Patent Publication Number: US-9854119-B2

Title: Image reading apparatus, image reading method, and non-transitory computer readable medium

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is based on and claims priority under 35 USC 119 from Japanese Patent Application No. 2015-111548 filed Jun. 1, 2015. 
     BACKGROUND 
     (i) Technical Field 
     The present invention relates to an image reading apparatus, an image reading method, and a non-transitory computer readable medium. 
     (ii) Related Art 
     There is known an image reading apparatus in which plural image sensors are disposed in the principal scanning direction and images captured by the image sensors are linked to optically read an object to be imaged. 
     SUMMARY 
     According to an aspect of the present invention, there is provided an image reading device including: a reading unit that reads an image from a recording medium via a first optical imaging system and a second optical imaging system, the first optical imaging system and the second optical imaging system being disposed such that respective reading regions partially overlap each other in a principal scanning direction on a reading surface of the image reading apparatus; a first calculation unit that calculates a sum of a distance over which a first image captured by the first optical imaging system is displaced in the principal scanning direction with respect to a reference point and a distance over which a second image captured by the second optical imaging system is displaced in the principal scanning direction with respect to the reference point, the reference point being included in a region in which the reading regions overlap each other on the reading surface; a second calculation unit that calculates a first distance, over which the first image is displaced in the principal scanning direction, and a second distance, over which the second image is displaced in the principal scanning direction, using the sum calculated by the first calculation unit, a first reading angle at which the first optical imaging system reads the reference point, and a second reading angle at which the second optical imaging system reads the reference point; and a correction unit that corrects a position of the first image in the principal scanning direction using the first distance calculated by the second calculation unit, and that corrects a position of the second image in the principal scanning direction using the second distance calculated by the second calculation unit. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       An exemplary embodiment of the present invention will be described in detail based on the following figures, wherein: 
         FIG. 1  illustrates the functional configuration of an image reading apparatus; 
         FIG. 2  is a block diagram illustrating the hardware configuration of the image reading apparatus; 
         FIG. 3  illustrates the configuration of an image reading section; 
         FIGS. 4A and 4B  illustrate reading of a document in an ideal state with no paper floating; 
         FIGS. 5A and 5B  illustrate reading of a document in a state with paper floating; 
         FIGS. 6A and 6B  illustrate the principle of a process for correcting displacement in captured images; 
         FIG. 7  is a flowchart illustrating operation of the image reading apparatus; 
         FIG. 8  illustrates block extraction; 
         FIG. 9  illustrates pattern matching; 
         FIG. 10  is a flowchart illustrating calibration; 
         FIG. 11  illustrates a reference chart; 
         FIGS. 12A and 12B  illustrate position data; and 
         FIG. 13  illustrates a scene of use of the image reading apparatus. 
     
    
    
