  101  to  104  are also formed so that the length of each of the recording heads  101  to  104  in a Y direction (predetermined direction) is larger than the width of a recording medium  106  in the Y direction. In this embodiment, the recording head group  107  is configured such that the recording heads  101  to  104  are arranged in an X direction (cross direction). 
     The recording medium  106  is conveyed (or moved) in the X direction by the rotation of conveyance rollers  105  (and other rollers (not illustrated)) due to the driving force of a conveyance motor (not illustrated). The conveyance (or movement) of the recording medium  106  in the X direction may provide advantages substantially equivalent to those achievable by the scanning of the recording head group  107  in the X direction. During the conveyance of the recording medium  106 , ink is ejected from a plurality of ejection openings (hereinafter also referred to as “nozzles”) arranged in each of the recording heads  101  to  104  in accordance with recording data described below. Through the ink ejection operation, an image is formed on the recording medium  106  by a single relative scan of the recording heads  101  to  104  to the recording medium  106  in the X direction. 
     The printer  100  further includes a scanner  108  for use in the detection of a failure in the ejection of ink described below. The scanner  108  has a resolution of 1200 dots per inch (dpi), by way of example. Instead, the scanner  108  may have a resolution greater than or equal to 1200 dpi or less than or equal to 1200 dpi. 
       FIG. 2A  is a schematic diagram illustrating a detailed configuration of the recording head  101  according to this embodiment for ejecting black ink. The recording head  101  includes 18 recording element substrates  201  to  218 , each having a plurality of ejection opening arrays (hereinafter also referred to as “nozzle arrays”) described below, and is configured such that the recording element substrates  201  to  218  are arranged in the Y direction so as to form a staggered pattern in which a first end of one of the recording element substrates  201  to  218  in the Y direction and a second end of another of the recording element substrates  201  to  218  in the Y direction are located at the same positions in the Y direction. Accordingly, the length of the recording head  101  in the Y direction is longer than the width of the recording medium  106  in the Y direction. Note that a recording head applicable to this embodiment is not limited to the recording head configured such that, as illustrated in  FIG. 2A , a plurality of recording element substrates are arranged in the Y direction. For example, the recording head may include a single recording element substrate having an ejection opening array with a length equal to or larger than the width of the recording medium  106 . 
       FIG. 2B  is a schematic diagram illustrating a detailed configuration of the recording element substrate  201  illustrated in  FIG. 2A  according to this embodiment. The recording element substrate  201  includes, arranged side-by-side in the X direction, eight (=N) ejection opening arrays  201   a ,  201   b ,  201   c ,  201   d ,  201   e ,  201   f ,  201   g , and  201   h . Each of the ejection opening arrays  201   a ,  201   b ,  201   c ,  201   d ,  201   e ,  201   f ,  201   g , and  201   h  has ejection openings, each ejecting black ink, arranged in the Y direction with a resolution of 1200 dpi (or at intervals of 1/1200 inches). The intervals between the ejection opening arrays  201   a ,  201   b ,  201   c ,  201   d ,  201   e ,  201   f ,  201   g , and  201   h  may be different to some extent as long as the ejection openings are arranged substantially at the same intervals even if a slight manufacturing error exists. 
       FIG. 3  is a block diagram illustrating a recording system according to an embodiment of the present invention. As illustrated in  FIG. 3 , the recording system includes the printer  100  illustrated in  FIG. 1 , and a personal computer (hereinafter referred to as a “host PC”)  300  serving as a host device of the printer  100 . 
     The host PC  300  includes the following elements. A central processing unit (CPU)  301  executes a process in accordance with a program held in a random access memory (RAM)  302  or a hard disk drive (HDD)  303  which serves as a storage unit. The RAM  302  is a volatile memory and temporarily holds a program and data. The HDD  303  is a non-volatile memory and also holds a program and data. In this embodiment, a data transfer interface (I/F)  304  controls transmission and reception of data to and from the printer  100 . Examples of the connection scheme for the transmission and reception of data to and from the printer  100  include Universal Serial Bus (USB), Institute of Electrical and Electronics Engineers (IEEE) 1394, and local area network (LAN). A keyboard mouse I/F  305  is an interface for controlling Human Interface Device (HID) compliant devices such as a keyboard and a mouse, and a user is able to perform an input operation through the keyboard mouse I/F  305 . A display I/F  306  controls a display operation with a display (not illustrated). 
     The printer  100  includes the following elements. A CPU  311  executes processes described below in accordance with programs held in a RAM  312  or a read-only memory (ROM)  313 . The RAM  312  is a volatile memory and temporarily holds a program and data. The ROM  313  is a non-volatile memory and is configured to hold table data and programs used for the processes described below. 
     A data transfer I/F  314  controls transmission and reception of data to and from the host PC  300 . A head controller  315  supplies recording data to the recording heads  101  to  104  illustrated in  FIG. 1 , and controls (ejection control) the ejection operation of each of the recording heads  101  to  104 . Specifically, the head controller  315  may be configured to read control parameters and recording data from a predetermined address on the RAM  312 . When the CPU  311  writes control parameters and recording data to the predetermined address on the RAM  312 , the head controller  315  starts processing, and ink is ejected from the recording heads  101  to  104 . 
     A scanner controller  316  may be configured to read control parameters from a predetermined address on the RAM  312 . When the CPU  311  writes control parameters to the predetermined address on the RAM  312 , the scanner controller  316  starts processing, and an image is read. If the scanner  108  optically obtains an image having a pattern for detecting a failure in the ejection of ink, a program for detecting an ejection failure, which is stored in the ROM  313 , is loaded onto the RAM  312  and is executed, and information indicating the state of the recording heads  101  to  104  is stored in the ROM  313 . 
     As described above, if the amount of conveyance of a recording medium is periodically shifted, the positions where ink drops land may be displaced among ejection opening arrays. In the following, a description will be given of shifts in the amount of conveyance among the ejection opening arrays  201   a  to  201   h  arranged on the recording element substrate  201  in the recording head  101  for ejecting black ink, for simplicity. 
       FIG. 4A  is a diagram schematically illustrating periodic variations in the amount of conveyance of a recording medium.  FIG. 4B  is an enlarged view of a portion illustrated in  FIG. 4A  where the recording medium is located at a position in the range from 0 to 4 mm in the X direction.  FIG. 4C  is a table illustrating values of shifts in the amount of conveyance of the recording medium in the X direction with respect to the respective positions of the recording medium in the X direction. 
     Here, the position of the recording medium in the X direction when each ejection opening array initially ejects ink onto the recording medium is represented as a reference position (0 mm). That is, when the position of the recording medium in the X direction is 0 mm relative to the ejection opening array  201   a , which is located most upstream in the X direction, the other ejection opening arrays  201   b  to  201   h  have not yet been located at positions facing the recording medium. When the position of the recording medium in the X direction is 0 mm relative to the ejection opening array  201   b , the position of the recording medium in the X direction is 1.05 mm relative to the ejection opening array  201   a.    
     First, shifts in the amount of conveyance of a recording medium onto which ink is ejected from the ejection opening array  201   a  will now be described in detail hereinafter. 
     When the recording onto the recording medium using the ejection opening array  201   a  is started, that is, when the position of the recording medium in the X direction is 0 mm, ink drops are ejected from the ejection opening array  201   a  without any displacement of the landing positions of the ink drops in the X direction (with the shift in the amount of conveyance being equal to 0.0 μm). 
     Thereafter, as the recording medium is conveyed in the X direction, the displacement of the landing positions of ink drops ejected from the ejection opening array  201   a  progressively increases in the positive X direction. When the position of the recording medium in the X direction reaches 7 mm, the landing positions of ink drops are displaced by 39.9 μm in the positive X direction (with the shift in the amount of conveyance being equal to 39.9 μm). The occurrence of such a displacement is considered to contribute to larger amounts of conveyance of the recording medium than a specified amount while the recording medium is conveyed during a period from when the process of recording onto the recording medium is started to when the position of the recording medium in the X direction becomes 7 mm. 