     DETAILED DESCRIPTION 
       FIG. 1  illustrates the functional configuration of an image reading apparatus  1  according to an exemplary embodiment of the present invention. The image reading apparatus  1  includes a reading unit  10 , a first calculation unit  11 , a second calculation unit  12 , a correction unit  13 , a combining unit  14 , and a transport unit  15 . The reading unit  10  reads an image from a recording medium that faces a reading surface of the image reading apparatus  1 . The reading unit  10  reads an image from a recording medium via a first optical imaging system and a second optical imaging system disposed such that respective reading regions of the first and second optical imaging systems partially overlap each other in the principal scanning direction on the reading surface. The first calculation unit  11  calculates the sum of the distance over which a first image captured by the first optical imaging system is displaced in the principal scanning direction with respect to a reference point and the distance over which a second image captured by the second optical imaging system is displaced in the principal scanning direction with respect to the reference point, the reference point being included in a region in which the reading regions overlap each other on the reading surface. The second calculation unit  12  calculates a first distance over which the first image is displaced in the principal scanning direction and a second distance over which the second image is displaced in the principal scanning direction. The second calculation unit  12  calculates the first distance and the second distance using the value calculated by the first calculation unit, a reading angle at which the first optical imaging system reads the reference point, and a reading angle at which the second optical imaging system reads the reference point. The correction unit  13  corrects the position of the first image in the principal scanning direction using the first distance calculated by the second calculation unit  12 . The correction unit  13  also corrects the position of the second image in the principal scanning direction using the second distance calculated by the second calculation unit  12 . The combining unit  14  combines the first image and the second image after being corrected by the correction unit  13 . The transport unit  15  transports the recording medium with the recording medium facing the reading surface of the image reading apparatus  1 . 
       FIG. 2  is a block diagram illustrating the hardware configuration of the image reading apparatus  1 . The image reading apparatus  1  is a computer that includes a controller  101 , a memory  102 , a display  103 , an operating section  104 , a communication section  105 , an image reading section  106 , an image processing section  107 , and a transport section  108 . In addition, the various sections of the image reading apparatus  1  are connected to a bus  109  to exchange various data via the bus  109 . 
     The controller  101  is a unit that controls operation of the various sections of the image reading apparatus  1 . The controller  101  includes a computation processing device such as a central processing unit (CPU), and a storage medium (principal storage device) such as a read only memory (ROM) and a random access memory (RAM). The CPU reads a program stored in the ROM and the memory  102 , and executes the program using the RAM as the working area. By executing the program, the controller  101  reads an image from a document to generate image data, communicates with another device via a communication line, and so forth. In the exemplary embodiment, the RAM of the controller  101  includes a line buffer that stores an image for one line read from the document. 
     The memory  102  is a unit that stores data. The memory  102  includes a storage medium (auxiliary storage device) such as a hard disk drive and a flash memory, and stores data received by the communication section  105 , data generated by the image reading apparatus  1 , and so forth. In addition, the memory  102  may include a removable storage medium (removable medium) such as a so-called memory card and a USB memory, and a unit that reads and writes data from and into the storage medium. 
     The display  103  includes a display device such as a liquid crystal display or an organic electroluminescence (EL) display, and a touch screen superposed on the display. A menu screen for operating the image reading apparatus  1  is displayed on the display  103  under control by the controller  101 . 
     The operating section  104  includes an operator (such as a button and a key) for inputting data or an instruction to the image reading apparatus  1 , and supplies the controller  101  with a control signal that matches the depressed operator. Input of various instructions to the image reading apparatus  1  is performed by a user by operating the touch screen of the display  103  or the operating section  104 . 
     The communication section  105  is a unit that transmits and receives data. The communication section  105  functions as a communication interface for communication with an external device. 
     The image reading section  106  is a unit that reads a document and that converts the document into image data. The image reading section  106  optically reads a document, and generates image data that represent an image of the read document. The image reading section  106  supplies the generated image data to the image processing section  107 . 
     The image processing section  107  is a unit that executes image processing on image data. In the exemplary embodiment, the image processing section  107  performs a process for correcting distortion of an image indicated by the image data read by the image reading section  106 . 
     The transport section  108  is a unit that transports a document (an example of a recording medium) with the document facing a reading surface R. The transport section  108  includes various rollers that separate sheets of a document loaded on a document reading tray and that transport the sheets to a reading surface of the image reading section  106  (the reading surface R to be discussed later) on which the document is read, for example. The transport section  108  transports the recording medium in the sub scanning direction which crosses the principal scanning direction. 
     In  FIG. 2 , the image reading section  106  which is controlled by the controller  101  which executes a control program for controlling operation of the various sections of the image reading apparatus  1  is an example of the reading unit  10 . The image processing section  107  which is controlled by the controller  101  which executes the control program is an example of the first calculation unit  11 , the second calculation unit  12 , the correction unit  13 , and the combining unit  14 . The transport section  108  which is controlled by the controller  101  which executes the control program is an example of the transport unit  15 . 
       FIG. 3  illustrates the configuration of the image reading section  106 . The image reading section  106  includes plural optical imaging systems  16  ( 16 S 1  to  16 Sn) arranged side by side in the principal scanning direction (the direction of the arrow X). The optical imaging systems  16  each include a line sensor  161  and an imaging lens  162 . The line sensor  161  is an image sensor array in which plural image sensors such as charge coupled devices (CCDs) are disposed in the principal scanning direction. The line sensor  161  captures an image of a document that faces the reading surface R (hereinafter referred to as “document on the reading surface R) of the image reading section  106 . In  FIG. 3 , a document P corresponds to the document on the reading surface R. The imaging lens  162  is a lens that optically reduces the size of an optical image reflected from the document on the reading surface R to condense light on the line sensor  161 . The line sensor  161  performs a photoelectric conversion on the incident light. Besides the components illustrated in  FIG. 3 , the image reading section  106  includes a light source that radiates light to the reading surface R, a mirror that receives an optical image reflected from the document on the reading surface R to condense light on the line sensor  161 , and so forth (none of which is illustrated). 