     As the recording medium is further conveyed, the displacement of the landing positions of ink drops ejected from the ejection opening array  201   a  increases in the negative X direction. When the position of the recording medium in the X direction reaches 15 mm, the landing positions of ink drops are displaced by 2.6 μm in the negative X direction (with the shift in the amount of conveyance being equal to −2.6 μm). The occurrence of such a displacement is considered to contribute to smaller amounts of conveyance of the recording medium than a specified amount while the recording medium is conveyed during a period from when the position of the recording medium in the X direction becomes 8 mm to when the position of the recording medium in the X direction becomes 15 mm. 
     Such repetitions of alternate large and small amounts of conveyance of the recording medium will presumably cause periodic shifts in the amount of conveyance of the recording medium. Such periodic variations in the amount of conveyance occur for various reasons. For example, the conveyance rollers  105  may have an elliptic shape in cross section due to its eccentricity. This may cause the occurrence of an area with a large amount of conveyance and an area with a small amount of conveyance in accordance with the rotational phase of the conveyance rollers  105 . 
     As may be seen from  FIG. 2B , since the ejection opening array  201   a  is located most upstream in the X direction, the ejection opening array  201   a  is first used for recording onto the recording medium among the ejection opening arrays  201   a  to  201   h . Accordingly, the timing of the first recording onto the recording medium using the ejection opening array  201   b  is slightly later than the timing of the first recording onto the recording medium using the ejection opening array  201   a . Thus, when the recording onto the recording medium using the ejection opening array  201   b  is started (or when the position of the recording medium in the X direction is 0 mm), the landing positions of ink drops have been displaced in the positive X direction (with the displacement of the landing positions being equal to 8.9 mm). 
     In the subsequent operation, when ink is ejected from the ejection opening array  201   b , the timing of recording is slightly delayed even though the recording is made at the same position on the recording medium as that when ink is ejected from the ejection opening array  201   a . For this reason, even at the same positions on the recording medium, the landing positions of ink drops from the ejection opening array  201   a  and the landing positions of ink drops from the ejection opening array  201   b  are displaced at different degrees. As the distance between ejection opening arrays increases, the difference in the timing of the ejection of ink increases. In consequence, as illustrated in  FIG. 4A , the periodic variations in the amount of conveyance of the recording medium for the ejection opening arrays  201   a  to  201   h  are shifted. 
     A displacement of the landing positions of ink drops among ejection opening arrays may cause degradation of the quality of an image to be recorded. For example, within an area where the position of the recording medium in the X direction is 13 mm, as may be seen from  FIG. 4C , the landing positions of ink drops ejected from the ejection opening array  201   a  are displaced by a maximum of 14.2 μm in the positive X direction. In addition, the landing positions of ink drops ejected from the ejection opening array  201   h  are displaced maximally in the negative X direction (or minimally in the positive X direction) by 37.4 μm (or by −37.4 μm in the positive X direction). In consequence, the difference in displacement of the landing positions of ink drops between the ejection opening arrays is 51.6 (=14.2−(−37.4)) μm. The amount of displacement is larger than the length (42.3 μm) of a pixel area corresponding to each pixel, which may result in the visual perception of a reduction in the quality of an image to be recorded. 
     If the number of ejection opening arrays to be used for recording is reduced and only adjacent ejection opening arrays in the X direction are used, the difference in displacement of the landing positions of ink drops described above may be reduced. For example, the use of only the ejection opening arrays  201   b ,  201   c , and  201   d  leads to a reduction in the difference in displacement of the landing positions of ink drops described above as follows: Within an area where the position of the recording medium in the X direction is 13 mm, the landing positions of ink drops (the shift in the amount of conveyance of the recording medium) ejected from the ejection opening array  201   b  are maximally displaced in the positive X direction by 5.5 μm. On the other hand, the landing positions of ink drops ejected from the ejection opening array  201   d  are displaced maximally in the negative X direction (or minimally in the positive X direction) by 12.2 μm (or by −12.2 μm in the positive X direction). The difference between these values is reduced to 17.7 μm (=5.5 μm−(−12.2) μm). This may enable recording with a less noticeable degradation in image quality. 
     In light of the foregoing, in this embodiment, in a specific recording mode among recording modes executable by the image recording apparatus  100 , the number of ejection opening arrays to be used is reduced, and only adjacent ejection opening arrays in the X direction are used to perform recording. More specifically, in the specific recording mode, dot recording data that defines the positions at which dots are recorded is distributed only to the ejection opening arrays  201   b ,  201   c , and  201   d.    
       FIG. 5  is a block diagram illustrating steps of image processing according to this embodiment.  FIG. 6  is a flowchart illustrating a process for the image processing performed in accordance with the block diagram illustrated in  FIG. 5 . 
     When a recording process is started, in the printer  100 , an image input unit A 01  obtains image data (step S 531 ). It is assumed here that the image data represents a color image having a resolution of 600 dpi and having 8 bits for each component of red (R), green (G), and blue (B) which allow 256 levels of gradation. 
     Then, a color conversion processing unit A 02  performs a color conversion process, and converts the image data into ink color data having a resolution of 600 dpi and having 8 bits for each component of CMYK which allow 256 levels of gradation (step S 532 ). The color conversion process is a process for converting image data represented by a combination of gradation values of R, G, and B into data represented by gradation values of the respective colors used for recording. As described above, the printer  100  records an image using ink of four colors of C, M, Y, and K. Accordingly, the color conversion processing unit A 02  according to this embodiment performs a process for converting image data represented by R, G, and B into ink color data represented by gradation values of the respective colors of C, M, Y, and K. 
     Then, a quantization processing unit A 03  performs a quantization process on the ink color data, and generates quantized data (step S 533 ). The quantization process is a process for appropriately reducing the number of gradation levels from ink color data having 8 bits and 256 levels of gradation to data having a number of gradation levels recordable with the printer  100  (in this embodiment, five gradation values from level 0 to level 4). Typical examples of the quantization process include error diffusion and dithering. The quantization process according to this embodiment is not limited to any specific technique. 
     Then, a dot recording position determination unit A 04  generates dot recording data that defines the positions at which dots are to be recorded based on the quantized data, by using a dot pattern (step S 534 ). In this embodiment, a dot pattern having a resolution of 1200 dpi is applied to five-value quantized data having a resolution of 600 dpi to generate dot recording data. 
       FIG. 7  is a diagram illustrating dot patterns applied in this embodiment. 
     For example, dot patterns C 11 , C 12 , C 13 , and C 14  are sequentially applied to quantized data whose value indicates level 1. Accordingly, when an image corresponding to quantized data of level 1 is to be recorded in a certain area on the recording medium, one dot is recorded in each unit of 600 dpi, and the dot recording positions given in the respective units are repeated in the rotation of the “upper left (C 11 )”, the “lower left (C 12 )”, the “lower right (C 13 )”, and the “upper right (C 14 )”. 
     For example, furthermore, dot patterns C 21  and C 22  are sequentially applied to quantized data whose value indicates level 2. Accordingly, when an image corresponding to quantized data of level 2 is to be recorded in a certain area on the recording medium, two dots are recorded in each unit of 600 dpi, and the dot recording positions given in the respective units are repeated in the rotation of the “upper left and lower right (C 21 )” and the “upper right and lower left (C 22 )”. 
     Then, a recording ejection opening array determination unit A 05  distributes the dot recording data to each ejection opening array by using a distribution pattern read from an ejection opening array distribution pattern storage unit A 11  to generate distribution data for each ejection opening array (steps S 535  and S 536 ). For example, dot recording data corresponding to cyan ink is distributed to an ejection opening array a (A 31   a ), an ejection opening array b (A 31   b ), an ejection opening array c (A 31   c ), an ejection opening array d (A 31   d ), an ejection opening array e (A 31   e ), an ejection opening array f (A 31   f ), an ejection opening array g (A 31   g ), and an ejection opening array h (A 31   h ) in a recording element substrate A 31  for cyan ink, and accordingly distribution data corresponding to each of the ejection opening arrays A 31   a  to A 31   h  in the recording element substrate A 31  for cyan ink is generated. Further, dot recording data corresponding to magenta ink is distributed to an ejection opening array a (A 41   a ), an ejection opening array b (A 41   b ), an ejection opening array c (A 41   c ), an ejection opening array d (A 41   d ), an ejection opening array e (A 41   e ), an ejection opening array f (A 41   f ), an ejection opening array g (A 41   g ), and an ejection opening array h (A 41   h ) in a recording element substrate A 41  for magenta ink, and accordingly distribution data corresponding to each of the ejection opening arrays A 41   a  to A 41   h  in the recording element substrate A 41  for magenta ink is generated. Further, dot recording data corresponding to yellow ink is distributed to an ejection opening array a (A 51   a ), an ejection opening array b (A 51   b ), an ejection opening array c (A 51   c ), an ejection opening array d (A 51   d ), an ejection opening array e (A 51   e ), an ejection opening array f (A 51   f ), an ejection opening array g (A 51   g ), and an ejection opening array h (A 51   h ) in a recording element substrate A 51  for yellow ink, and accordingly distribution data corresponding to each of the ejection opening arrays A 51   a  to A 51   h  in the recording element substrate A 51  for yellow ink is generated. Further, dot recording data corresponding to black ink is distributed to an ejection opening array a (A 21   a ), an ejection opening array b (A 21   b ), an ejection opening array c (A 21   c ), an ejection opening array d (A 21   d ), an ejection opening array e (A 21   e ), an ejection opening array f (A 21   f ), an ejection opening array g (A 21   g ), and an ejection opening array h (A 21   h ) in a recording element substrate A 21  for black ink, and accordingly distribution data corresponding to each of the ejection opening arrays A 21   a  to A 21   h  in the recording element substrate A 21  for black ink is generated. Here, a recording element substrate A 22  for black ink is further provided, and the dot recording data corresponding to black ink is also distributed to an ejection opening array a (A 22   a ), an ejection opening array b (A 22   b ), an ejection opening array c (A 22   c ), an ejection opening array d (A 22   d ), an ejection opening array e (A 22   e ), an ejection opening array f (A 22   f ), an ejection opening array g (A 22   g ), and an ejection opening array h (A 22   h ) in the recording element substrate A 22  for black ink. However, this configuration is not essential. The ejection opening array distribution pattern storage unit A 11  stores a plurality of different distribution patterns, and the recording ejection opening array determination unit A 05  is capable of selectively reading a distribution pattern in accordance with recording conditions such as a recording mode and performing a distribution process. 
       FIG. 8A  is a schematic diagram illustrating a distribution pattern D 11  used in the specific recording mode. In  FIG. 8A , distribution parameters a to h in grids, each corresponding to a pixel, represent the ejection opening arrays  201   a  to  201   h , respectively, and, when a signal defining the ejection of ink is input to each pixel, it is determined to which of the ejection opening arrays  201   a  to  201   h  the signal is distributed. For example, when a signal defining the ejection of ink is input to a pixel  91  in the distribution pattern D 11 , the signal is distributed to the ejection opening array  201   b . When a signal defining the ejection of ink is input to a pixel  92  in the distribution pattern D 01 , the signal is distributed to the ejection opening array  201   c.    
       FIG. 8B  is a diagram schematically illustrating dot recording data D 12 , which is an example of input dot recording data. In  FIG. 8B , black solid grids represent pixels for which ejection of ink is defined, and blank white grids represent pixels for which non-ejection of ink is defined. 
       FIG. 8C  is a diagram schematically illustrating pieces of distribution data D 13   a  to D 13   h  generated by, upon receipt of input of the dot recording data illustrated in  FIG. 8B , the distribution of the dot recording data to the ejection opening arrays  201   a  to  201   h  by using the distribution pattern D 11  illustrated in  FIG. 8A . 
     The distribution pattern D 11  illustrated in  FIG. 8A  does not have the distribution parameters a and e to h, but have the distribution parameters b to d arranged so that the numbers of distribution parameters b to d are substantially equal to one another. That is, the proportions of the ejection opening arrays  201   a  and  201   e  to  201   h  to which the dot recording data is distributed are set to zero while the proportions of the ejection opening arrays  201   b  to  201   d  to which the dot recording data is distributed are substantially equal to each other, or are set to approximately 33% (=100/3). Accordingly, when the distribution pattern D 11  is applied, as illustrated in  FIGS. 8B and 8C , no dot recording data is distributed to the ejection opening arrays  201   a  and  201   e  to  201   h , whereas the dot recording data is distributed to the three adjacent ejection opening arrays  201   b  to  201   d  by substantially an equal amount. Recording according to the distribution data generated in the way described above may result in the occurrence of the displacement of the landing positions of ink drops described above being suppressed or reduced. 
     If an ejection opening arranged in any of the ejection opening arrays  201   b  to  201   d  has experienced a failure to eject ink when the dot recording data is distributed to the ejection opening arrays  201   b  to  201   d  in the manner described above, no ink will be actually ejected onto an area where ink normally would be ejected from the ejection opening that has experienced a failure to eject ink. 
     Accordingly, in this embodiment, as the maintenance of the printer  100  before recording is carried out, a detection pattern is recorded on a recording medium to detect the presence of a failure in the ejection of ink. The ejection failure is detected in units of ejection openings, enabling any ejection opening that has actually suffered an ejection failure (hereinafter also referred to as an “inoperative nozzle”) to be detected. If an inoperative nozzle is detected in the ejection opening arrays  201   b  to  201   d  through the detection process described above, the distribution data for the inoperative nozzle is complementarily assigned to an ejection opening in the ejection opening arrays  201   a  and  201   e  to  201   h  which is located at the same position in the Y direction as the position of the inoperative nozzle. For example, in  FIG. 2B , an ejection opening  211   c  in the ejection opening array  201   c  has experienced a failure to eject ink. In this case, the distribution data for the ejection opening  211   c  is complementarily assigned to any of ejection openings  211   a  and  211   e  to  211   h  located at the same positions in the Y direction as the position of the ejection opening  211   c , and complementary data for complementarily ejecting ink from the corresponding ejection opening is generated. Then, ink is complementarily ejected from the ejection opening in accordance with the complementary data, enabling recording which may compensate for the failure in the ejection of ink from the ejection opening  211   c.    
     Some nozzles substitute for an inoperative nozzle, which ejects ink instead, may also cause displacement of the landing positions of ink drops. 
     For example, if no failure in the ejection of ink occurs within an area where the position of the recording medium in the X direction is 13 mm, as described above, the use of only the ejection opening arrays  201   b  to  201   d  allows the landing positions of ink drops to be displaced maximally in the positive X direction by 5.5 μm and the landing positions of ink drops to be displaced maximally in the positive X direction by 12.2 μm. This enables the difference in displacement of the landing positions of ink drops between the ejection opening arrays to be comparatively as small as 17.7 μm, resulting in the degradation of image quality being suppressed or reduced. 
     A description will now be given of the case where the ejection opening  211   c  in the ejection opening array  201   c  has experienced a failure to eject ink and the distribution data for the ejection opening  211   c  is complementarily assigned to the ejection opening  211   h  in the ejection opening array  201   h.    
     In the case where the distribution data for the ejection opening  211   c  is complementarily assigned to the ejection opening  211   h , ink drops are ejected from the ejection openings  211   b ,  211   d , and  211   h  onto an area on the recording medium at the position corresponding to the ejection openings  211   c  and  211   h  in the Y direction. In this case, as may be seen from  FIG. 4C , the landing positions of ink drops ejected from the ejection opening  211   b  in the ejection opening array  201   b  are displaced maximally in the positive X direction by 5.5 μm, and the landing positions of ink drops ejected from the ejection opening  211   h  in the ejection opening array  201   h  are maximally displaced in the positive X direction by 37.4 μm. Accordingly, the difference in displacement of the landing positions of ink drops between the ejection opening arrays is comparatively as large as 42.9 (=5.5−(−37.4)) μm. This may result in degradation of image quality being more likely to be noticeable. 
     As described above, complementary assignment of distribution data for an inoperative nozzle without restriction of substitutes to which the distribution data is complementarily assigned may result in the reduction in image quality due to the displacement of the landing positions of ink drops being more likely to be visually perceived. 
     In light of the foregoing, in this embodiment, if any of the ejection openings in the ejection opening arrays  201   b  to  201   d  to be used in the specific recording mode has suffered an ejection failure, a process for complementarily assigning the distribution data for such an inoperative ejection opening that has suffered an ejection failure is performed by taking into account substitutes to which the distribution data is complementarily assigned. It is assumed that the complementary assignment process according to this embodiment is performed each time the recording onto a predetermined number of recording media is completed. While the foregoing description has been made of the recording on a cut sheet of paper, the present invention is also applicable to the recording on a rolled sheet. In the case of recording on a rolled sheet, it is sufficient that the complementary assignment process according to this embodiment be performed at the timing when images, the number of which corresponds to the predetermined number of recording media after the rolled sheet has been cut, are recorded. 