     Each of the optical imaging systems  16  is disposed such that a reading region A (A 1  to An) of the optical imaging system  16  partially overlaps that of an adjacent optical imaging system  16  in the principal scanning direction on the reading surface R. The image reading apparatus  1  combines images (hereinafter referred to as “captured images”) captured by the optical imaging systems  16  to acquire an image (hereinafter referred to as “line image”) with no seam in the principal scanning direction. In the configuration illustrated in  FIG. 3 , the document on the reading surface R is occasionally spaced from the reading surface R depending on the attitude of the document at the time when the document is transported. Hereinafter, such a state is referred to as “paper floating”. 
       FIGS. 4A and 4B  illustrate reading of a document in an ideal state with no paper floating.  FIGS. 4A and 4B  illustrate how an alphabetic letter “A” printed on the document P is read by the image reading section  106  at a position x 0  in the principal scanning direction. In  FIGS. 4A and 4B  and the subsequent drawings, the imaging lens  162  is not illustrated.  FIG. 4A  illustrates the positional relationship between the position x 0  and the optical imaging system  16 . As illustrated in  FIG. 4A , the position x 0  is included in a region in which a reading region Aa of the optical imaging system  16 Sa and a reading region Ab of the optical imaging system  16 Sb overlap each other, and an image of the letter “A” is captured by each of the optical imaging system  16 Sa and the optical imaging system  16 Sb.  FIG. 4B  illustrates a captured image IA 1  from the optical imaging system  16 Sa and a captured image IB 1  from the optical imaging system  16 Sb obtained with the positional relationship illustrated in  FIG. 4A . With no paper floating, the optical imaging system  16 Sa and the optical imaging system  16 Sb capture an image of the letter “A” using an image sensor that captures an image at the position x 0 , among the plural image sensors disposed in the principal scanning direction. Thus, as illustrated in  FIG. 4B , the letter “A” appears at the position x 0  in the captured image IA 1  and the captured image IB 1 . In this way, in the case where a document is read with no paper floating, there is no displacement from the actual position of a document P in the captured images, and therefore no distortion is caused in the image read by the image reading section  106 . 
       FIGS. 5A and 5B  illustrate reading of a document in a state with paper floating.  FIGS. 5A and 5B  illustrate reading of the document P with paper floating of a distance dp (see  FIG. 5A ). As with  FIGS. 4A and 4B ,  FIGS. 5A and 5B  illustrate how a letter “A” printed on the document P is read by the image reading section  106  at the position x 0  in the principal scanning direction.  FIG. 5B  illustrates a captured image IA 2  from the optical imaging system  16 Sa and a captured image IB 2  from the optical imaging system  16 Sb obtained with the positional relationship illustrated in  FIG. 5A . With paper floating, the optical imaging system  16 Sa and the optical imaging system  16 Sb capture an image of the letter “A” using an image sensor that is different from the image sensor that captures an image at the position x 0 , among the plural image sensors disposed in the principal scanning direction. In  FIGS. 5A and 5B , the optical imaging system  16 Sa captures an image of the letter “A” using an image sensor that captures an image at a position x 1  which is on the right side with respect to the position x 0  in the principal scanning direction. In the captured image IA 2 , as illustrated in  FIG. 5B , the letter “A” appears at the position x 1 . In addition, the optical imaging system  16 Sb captures an image of the letter “A” using an image sensor that captures an image at a position x 2  which is on the left side with respect to the position x 0  in the principal scanning direction. In the captured image IB 2 , as illustrated in  FIG. 5B , the letter “A” appears at the position x 2 . In this way, in the case where a document is read in a state with paper floating, there is displacement in the principal scanning direction from the actual position of the document P in the captured images, and therefore distortion is occasionally caused in the image read by the image reading section  106 . The image reading apparatus  1  according to the exemplary embodiment corrects displacement in the captured images to prevent occurrence of distortion in the image read by the image reading section  106 . 
       FIGS. 6A and 6B  illustrate the principle of a process for correcting displacement in captured images. The image reading apparatus  1  corrects displacement in the captured images on the basis of a reading angle (hereinafter referred to as “imaging angle”) at which the optical imaging system  16  reads a certain point (hereinafter referred to as “reference point”) on the reading surface R. The reference point is a point that serves as the reference for calculating the sum (hereinafter referred to as “total displacement amount”) of the distances over which the captured images from the adjacent optical imaging systems  16  are displaced in the principal scanning direction because of the paper floating. The reference point is set in a region in which the reading regions A of the adjacent optical imaging systems  16  overlap each other. In  FIGS. 6A and 6B , the reference point is set to the position x 0  (hereinafter the reference point will be referred to as “reference point x 0 ”). 
       FIG. 6A  illustrates an imaging angle relative to a reference point. The graph illustrated in  FIG. 6A  represents the relationship between the position of the reading surface R in the principal scanning direction and the imaging angle of the optical imaging system  16 Sa and the optical imaging system  16 Sb. In the graph, Ang 1  indicates the imaging angle of the optical imaging system  16 Sa, and Ang 2  indicates the imaging angle of the optical imaging system  16 Sb. In  FIG. 6A , in addition, the broken line L 0  is a line that passes through the reference point x 0  and that is perpendicular to the reading surface R. The dot-and-dash line L 1  indicates the optical axis of the optical imaging system  16 Sa. The dot-and-dash line L 2  indicates the optical axis of the optical imaging system  16 Sb. As illustrated in  FIG. 6A , the imaging angle of the optical imaging system  16 Sa and the optical imaging system  16 Sb is different for each position in the principal scanning direction. In the example, the imaging angle of the optical imaging system  16 Sa relative to the reference point x 0  is a 1 , and the imaging angle of the optical imaging system  16 Sb relative to the reference point x 0  is a 2 . 
       FIG. 6B  illustrates the relationship between the total displacement amount and the distances (hereinafter referred to as “displacement amounts”) over which captured images are displaced in the principal scanning direction because of paper floating using the captured image IA 2  and the captured image IB 2  illustrated in  FIG. 5B  as examples. In  FIG. 6B , w represents the total displacement amount, d 1  represents the displacement amount of the captured image IA 2 , and d 2  represents the displacement amount of the captured image IB 2 . As illustrated in  FIG. 6B , the total displacement amount w is equal to the sum of the displacement amount d 1  and the displacement amount d 2 . The ratio between the displacement amount d 1  and the displacement amount d 2  and the ratio between the imaging angle a 1  and the imaging angle a 2  indicated in  FIG. 6A  meet the relation of the following formula (1):
 
 d 1: d 2= a 1: a 2  (1)
 
     From the formula (1), the displacement amount d 1 , the displacement amount d 2 , the total displacement amount w, the imaging angle a 1 , and the imaging angle a 2  meet the following formulas (2) and (3): 
     
       
         
           
             
               
                 
                   
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     The image reading apparatus  1  calculates the displacement amount d 1  and the displacement amount d 2  using the relationship indicated in the formulas (2) and (3). In addition, the image reading apparatus  1  corrects displacement of the captured image IA 2  using the displacement amount d 1 , and corrects displacement of the captured image IB 2  using the displacement amount d 2 . A specific method of calculating the total displacement amount w will be discussed later. 
       FIG. 7  is a flowchart illustrating operation of the image reading apparatus  1 . The process illustrated in  FIG. 7  is performed repeatedly while the image reading apparatus  1  is reading an image from a document. In step SA 1 , the controller  101  reads an image for one line in the principal scanning direction from a document. Specifically, the controller  101  acquires a captured image via the plural optical imaging systems  16  arranged side by side in the principal scanning direction. The controller  101  stores the read image in the line buffer. 
     In step SA 2 , the controller  101  sets a reference point in a region in which the reading regions A of the adjacent optical imaging systems  16  overlap each other. The memory  102  stores an initial value of the reference point determined in advance. The controller  101  sets a reference point at a position indicated by the initial value stored in the memory  102 . 
     In step SA 3 , the controller  101  specifies the position in the image sensors corresponding to the reference point in the optical imaging system  16 . The wording “position in the image sensors corresponding to the reference point” represents in what pixel of the captured image in the principal scanning direction the reference point appears (i.e. the position of a pixel in the captured image in which the reference point appears). As discussed above, the reference point is set in a region in which the reading regions A of the adjacent optical imaging systems  16  overlap each other. Thus, the controller  101  specifies the position in the image sensors corresponding to the reference point for each of the line sensors  161  of the adjacent optical imaging systems  16 . Specifically, the controller  101  specifies the position in the image sensors corresponding to the reference point using the function indicated by the following formula (4):
 
 x pos( x )=[ Sa ,pixel A,Sb ,pixel B]   (4)
 