       FIG. 9  is a flowchart illustrating steps of the complementary assignment process according to this embodiment. 
     First, in step S 511 , a defective ejection nozzle detection process is performed before the recording of an actual image. 
       FIG. 10  is a flowchart illustrating steps of the defective ejection nozzle detection process according to this embodiment. 
     In step S 521 , a detection image stored in the ROM  313  is read. Then, in step S 522 , detection pattern recording data is generated based on the detection image read in step S 521 . 
     In step S 523 , detection patterns are recorded based on the recording data generated in step S 522 . In this embodiment, each of the detection patterns is an image in which, for each of the ejection opening arrays of each of the recording heads  101  to  104  in the recording head group  107 , ink is ejected onto four adjacent pixel areas per ejection opening array in the X direction by using all the ejection openings within the ejection opening array.  FIG. 11  is a schematic diagram illustrating detection patterns  601   a  to  601   h  to be recorded on a recording medium  3  by using the ejection opening arrays  201   a  to  201   h  illustrated in  FIG. 2B , respectively, among detection patterns recorded in this embodiment. As may be seen from  FIG. 11 , the detection patterns according to this embodiment are recorded so as to be displaced from one another in the X direction in such a manner that the detection patterns for the respective ejection opening arrays do not overlap. Of the detection patterns  601   a  to  601   h  illustrated in  FIG. 11 , the detection pattern  601   h  recorded from the ejection opening array  201   h  has a blank area  611 . The formation of the blank area  611  is considered to be caused by the occurrence of a failure in the ejection of ink in an ejection opening in the ejection opening array  201   h  which is located at the position corresponding to the area  611  in the Y direction. 
     Then, in step  524 , the recorded detection patterns are read by the scanner  108 .  FIG. 12  is a schematic diagram of read images  701   a  to  701   h  displayed on the display of the host PC  300  when the detection patterns  601   a  to  601   h  schematically illustrated in  FIG. 11  are read at a predetermined resolution. In this embodiment, the resolution of each ejection opening has the same value (1200 dpi) as the resolution at which the scanner  108  reads an image. Thus, each individual inoperative nozzle is detectable. When the scanner  108  reads an image, an identical signal value is output pixel-by-pixel at the predetermined resolution. Accordingly, read images are obtained in units of rectangular pixels as illustrated in  FIG. 12 , and the circular dots are represented as rectangular pixels. In the read images  701   a  to  701   h , furthermore, black solid portions represent areas where ink has been ejected, and blank white portions represent areas where no ink has been ejected. In  FIG. 12 , an area  711  is located at the position corresponding to the area  611  illustrated in  FIG. 11 , and is displayed as blank due to presumably the occurrence of a failure in the ejection of ink in the ejection opening array  201   h . In this embodiment, a user estimates an inoperative nozzle on the basis of the indication of a blank white portion in the read images  701   a  to  701   h  displayed on the display. Alternatively, the read images  701   a  to  701   h  may be analyzed automatically by a computer and the computer may estimate an inoperative nozzle. 
     In step S 525 , information concerning the designation of an inoperative nozzle, which is input by the user, is obtained based on the read images  701   a  to  701   h  displayed in step S 524 , and the inoperative nozzle is determined based on the obtained information. Based on the read images  701   a  to  701   h  illustrated in  FIG. 12 , the ejection opening corresponding to the area  711  in the ejection opening array  201   h  is determined to be an inoperative nozzle. 
     In step S 526 , information on the inoperative nozzle determined in step S 525  is updated. If a new inoperative nozzle has been found, a new inoperative nozzle occurrence flag is set to 1, or otherwise, the new inoperative nozzle occurrence flag is set to 0. In this embodiment, the new inoperative nozzle occurrence flag is saved in the RAM  312 . Alternatively, the new inoperative nozzle occurrence flag may be saved in a storage device included in the host PC  300 . 
     When the defective ejection nozzle detection process described above is completed in step S 511 , then in step S 512  in  FIG. 9 , the value of the new inoperative nozzle occurrence flag is referred to, and it is determined whether or not a new inoperative nozzle has been found. If a new inoperative nozzle has been found, the process proceeds to step S 513 . If it is determined that no new inoperative nozzle has been found, the process proceeds to step S 515 . 
     In step S 513 , it is determined whether or not the number of inoperative ejection openings among ejection openings located at the same positions in the Y direction in each of the ejection opening arrays  201   a  to  201   h  is less than or equal to five. If it is determined that the number of inoperative ejection openings is less than or equal to five, a number of ejection openings equal to or more than three, which is equal to the number of ejection opening arrays used in the specific recording mode according to this embodiment, are available at respective positions of the corresponding recording head in the X direction, and thus the process proceeds to step S 514 . Then, the complementary assignment process continues. If it is determined that the number of inoperative ejection openings is more than five, there is no substitute to which the distribution data for the inoperative nozzles is complementarily assigned. Thus, an error is issued and the recording operation is interrupted. 
     Then, in step S 514 , an ejection opening (hereinafter also referred to as a “complementary nozzle”) serving as a substitute to which the distribution data for each inoperative nozzle is complementarily assigned is determined, and information on the determined complementary nozzle is stored in the ROM  313 . The method for determining a complementary nozzle will be described below. 
     Then, in step S 515 , the dot recording data is distributed to each ejection opening array and distribution data is generated in accordance with the flowchart illustrated in  FIG. 6 . In consequence, as described above, in the specific recording mode, the dot recording data is distributed only to an ejection opening array group formed by the ejection opening arrays  201   b ,  201   c , and  201   d  among the ejection opening arrays  201   a  to  201   h.    
     In step S 516 , the information concerning the complementary nozzle is read from the ROM  313 , and the distribution data for the inoperative nozzle is complementarily assigned to the complementary nozzle. For instance, the ejection opening  211   c  has experienced a failure to eject ink, and the ejection opening  211   f  is determined to be a complementary nozzle. In this case, all the distribution data that defines the recording of the dot at the position corresponding to the ejection opening  211   c  within the distribution data for the ejection opening array  201   c  is re-distributed into distribution data for the ejection opening  211   f  to generate complementary data for the ejection opening array  201   f.    
     In this embodiment, recording data used for recording is generated based on the distribution data generated in step S 515  and the complementary data generated in step  516 . 
     Then, in step S 517 , the recording data is transferred to the corresponding ejection opening arrays, and dots are recorded on the recording medium in accordance with the recording data. 
     Then, in step S 518 , it is determined whether or not the recording of the actual image has been completed. If the recording operation has been completed, the process proceeds to End, and all the recording operation ends. If the recording operation has not been completed, then in step S 519 , it is determined whether the predetermined number of images has been reached. If it is determined in step S 519  that the predetermined number of images has been reached, the detection process in step S 511  is performed again. If the predetermined number of images has not been reached, the process proceeds to step S 515  and the recording operation continues. 
     The complementary nozzle determination method in step S 514  will now be described in detail. 
     As described above, the determination of a complementary nozzle in the specific recording mode without any restriction may cause the reduction in image quality due to the displacement of the landing positions of ink drops to be likely to be visually perceived depending on the substitute to which distribution data is complementarily assigned. To address this issue, in this embodiment, in accordance with the program stored in the ROM  313 , if K (K≦M) ejection openings among M (M&lt;N), e.g., three, ejection openings (first ejection opening group) used in the specific recording mode among N, e.g., eight, ejection openings capable of ejecting ink onto the same pixel area on a recording medium in the Y direction are inoperative nozzles, K complementary nozzles are determined from among (N−M) ejection openings other than the M ejection openings in accordance with the following three conditions. Note that the distribution data for (3−K) (=M−K) ejection openings, which are not inoperative nozzles, is not complementarily assigned, and the distribution data for the (M−K) ejection openings is used directly as recording data for ejecting ink from the (M−K) ejection openings. Accordingly, the (M−K) ejection openings, which are not inoperative, and the K complementary nozzles, that is, a total of M ejection openings (second ejection opening group), are used for recording. 