     The function indicated by the formula (4) (hereinafter referred to as “function xpos(x)”) is a function that outputs two optical imaging systems  16  and pixels in the optical imaging systems  16  corresponding to the position x on the reading surface in the principal scanning direction. That is, the function xpos(x) is a function that outputs pixelA of the optical imaging system  16 Sa and pixelB of the optical imaging system  16 Sb as the position in the image sensors corresponding to the position x. The function xpos(x) has been derived by performing calibration in the image reading apparatus  1  in advance and registered in the image reading apparatus  1  before the process illustrated in  FIG. 7  is started. The calibration for deriving the function xpos(x) will be discussed later. The controller  101  stores the specified position of the image sensor in the RAM. 
     In step SA 4 , the controller  101  specifies the imaging angle a 1  of the optical imaging system  16 Sa relative to the reference point and the imaging angle a 2  of the optical imaging system  16 Sb relative to the reference point. Specifically, the controller  101  specifies the imaging angle relative to the reference point using the function indicated by the following formula (5):
 
ang(pixel)=[angle]  (5)
 
     The function indicated by the formula (5) (hereinafter referred to as “function ang(pixel)”) is a function that outputs an imaging angle in response to input of a single pixel of the line sensor  161 . The controller  101  inputs pixelA specified in step SA 3  to the function ang(pixel) to specify the imaging angle a 1 . In addition, the controller  101  inputs pixelB specified in step SA 3  to the function ang(pixel) to specify the imaging angle a 2 . The controller  101  stores the specified imaging angle a 1  and imaging angle a 2  in the RAM. 
     In step SA 5 , the controller  101  extracts blocks from the captured image IA from the optical imaging system  16 Sa and the captured image IB from the optical imaging system  16 Sb. The term “blocks” as used herein refers to partial regions in the captured images. Blocks are extracted for the purpose of pattern matching to be performed in step SA 6  to be discussed later. 
       FIG. 8  illustrates block extraction. In step SA 5 , the controller  101  extracts a block Ba having a width Wa determined in advance and centered on pixelA (reference point x) from the captured image IA from the optical imaging system  16 Sa. In addition, the controller  101  extracts a block Bb 1  having a width Wb determined in advance and centered on pixelB (reference point x) from the captured image IB from the optical imaging system  16 Sb. As illustrated in  FIG. 8 , the width Wb is larger than the width Wa. 
       FIG. 7  is referenced again. In step SA 6 , the controller  101  performs pattern matching between the block Ba and the block Bb 1  extracted in step SA 5 . The controller  101  calculates differences in tone value for pixels in the block Ba and pixels in the block Bb 1  and calculates the sum of the absolute values of the differences to quantify the degree of coincidence between the two regions, for example. The controller  101  determines that patterns correspond to each other in the case where the sum of the absolute values of the differences is equal to or less than a threshold determined in advance. 
       FIG. 9  illustrates pattern matching. In step SA 6 , when it is determined that patterns in the block Ba and the block Bb 1  correspond to each other in a certain region of the block Bb 1 , the controller  101  specifies a position xa, in the principal scanning direction, of a pixel corresponding to pixelA and a position xb, in the principal scanning direction, of a pixel corresponding to pixelB in the block Bb 1 . The controller  101  stores the specified position xa and the specified position xb in the RAM. In the case where no displacement is caused in the captured images with no paper floating, the position xa and the position xb coincide with each other. 
       FIG. 7  is referenced again. In step SA 7 , the controller  101  calculates a total displacement amount w. Specifically, the controller  101  calculates a total displacement amount w using the following formula (6). The controller  101  stores the calculated total displacement amount w in the RAM.
 
 w=xa−xb   (6)
 
     In step SA 8 , the controller  101  extracts a block Bb 2  having a width Wa and centered on the position xa from the block Bb 1 . The extraction of the block Bb 2  is performed in order to align regions in which displacement of the captured image is corrected in step SA 10  to be discussed later between the captured image IA and the captured image IB. In step SA 9 , the controller  101  calculates a displacement amount d 1  and a displacement amount d 2 . Specifically, the controller  101  calculates a displacement amount d 1  and a displacement amount d 2  by substituting the imaging angle specified in step SA 4  and the total displacement amount w calculated in step SA 7  into the formulas (2) and (3) discussed above. The controller  101  stores the calculated displacement amount d 1  and displacement amount d 2  in the RAM. 
     In step SA 10 , the controller  101  corrects the captured image IA and the captured image IB. Specifically, the controller  101  corrects the position, in the principal scanning direction, of the block Ba in the captured image IA using the displacement amount d 1  calculated in step SA 9 . In addition, the controller  101  corrects the position, in the principal scanning direction, of the block Bb 2  in the captured image IB using the displacement amount d 2  calculated in step SA 9 . The controller  101  corrects the block Ba and the block Bb 2  through resampling, for example. 
     In step SA 11 , the controller  101  determines whether or not a correction has been finished for a captured image for one line. The controller  101  determines that a correction has been finished for an image for one line in the case where the reference point has reached a position determined in advance in the principal scanning direction, for example. In the case where it is determined that a correction has been finished for an image for one line (SA 11 : YES), the controller  101  proceeds to step SA 12 . In the case where it is determined that a correction has not been finished for an image for one line (SA 11 : NO), the controller  101  proceeds to step SA 13 . 
     In step SA 12 , the controller  101  combines the captured images for one line to generate a line image. To combine the captured images, the controller  101  performs one of the following processes (a) to (c), for example, for a region in which the reading regions A overlap each other. 
     (a) To select the tone value of a pixel in a captured image from one of the two adjacent optical imaging systems  16  with a smaller degree of field curvature. 
     For example, a case where the optical imaging system  16 Sa provides a smaller degree of field curvature relative to the position x 0  than that of the optical imaging system  16 Sb is considered when combining the captured image IA from the optical imaging system  16 Sa and the captured image IB from the optical imaging system  16 Sb. In this case, the controller  101  selects, as the tone value of a pixel at the position x 0 , the tone value of a pixel in the captured image IA. In another example, a case where the optical imaging system  16 Sb provides a smaller degree of field curvature relative to a position x 3  which is different from the position x 0  in a region in which the reading regions A overlap each other than that of the optical imaging system  16 Sa is considered. In this case, the controller  101  selects, as the tone value of a pixel at the position x 3 , the tone value of a pixel in the captured image IB. In the case where the process (a) is performed, the controller  101  has stored in advance, in the memory  102 , information that indicates an optical imaging system  16  with a smaller degree of field curvature than that of other optical imaging systems  16  for each position in the principal scanning direction. The controller  101  refers to the information stored in the memory  102 , and selects the tone value of a pixel in a captured image from the optical imaging system  16  indicated in the information. 
     (b) To obtain a weighted average of the tone values of pixels in the two captured images from the two adjacent optical imaging systems  16  such that the weight of the tone value of a pixel in the captured image from one of the optical imaging systems  16  with a smaller degree of field curvature is larger than the weight of the tone value of a pixel in the captured image from the other optical imaging system  16 . 
     For example, a case where the optical imaging system  16 Sa provides a smaller degree of field curvature relative to the position x 0  than that of the optical imaging system  16 Sb is considered when combining the captured image IA from the optical imaging system  16 Sa and the captured image IB from the optical imaging system  16 Sb. In this case, the controller  101  obtains, as the tone value of a pixel at the position x 0 , a weighted average of the tone values of pixels in the captured images IA and IB with a larger weight given to the tone value of a pixel in the captured image IA than the weight given to the tone value of a pixel in the captured image IB. In another example, a case where the optical imaging system  16 Sb provides a smaller degree of field curvature relative to a position x 3  than that of the optical imaging system  16 Sa is considered. In this case, the controller  101  obtains, as the tone value of a pixel at the position x 3 , a weighted average of the tone values of pixels in the captured images IA and IB with a larger weight given to the tone value of a pixel in the captured image IB than the weight given to the tone value of a pixel in the captured image IA. In the case where the process (b) is performed, the controller  101  has stored in advance, in the memory  102 , the information described in (a) or information that indicates the degree of field curvature for each position in the principal scanning direction. The controller  101  refers to the information stored in the memory  102 , and obtains a weighted average of the tone values of pixels in the two captured images. 