     First Condition 
     A combination of K complementary nozzles is determined for which a distance D_1 between ejection openings at opposite ends of a total of M ejection openings including (M−K) ejection openings in the first ejection opening group, which are not inoperative nozzles, and K complementary nozzles in the X direction is minimum.
 
Second Condition
 
If there is a plurality of combinations of K complementary nozzles satisfying the first condition, a combination of K complementary nozzles is determined for which the absolute value of a difference D_2 between the position P_u of an ejection opening at the center of the total of M ejection openings including the (M−K) ejection openings in the first ejection opening group, which are not inoperative nozzles, and the K complementary nozzles and the position P_c of an ejection opening at the center of M ejection openings obtained before the complementary assignment process is minimum.
 
Third Condition
 
If there is a plurality of combinations of K complementary nozzles satisfying the first and second conditions, a combination of K complementary nozzles is determined for which the position P_u of the ejection opening at the center of the total of M ejection openings (second ejection opening group) including the (M−K) ejection openings in the first ejection opening group, which are not inoperative nozzles, and the K complementary nozzles is minimum.
 
     In this embodiment, the complementary nozzle determination process is based on the three conditions described above. 
     In the following description, the complementary assignment process is performed on the ejection openings  211   a  to  211   h  capable of ejecting ink onto the same pixel area respectively arranged for the ejection opening arrays  201   a  to  201   h , for simplicity. 
     In addition, the position of each ejection opening array and the distance between ejection opening arrays are defined, where, also for simplicity, the position of the ejection opening array  201   a  in the X direction is used as a reference position and the distance between adjacent ejection opening arrays in the X direction is set to 1. For instance, the position of the ejection opening array  201   a  in the X direction is a reference position and is set to 0. Further, the position of the ejection opening array  201   b  in the X direction is set to 1 since the ejection opening array  201   b  is adjacent to the ejection opening array  201   a  in the X direction. Also, the positions of the ejection opening arrays  201   c ,  201   d ,  201   e ,  201   f ,  201   g , and  201   h  in the X direction are set to 2, 3, 4, 5, 6, and 7, respectively. 
     For simplicity, furthermore, ejection openings used after the complementary assignment process among the ejection openings  211   a  to  211   h  are represented by L_1, L_2, and L_3. For example, when the ejection openings  211   b ,  211   c , and  221   d  are used, (L_1, L_2, L_3)=(b, c, d) is set. In this case, the distance D_1 between ejection openings at opposite ends of the ejection openings  211   b ,  211   c , and  221   d  in the X direction is the distance between the ejection opening arrays  201   b  and  201   d , and is given by D_1=3−1=2. The center position P_c of the three ejection openings  211   b ,  211   c , and  211   d  is given by P_c=(1+2+3)/3=2. 
       FIG. 13  is a flowchart illustrating steps of the complementary nozzle determination process according to this embodiment.  FIG. 14  is a diagram schematically illustrating the complementary nozzle determination method. A description will now be given of an example in which, as illustrated in section (a) in  FIG. 14 , recording is performed in the specific recording mode by using only the ejection openings  211   b ,  211   c , and  211   d  while no inoperative nozzle exists, and thereafter the occurrence of an ejection failure in the ejection opening  211   c  is detected through the detection process described above. 
     First, in step S 1001 , inoperative nozzle information stored in the ROM  313  of the printer  100  is referred to, and a NULL value is assigned to an inoperative nozzle. Here, first, as illustrated in section (a) in  FIG. 14 , information of (L_1, L_2, L_3)=(b, c, d) is referred to. Further, since the ejection opening  211   c  is inoperative, L_2=NULL is set, yielding (L_1, L_2, L_3)=(b, NULL, d). 
     Then, in step S 1002 , it is determined whether or not the initially used ejection openings include an inoperative nozzle. Specifically, it is checked whether at least one of L_1, L_2, and L_3 is set to a NULL value. If none of L_1, L_2, and L_3 is set to a NULL value, there is no need for further operation to determine a complementary nozzle. Then, the complementary nozzle determination process ends. Here, L_2=NULL is obtained. Thus, the process proceeds to step S 1003 . 
     In step S 1003 , a complementary nozzle to an ejection opening corresponding to any of L_1, L_2, and L_3 set to a NULL value is determined in accordance with the first condition described above. Here, the ejection opening  211   c  becomes inoperative, and L_2=NULL is obtained. Thus, a combination of (L_1, L_2, L_3) for which the distance D_1 between ejection openings at opposite ends of L_1, L_2, and L_3 in the X direction is minimum is determined from among the combinations of (L_1, L_2, L_3)=(b, a, d), (b, e, d), (b, f, d), (b, g, d), and (b, h, d). In consequence, the distance D_1 is minimum (D_1=3) for the two combinations of (L_1, L_2, L_3)=(b, a, d) and (b, e, d). 
     Then, in step S 1004 , it is determined whether or not there is a plurality of combinations of (L_1, L_2, L_3) determined in step S 1003 . That is, it is determined whether or not there is a plurality of combinations of ejection openings satisfying the first condition. If a single combination of (L_1, L_2, L_3) has been determined, the obtained ejection opening is determined to be a complementary nozzle, and then the complementary nozzle determination process ends. On the other hand, if there is a plurality of combinations of ejection openings satisfying the first condition, the process proceeds to step S 1005 . 
     In step S 1005 , a complementary nozzle to an ejection opening corresponding to any of L_1, L_2, and L_3 set to a NULL value is determined in accordance with the second condition described above. First, the middle position P_u of the ejection openings in each of the combinations of L_1, L_2, and L_3 determined in step S 1003  is determined. Further, the middle position P_c of the ejection openings in the combination of L_1, L_2, and L_3 obtained before the assignment of the NULL value in step S 1001  is determined. Then, a combination of (L_1, L_2, L_3) for which the difference D_2 between the middle positions P_c and P_u is minimum is determined. Here, the middle position P_c for the combination of (L_1, L_2, L_3)=(b, c, d) obtained before the assignment of the NULL value is given by P_c=(1+2+3)/3=2. Further, the middle position P_c for the combination of (L_1, L_2, L_3)=(b, a, d) determined in step S 1003  is given by P_c=(1+0+3)/3=4/3. Thus, the difference D_2 for the combination of (L_1, L_2, L_3)=(b, a, d) is given by D_2=|4/3−2|=2/3. In addition, the middle position P_u for the combination of (L_1, L_2, L_3)=(b, e, d) determined in step S 1003  is given by P_u=(1+4+3)/3=8/3. Thus, the difference D_2 for the combination of (L_1, L_2, L_3)=(b, e, d) is given by D_2=|8/3−2|=2/3. Accordingly, the two combinations of (L_1, L_2, L_3)=(b, a, d) and (b, e, d) are determined as combinations for which the absolute value of the difference D_2 is minimum. 
     Then, in step S 1006 , it is determined whether or not there is a plurality of combinations of (L_1, L_2, L_3) determined in step S 1005 . That is, it is determined whether or not there is a plurality of ejection openings satisfying the second condition. If a single combination of (L_1, L_2, L_3) has been determined, the obtained ejection opening is determined to be a complementary nozzle, and then the complementary nozzle determination process ends. On the other hand, if there is a plurality of combinations of ejection openings satisfying the second condition, the process proceeds to step S 1007 . 
     The combinations of (L_1, L_2, L_3) which have been determined at step S 1007  are considered to be substantially equivalently affected by the displacement of the landing positions of ink drops. In step S 1007 , accordingly, the selection is narrowed down so that any one of the plurality of obtained combinations is selected with certainty. In this embodiment, a combination of (L_1, L_2, L_3) for which the middle position P_u obtained after complementary assignment is minimum is reserved as an option. Here, the middle position P_u for (L_1, L_2, L_3)=(b, a, d) is given by P_u=4/3 and the middle position P_u for (L_1, L_2, L_3)=(b, e, d) is given by P_u=8/3. Therefore, the determined combination (second ejection opening group) is (L_1, L_2, L_3)=(b, a, d). Accordingly, as illustrated in section (b) in  FIG. 14 , the ejection opening  211   a  is used as a complementary nozzle to the ejection opening  211   c , and the distribution data for the ejection opening  211   c  is complementarily assigned to the ejection opening  211   a  to generate complementary data. In step S 1007 , it is sufficient that a process which enables the selection of one of a plurality of combinations of (L_1, L_2, L_3) be performed, and, by way of example, a combination of (L_1, L_2, L_3) for which the middle position P_u is maximum may be selected. 