     (c) To obtain an arithmetic average of the tone values of pixels in images captured by the two adjacent optical imaging systems  16 . 
     For example, a case where the tone value of a pixel at the position x 0  in the captured image IA is “200” and the tone value of a pixel at the position x 0  in the captured image IB is “198” is considered when combining the captured image IA from the optical imaging system  16 Sa and the captured image IB from the optical imaging system  16 Sb. In this case, the tone value of a pixel at the position x 0  is calculated as “199”. 
     In step SA 13 , the controller  101  updates the reference point. The controller  101  sets a new reference point with a predetermined space apart from the current reference point in the principal scanning direction, for example. As in step SA 2 , the new reference point is set in a region in which the reading regions A of the adjacent optical imaging systems  16  overlap each other. The controller  101  may set reference points continuously with no space in the principal scanning direction. Upon updating the reference point, the controller  101  proceeds to step SA 3 . 
       FIG. 10  is a flowchart illustrating calibration for deriving the function xpos(x). The calibration may be performed before shipment of the image reading apparatus  1 , or may be performed for the purpose of correcting temporal fluctuations of the optical imaging system  16  when the image reading apparatus  1  is maintained after shipment. The calibration is performed by causing the image reading section  106  to read a figure (hereinafter referred to as “reference chart”) determined in advance. Thus, the process illustrated in  FIG. 10  is started with the reference chart placed at a position on the reading surface R at which the reference chart faces the optical imaging system  16 . 
       FIG. 11  illustrates a reference chart. The reference chart is a chart in which plural lines (hereinafter referred to as “reference lines”) are drawn. In the example, the reference chart includes T reference lines arranged at intervals of a clearance S in the principal scanning direction. The clearance S is set such that it is possible to specify the number of a reference line that appears in a captured image of the reference chart in the principal scanning direction in the reference chart. The clearance S is also set such that plural reference lines appear in each of captured images from the optical imaging systems  16 . The reference chart is not limited to that illustrated in  FIG. 11 . The reference chart may be a chart in which reference lines of different thicknesses are drawn, for example. The placement of the reference chart in the calibration is performed by placing a metal plate or a glass plate, to which paper with a printed reference chart has been affixed, at a position on the reading surface R at which the reference chart faces the optical imaging system  16 , for example. In another example, the reference chart may be drawn in advance at a position on the reading surface R at which the reference chart faces the optical imaging system  16 . In this case, in order to prevent the reference chart from being rubbed to fade away when the document is transported on the reading surface R, it is desirable that the reference chart should be retracted from a position at which the reference chart faces the optical imaging system  16  when the document is transported on the reading surface R. In a specific example, the reference chart may be drawn on a part of a side surface of a cylindrical roller that extends in the principal scanning direction, and the roller may be rotated such that the reference chart faces the optical imaging system  16  when the calibration is performed and the reference chart does not face the optical imaging system  16  when the calibration is not performed. In the example, the side surface of the roller which extends in the principal scanning direction corresponds to the reading surface R. 
       FIG. 10  is referenced again. In step SB 1 , the controller  101  initializes a loop counter i for a process loop  1 . The loop counter i is a parameter that specifies an optical imaging system  16  that captures an image of the reference chart. In the example, the loop counter i is initialized with i=1. The loop counter i is incremented by one at a time at the loop end. In the example, the process loop  1  is repeated for the number of the optical imaging systems  16  arranged side by side in the principal scanning direction, that is, until i=n is met. 
     In step SB 2 , the controller  101  captures an image of the reference chart via the optical imaging system  16  specified by the loop counter i. For example, in the case where the loop counter i indicates i=1, the controller  101  captures an image of the reference chart via the optical imaging system  16 S 1 . In another example, in the case where the loop counter i indicates i=2, the controller  101  captures an image of the reference chart via the optical imaging system  16 S 2 . The controller  101  stores the captured image in the RAM. 
     In step SB 3 , the controller  101  specifies the position in the image sensors corresponding to the reference line. The wording “position in the image sensors corresponding to the reference line” represents in what pixel of the captured image in the principal scanning direction the reference line appears. The controller  101  specifies the position in the image sensors corresponding to the reference line by analyzing the captured image obtained in step SB 2 . Specifically, the controller  101  specifies a region in the captured image with a smaller tone value than that of other regions, and specifies a pixel at the center, in the principal scanning direction, of the specified region as the position in the image sensors corresponding to the reference line. As discussed above, plural reference lines appear in a captured image of the reference chart. The controller  101  specifies the position in the image sensors corresponding to each of the plural reference lines. 