     A description will be given of the case where a further inoperative nozzle exists thereafter. A method for determining a complementary nozzle in a case where the ejection opening  211   d  also becomes inoperative in the state illustrated in section (b) in  FIG. 14  will be described in accordance with the flowchart illustrated in  FIG. 13 . 
     First, in step S 1001 , the initially used ejection opening arrays are checked. Since the ejection opening arrays to be originally used are the ejection opening arrays  201   b ,  201   c , and  201   d , the values of (L_1, L_2, L_3) are reset to (L_1, L_2, L_3)=(b, c, d). Here, the ejection openings  211   c  and  211   d  are not available, and accordingly L_2=NULL and L_3=NULL are set, yielding (L_1, L_2, L_3)=(b, NULL, NULL). 
     In step S 1003 , a combination of ejection openings for which, as a result of the application of combinations of ejection openings in normal operation other than the ejection opening arrays  201   b  to  201   d  to an ejection opening corresponding to any of L_1, L_2, and L_3 set to a NULL value, here, L_2 and L_3, the distance D_1 between ejection openings at both ends of the ejection opening group in each of the combinations is minimum is determined. In consequence, two combinations of (L_1, L_2, L_3)=(b, a, e) and (b, e, f), for which D_1=4 is obtained, are determined as combinations for which the distance D_1 is minimum. In this embodiment, ejection openings are assigned to L_2 and L_3 in alphabetical order (a, b, c). Alternatively, any other assignment order may be used, or ejection openings may be assigned randomly. 
     Since there is a plurality of combinations of L_1, L_2, and L_3, the process proceeds to step S 1005  on the “YES” branch from step S 1004 . 
     In step S 1005 , a combination of ejection openings for which the absolute value of the difference D_2 in distance between the middle position P_u and the middle position P_c is minimum is determined from among the combinations of L_1, L_2, and L_3 determined in step S 1003 . Since P_u=2, D_2=|5/3−2|=1/3 is obtained when the middle position P_u for (L_1, L_2, L_3)=(b, a, e) is given by P_u=(1+0+4)/3=5/3, and D_2=|10/3−2|=4/3 is obtained when the middle position P_u for (L_1, L_2, L_3)=(b, e, f) is given by P_u=(1+4+5)/3=10/3. Accordingly, the combination of (L_1, L_2, L_3)=(b, a, e) is determined to be a combination for which the absolute value of the difference D_2 is minimum. 
     A single combination of L_1, L_2, and L_3, that is, (L_1, L_2, L_3)=(b, a, e), has been successfully determined. Thus, the complementary nozzle selection process ends on the “YES” branch from step S 1006 . As illustrated in section (c) in  FIG. 14 , which is a schematic view of this state, the ejection opening  211   a  is selected as a complementary nozzle to the ejection opening  211   c , and the ejection opening  211   e  is selected as a complementary nozzle to the ejection opening  211   d.    
     A description will be given of the case where a further inoperative nozzle exists thereafter. A method for selecting a complementary nozzle in a case where the ejection opening  211   b  also becomes inoperative in the state illustrated in section (c) in  FIG. 14  will be described in accordance with the flowchart illustrated in  FIG. 13 . 
     First, in step S 1001 , the initially used ejection opening arrays are checked, and a NULL value is assigned to an ejection opening that is not available. Since the ejection opening arrays to be originally used are the ejection opening arrays  201   b ,  201   c , and  201   d , the values of (L_1, L_2, L_3) are reset to (L_1, L_2, L_3)=(b, c, d). Here, the ejection openings  211   b ,  211   c , and  211   d  are not available, and accordingly L_1=NULL, L_2=NULL, and L_3=NULL are set, yielding (L_1, L_2, L_3)=(NULL, NULL, NULL). 
     Then, in step S 1002 , it is checked whether there is any ejection opening that is not available. Specifically, it is checked whether at least one of L_1, L_2, and L_3 is set to a NULL value. Here, since L_1=L_2=L_3=NULL, there are specific ejection openings that are not available. Thus, the process proceeds to step S 1003 . 
     In step S 1003 , as a result of the application of combinations of ejection openings in normal operation other than the ejection opening arrays  201   b  to  201   d  to an ejection opening corresponding to any of L_1, L_2, and L_3 set to a NULL value, a combination of ejection openings for which the distance D_1 for each combination is minimum is determined. In consequence, two combinations of (L_1, L_2, L_3)=(e, f, g) and (f, g, h), for which D_1=2 is obtained, are determined as combinations for which the distance D_1 is minimum. In this embodiment, ejection openings are assigned to L_1, L_2, and L_3 in alphabetical order (a, b, c). Alternatively, any other assignment order may be used, or ejection openings may be assigned randomly. 
     Since there is a plurality of combinations of L_1, L_2, and L_3, the process proceeds to step S 1005  on the “YES” branch from step S 1004 . 
     In step S 1005 , a combination of ejection openings for which the absolute value of the difference D_2 in distance between the middle position P_u and the middle position P_c is minimum is determined from among the combinations of L_1, L_2, and L_3 determined in step S 1003 . Since P_u=2, D_2=|5−2|=3 is obtained when the middle position P_u for (L_1, L_2, L_3)=(e, f, g) is given by P_u=(4+5+6)/3=5, and D_2=|6−2|=4 is obtained when the middle position P_u for (L_1, L_2, L_3)=(f, g, h) is given by P_u=(5+6+7)/3=6. Accordingly, the combination of (L_1, L_2, L_3)=(e, f, g) is determined to be a combination for which the absolute value of the difference D_2 is minimum. 
     A single combination of L_1, L_2, and L_3, that is, (L_1, L_2, L_3)=(e, f, g), has been successfully determined. Thus, the complementary nozzle selection process ends on the “YES” branch from step S 1006 . As illustrated in section (d) in  FIG. 14 , which is a schematic view of this state, the ejection opening  211   e  is selected as a complementary nozzle to the ejection opening  211   b , the ejection opening  211   f  as a complementary nozzle to the ejection opening  211   c , and the ejection opening  211   g  as a complementary nozzle to the ejection opening  211   d.    
     A method for selecting a complementary nozzle in a case where the ejection opening  211   e  also becomes inoperative thereafter in the state illustrated in section (d) in  FIG. 14  will be described in accordance with the flowchart illustrated in  FIG. 13 . 
     First, in step S 1001 , the initially used ejection opening arrays are checked, and a NULL value is assigned to an ejection opening that is not available. Since the ejection opening arrays to be originally used are the ejection opening arrays  201   b ,  201   c , and  201   d , the values of (L_1, L_2, L_3) are reset to (L_1, L_2, L_3)=(b, c, d). Here, the ejection openings  211   b ,  211   c , and  211   d  are not available, and accordingly L_1=NULL, L_2=NULL, and L_3=NULL are set, yielding (L_1, L_2, L_3)=(NULL, NULL, NULL). 
     Then, in step S 1002 , it is checked whether there is any ejection opening that is not available. Specifically, it is checked whether any or all of L_1, L_2, and L_3 are set to a NULL value. Here, since L_1=L_2=L_3=NULL, there are ejection openings that are not available. Thus, the process proceeds to step S 1003 . 
     In step S 1003 , a combination of ejection openings for which, as a result of the application of combinations of ejection openings in normal operation other than the ejection openings  211   b ,  211   c , and  211   d  to an ejection opening corresponding to any of L_1, L_2, and L_3 set to a NULL value, the distance D_1 between ejection openings at both ends of the ejection opening group in each of the combinations is minimum is determined. In consequence, the combination of (L_1, L_2, L_3)=(f, g, h), for which D_1=2 is obtained, is determined to be a combination for which the distance D_1 is minimum. 
     A single combination of L_1, L_2, and L_3 has been successfully determined. Thus, the complementary nozzle selection process ends on the “YES” branch from step S 1004 . As illustrated in section (e) in  FIG. 14 , which is a schematic view of this state, the ejection opening  211   f  is selected as a complementary nozzle to the ejection opening  211   b , the ejection opening  211   g  as a complementary nozzle to the ejection opening  211   c , and the ejection opening  211   h  as a complementary nozzle to the ejection opening  211   d.    
     A method for selecting a complementary nozzle in a case where the ejection opening  211   f  also becomes inoperative thereafter in the state illustrated in section (e) in  FIG. 14  will be described in accordance with the flowchart illustrated in  FIG. 13 . 
     First, in step S 1001 , specific ejection opening arrays that are available are checked, and a NULL value is assigned to an ejection opening that is not available. Since the ejection opening arrays to be originally used are the ejection opening arrays  201   b ,  201   c , and  201   d , the values of (L_1, L_2, L_3) are reset to (L_1, L_2, L_3)=(b, c, d). Here, the ejection openings  211   b ,  211   c , and  211   d  are not available, and accordingly L_1=NULL, L_2=NULL, and L_3=NULL are set, yielding (L_1, L_2, L_3)=(NULL, NULL, NULL). 
     Then, in step S 1002 , it is checked whether there is any ejection opening that is not available. Specifically, it is checked whether at least one of L_1, L_2, and L_3 is set to a NULL value. Here, since L_1=L_2=L_3=NULL, there are ejection openings that are not available. Thus, the process proceeds to step S 1003 . 
     In step S 1003 , a combination of ejection openings for which, as a result of the application of combinations of ejection openings in normal operation other than the ejection openings  211   b ,  211   c , and  211   d  to an ejection opening corresponding to any of L_1, L_2, and L_3 set to a NULL value, the distance D_1 between ejection openings at both ends of the ejection opening group in each of the combinations is minimum is determined. Since there are only three ejection openings that are available, that is, the ejection openings  211   a ,  211   g , and  211   h , the combination of (L_1, L_2, L_3)=(a, g, h) is determined to be a combination for which the distance D_1 is minimum. 
     A single combination of L_1, L_2, and L_3 has been successfully determined. Thus, the complementary nozzle selection process ends on the “YES” branch from step S 1004 . As illustrated in section (f) in  FIG. 14 , which is a schematic view of this state, the ejection opening  211   a  is selected as a complementary nozzle to the ejection opening  211   b , the ejection opening  211   g  as a complementary nozzle to the ejection opening  211   c , and the ejection opening  211   h  as a complementary nozzle to the ejection opening  211   d.    
     As described above, this embodiment may provide recording with suppressed or reduced displacement of the landing positions of ink drops between ejection opening arrays even in the case of complementary recording upon occurrence of a failure in the ejection of ink. 
     Second Embodiment 
     In the first embodiment, if K (K≦M) ejection openings among M ejection openings (first ejection opening group) used in the specific recording mode are inoperative nozzles, the distribution data for (M−K) ejection openings, which are not inoperative nozzles, is not complementarily assigned. 
     In a second embodiment, in contrast, if K ejection openings among M ejection openings used in the specific recording mode become inoperative nozzles, the distribution data for all the M ejection openings used in the specific recording mode can be complementarily assigned. 
     Portions similar to those in the first embodiment described above are not described herein. 
     In this embodiment, if M ejection openings (first ejection opening group) include K inoperative nozzles, M complementary nozzles (second ejection opening group) are determined from among (N−K) ejection openings other than the K inoperative nozzles in accordance with the following three conditions. 
     First Condition 
     A combination of M complementary nozzles is determined for which the distance D_1 between ejection openings at opposite ends of the M complementary nozzles in the X direction is minimum. 
     Second Condition 
     If there is a plurality of combinations of M complementary nozzles satisfying the first condition, a combination of M complementary nozzles is determined for which the absolute value of a difference D_2 between the position P_u of an ejection opening at the center of the M complementary nozzles and the position P_c of an ejection opening at the center of M ejection openings in the first ejection opening group obtained before the complementary assignment process is minimum.
 
Third Condition
 
If there is a plurality of combinations of M complementary nozzles satisfying the first and second conditions, a combination of M complementary nozzles is determined for which the position P_u of the ejection opening at the center of the M complementary nozzles is minimum.
 
     In this embodiment, the complementary nozzle determination process is based on the three conditions described above. 
       FIG. 15  is a flowchart illustrating steps of the complementary nozzle determination process according to this embodiment.  FIG. 16  is a diagram schematically illustrating the complementary nozzle determination method. 
     In step S 1101 , it is determined whether the first ejection opening group includes an inoperative nozzle. If no inoperative nozzle is included, there is no need to perform a complementary assignment process. Thus, the complementary nozzle selection process ends. If an inoperative nozzle is included, the process proceeds to step S 1102 . 
     In step S 1102 , a combination of three ejection openings for which the distance D_1 is minimum is determined from among ejection openings in normal operation. 
     In step S 1103 , it is determined whether or not there is a plurality of combinations of ejection openings determined in step S 1102 . If a single combination of ejection openings has been determined, the combination of ejection openings determined in step S 1102  is determined to be a combination of ejection openings to be used for recording, and then the process ends. If there is a plurality of combinations of ejection openings determined in step S 1102 , the process proceeds to step S 1104 . 
     In step S 1104 , a combination of ejection openings for which the difference D_2 is minimum is determined from among the plurality of combinations of ejection openings determined in step S 1102 . 
     In step S 1105 , it is determined whether or not there is a plurality of combinations of ejection openings determined in step S 1104  for which the difference D_2 is minimum. If a single combination of ejection openings has been determined, the combination of ejection openings determined in step S 1104  is determined to be a combination of ejection openings to be used for recording, and then the process ends. If there is a plurality of combinations of ejection openings determined in step S 1104  for which the difference D_2 is minimum, the process proceeds to step S 1106 . 
     In step S 1106 , a combination of ejection openings for which the center position P_u is minimum is selected from among the combinations selected in step S 1104 , and is determined to be a combination of ejection openings to be used for recording. In step S 1106 , as in step S 1007  according to the first embodiment, it is sufficient that a process which enables the selection of one of a plurality of combinations of ejection openings be performed, and, by way of example, a combination of ejection openings for which the middle position P_u is maximum may be selected. 
     Then, in step S 1107 , the correspondence between nozzles for use before the determination of complementary nozzles and nozzles for use after the determination of complementary nozzles is determined. In this embodiment, the correspondence between nozzles for use is determined in alphabetical order. For example, nozzles for use before the determination of complementary nozzles are the ejection openings  211   b ,  211   c , and  211   d , and nozzles for use after the determination of complementary nozzles are the ejection openings  211   e ,  211   f , and  211   g . In this case, the distribution data for the ejection opening  211   b  is complementarily assigned to the ejection opening  211   e , the distribution data for the ejection opening  211   c  by using the ejection opening  211   f , and the distribution data for the ejection opening  211   c  by using the ejection opening  211   g.    
     In the following, a complementary nozzle determination process will be described step-by-step in accordance with the flowchart illustrated in  FIG. 15  when, as illustrated in section (a) in  FIG. 16 , only the ejection opening arrays  201   b ,  201   c , and  201   d  are used in the specific recording mode for recording. 
     In step S 1101 , inoperative nozzle information stored in the ROM  313  of the printer  100  is referred to, and it is checked whether there is any specific ejection opening that is not available in each of columns. Here, it is assumed that the ejection opening  211   c  first becomes inoperative. Even in a case where an inoperative nozzle exists, there is no need to perform a complementary assignment process so long as all the ejection openings  211   b ,  211   c , and  211   d  are available. Thus, the complementary nozzle selection process ends. Here, however, the ejection opening  211   c  is not available. Thus, the process proceeds to step S 1102 . 
     In step S 1102 , a combination of ejection openings for which the distance D_1 between ejection openings at both ends of the combination of ejection openings in the X direction is minimum is determined from among combinations of three ejection openings in normal operation. As a result, three combinations of (L_1, L_2, L_3)=(d, e, f), (e, f, g), and (f, g, h), for which D_1=2 is obtained, are determined as combinations for which the distance D_1 is minimum. 
     Then, in step S 1103 , it is checked whether or not there is a plurality of combinations of M ejection openings determined in step S 1102 . If a single combination of ejection openings has been determined, the combination is selected as a combination of ejection openings to be used, and then the complementary nozzle selection process ends. If there is a plurality of combinations, no complementary nozzle has been determined. Thus, the process proceeds to step S 1104 . 
     In step S 1104 , a combination of ejection openings for which the absolute value of a difference D_2 in distance between the middle position P_u of the complementary nozzles and the middle position P_c of the M ejection openings obtained before complementary assignment is minimum is determined from among the combinations of ejection openings determined in step S 1102 . Since P_u=(1+2+3)/3=2, D_2=|4−2|=2 is obtained when the middle position P_u for (d, e, f) as a combination of ejection openings to be used is given by P_u=(3+4+5)/3=4, D_2=|5−2|=3 is obtained when the middle position P_u for (e, f, g) is given by P_u=(4+5+6)/3=5, and D_2=|6−2|=4 is obtained when the middle position P_u for (f, g, h) is given by P_u=(5+6+7)/3=6. Accordingly, the combination of (d, e, f) is determined to be a combination for which the absolute value of the difference D_2 is minimum. 
     A single combination of ejection openings to be used, that is, (d, e, f), has been successfully determined. Thus, the process proceeds to step S 1107  on the “YES” branch from step S 1105 . 
     Then, in step S 1107 , it is determined which ejection opening corresponds to each of the complementary nozzles to b, c, and d. Here, (d, e, f) are selected as complementary nozzles to (b, c, d), respectively. A schematic view of the state after the shifting of ejection openings is illustrated in section (b) in  FIG. 16 . 
     A method for selecting a complementary nozzle in a case where the ejection opening  211   f  also becomes inoperative thereafter in the state illustrated in section (b) in  FIG. 16  will be described in accordance with the flowchart illustrated in  FIG. 15 . 
     In step S 1101 , it is checked whether the first ejection opening group includes an ejection opening that is not available. Here, there are ejection openings that are not available. Thus, the process proceeds to step S 1102 . 
     In step S 1102 , a combination of ejection openings for which the distance D_1 between ejection openings at both ends of the combination of ejection openings is minimum is determined from among combinations of three ejection openings in normal operation. In consequence, four combinations of (a, b, d), (b, d, e), (d, e, g), and (e, g, h), for which D_1=3 is obtained, are determined as combinations of three nozzles for which the distance D_1 is minimum. 
     Then, in step S 1103 , it is checked whether there is a plurality of combinations of ejection openings determined in step S 1102 . Here, there are four combinations, and thus the process proceeds to step S 1104 . 
     In step S 1104 , a combination of ejection openings for which the absolute value of the difference D_2 in distance between the middle position P_u and the middle position P_c is minimum is determined from among the combinations of three ejection openings determined in step S 1102 . Since P_u=2, the middle position P_u for (a, b, d) as a combination of ejection openings is given by P_u=(0+1+3)/3=4/3. Accordingly, the difference D_2 is given by D_2=|4/3−2|=2/3. Further, since the middle position P_u for (b, d, e) as a combination of ejection openings is given by P_u=(1+3+4)/3=8/3, the difference D_2 is given by D_2=|8/3−2|=2/3. Since the middle position P_u for (d, e, g) as a combination of ejection openings is given by P_u=(3+4+6)/3=13/3, the difference D_2 is given by D_2=|13/3−2|=7/3. Since the middle position P_u for (e, g, h) as a combination of ejection openings is given by P_u=(4+6+7)/3=17/3, the difference D_2 is given by D_2=|17/3−2|=11/3. Accordingly, the two combinations of (a, b, d) and (b, d, e) are determined as combinations of three ejection openings for which the absolute value of the difference D_2 is minimum. 
     Then, in step S 1105 , it is checked whether there is a plurality of combinations of ejection opening arrays determined in step S 1104 . Since there are two combinations, the process proceeds to step S 1106 . 
     The combinations of three ejection openings which have been determined at step S 1006  are considered to be equivalently affected by the displacement of the landing positions of ink drops. In step S 1006 , accordingly, a combination of ejection openings for which the middle position P_u is minimum is selected. In this embodiment, the middle position P_u for (a, b, d) as a combination of ejection openings is given by P_u=4/3, and the middle position P_u for (b, d, e) is given by P_u=8/3. Therefore, the determined combination is (a, b, d), and is used as a combination of ejection openings (second ejection opening group) to be used for recording. A schematic view of this state is illustrated in section (c) in  FIG. 16 . 
     Then, in step S 1107 , (a, b, d) are selected as nozzles substitute for (b, c, d), respectively. 
     A method for selecting a complementary nozzle in a case where the ejection opening  211   e  also becomes inoperative thereafter in the state illustrated in section (c) in  FIG. 16  will be described in accordance with the flowchart illustrated in  FIG. 15 . 
     In step S 1101 , it is checked whether the first ejection opening group includes an ejection opening that is not available. Here, there are ejection openings that are not available. Thus, the process proceeds to step S 1102 . 
     In step S 1202 , a combination of ejection openings for which the distance D_1 between ejection openings at both ends of the combination of ejection openings is minimum is determined from among combinations of three ejection openings in normal operation. In consequence, the combination of (a, b, d), for which D_1=3 is obtained, is determined to be a combination for which the distance D_1 is minimum. 
     A single combination of complementary nozzles, that is (a, b, d), has been successfully determined, and is thus used as a combination of ejection openings to be used for recording. A schematic view of this state is illustrated in section (d) in  FIG. 16 . Thus, the process proceeds to step S 1107  on the “YES” branch from step S 1105 . 
     Then, in step S 1107 , (a, b, d) are selected as complementary nozzles to (b, c, d), respectively. 
     A method for selecting a complementary nozzle in a case where the ejection opening  211   d  also becomes inoperative thereafter in the state illustrated in section (d) in  FIG. 16  will be described in accordance with the flowchart illustrated in  FIG. 15 . 
     In step S 1101 , it is checked whether the first ejection opening group includes an ejection opening that is not available. Here, there are ejection openings that are not available. Thus, the process proceeds to step S 1102 . 
     In step S 1102 , a combination of ejection openings for which the distance D_1 between ejection openings at both ends of the combination of ejection openings is minimum is determined from among combinations of three ejection openings in normal operation. In consequence, the combination of (a, b, g), for which D_1=6 is obtained, is determined to be a combination of three ejection openings for which the distance D_1 is minimum. 
     A single combination of ejection openings, that is, (a, b, g), has been successfully determined, and is thus determined as a combination of ejection openings to be used for recording. A schematic view of this state is illustrated in section (e) in  FIG. 16 . Thus, the process proceeds to step S 1107  on the “YES” branch from step S 1105 . 
     Then, in step S 1107 , (a, b, g) are selected as nozzles substitute for (b, c, d), respectively. 
     A method for selecting a complementary nozzle in a case where the ejection opening  211   b  also becomes inoperative thereafter in the state illustrated in section (e) in  FIG. 16  will be described in accordance with the flowchart illustrated in  FIG. 15 . 
     In step S 1101 , it is checked whether the first ejection opening group includes an ejection opening that is not available. Here, there are ejection openings that are not available. Thus, the process proceeds to step S 1102 . 
     In step S 1102 , a combination of ejection openings for which the distance D_1 between ejection openings at both ends of the combination of ejection openings is minimum is determined from among combinations of three ejection openings in normal operation. Since there are only three ejection openings that are available, that is, the ejection openings  211   a ,  211   g , and  211   h , the combination of (a, g, h), for which D_1=7 is obtained, is determined to be a combination for which the distance D_1 is minimum. 
     A single combination of ejection openings, that is, (a, g, h), has been successfully determined, and is thus used as a combination of ejection openings to be used for recording. A schematic view of this state is illustrated in section (f) in  FIG. 16 . Thus, the process proceeds to step S 1007  on the “YES” branch from step S 1005 . 
     Then, in step S 1007 , (a, g, h) are selected as complementary nozzles to (b, c, d), respectively. 
     As described above, this embodiment may also provide recording with suppressed or reduced displacement of the landing positions of ink drops between ejection opening arrays even in the case of complementary recording upon occurrence of a failure in the ejection of ink. 
     OTHER EMBODIMENTS 
     Embodiment(s) of the present invention 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. 
     An image processing apparatus, an image processing method, and an image recording apparatus according to embodiments of the present invention may provide recording with suppressed or reduced displacement of the landing positions of ink drops even in a case where complementary recording is performed upon occurrence of a failure in the ejection of ink. 
     While the present invention has been described with reference to exemplary embodiments, it is to be understood that the invention 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. 2014-247331, filed Dec. 5, 2014, which is hereby incorporated by reference herein in its entirety.