     In step SB 4 , the controller  101  performs a process for the loop end of the process loop  1 . Specifically, the controller  101  determines whether or not the loop counter i indicates i=n. If i=n is not met, the controller  101  increments the loop counter i, and proceeds to step SB 1 . If i=n is met, the controller  101  proceeds to step SB 5 . In step SB 5 , the controller  101  generates data (hereinafter referred to as “position data”) that indicate, for each of the optical imaging systems  16 , the position in the image sensors corresponding to the reference line specified through the processes in steps SB 1  to SB 4 , and stores the generated data in the RAM. 
       FIGS. 12A and 12B  illustrate position data.  FIG. 12A  illustrates position data represented in the table format, with the columns indicating the number that specifies the reference line and with the rows indicating the number that specifies the optical imaging system  16 .  FIG. 12B  illustrates position data represented in the graph format, with the horizontal axis representing the number that specifies the reference line and with the vertical axis representing the position of the image sensor.  FIG. 12B  illustrates a part of the position data illustrated in  FIG. 12A  (specifically, position data for the optical imaging systems  16 S 1  to  16 S 3 ). In the example of  FIGS. 12A and 12B , the line sensor  161  of the optical imaging system  16  includes image sensors for 7600 pixels. In the position data illustrated in  FIGS. 12A and 12B , for example, the position in the image sensors corresponding to the first reference line is the 150-th pixel in the captured image from the optical imaging system  16 S 1 . In another example, the position in the image sensors corresponding to the third reference line is the 3750-th pixel in the captured image from the optical imaging system  16 S 1 , and the 140-th pixel in the captured image from the optical imaging system  16 S 2 . In still another example, the position in the image sensors corresponding to the sixth reference line is the 6100-th pixel in the captured image from the optical imaging system  16 S 2 , and the 2100-th pixel in the captured image from the optical imaging system  16 S 3 . 
       FIG. 10  is referenced again. In step SB 6 , the controller  101  derives a function xpos(x) using the position data stored in the RAM. Specifically, the controller  101  performs an interpolation between discrete values indicated in the position data to specify the position in the image sensors corresponding to a position on the reading surface R in the principal scanning direction, and derives a function xpos(x) from the specified data. The controller  101  stores the derived function xpos(x) in the memory  102 . 
       FIG. 13  illustrates an example of a scene in which the image reading apparatus  1  is used. In the example, the image reading apparatus  1  is used to evaluate the printing quality. Specifically, the image reading apparatus  1  evaluates the printing quality by comparing image data (hereinafter referred to as “read image data”) acquired by reading a document with a printed image and image data (hereinafter referred to as “original image data”) on the basis of which printing has been performed. In the example of  FIG. 13 , the image reading apparatus  1  divides an original image indicated by the original image data into a lattice, and performs pattern matching on individual compartments C with a read image indicated by the read image data. The pattern matching is performed by calculating a difference in tone value between a pixel in a compartment C and a pixel in a matching region J, which is set in the read image as centered on a coordinate corresponding to the center coordinate of the compartment C, within the range of the matching region J. The image reading apparatus  1  specifies, in the matching region J, a position c 1  (hereinafter referred to as “maximum score position”) at which the degree of coincidence with the compartment C is maximum, and evaluates the printing quality using displacement between a center point c 0  of the matching region J and the maximum score position c 1 . In the case where the image reading apparatus  1  is used to evaluate the printing quality, the process for combining the captured images to generate a line image (step SA 12 ) may be omitted. 
     The present invention is not limited to the exemplary embodiment described above, and a variety of modifications may be made. Some modifications will be described below. The modifications described below may be used in combination of two or more. 
     In the pattern matching in step SA 6 , it is possibly determined that the block Ba does not correspond to any of the regions in the block Bb 1 . In this case, in step SA 7 , the controller  101  may estimate a current total displacement amount w (hereinafter referred to as “total displacement amount w n ”) using at least one of a total displacement amount w obtained in the preceding calculation (hereinafter referred to as “total displacement amount w n−1 ”) and a total displacement amount w obtained in the next calculation (hereinafter referred to as “total displacement amount w n+1 ”). The estimation of the total displacement amount w n  is performed by calculating the average value of the total displacement amount w n−1  and the total displacement amount w n+1 . In another example, the total displacement amount w n−1  may be used as the total displacement amount w n . 
     The controller  101  may correct the total displacement amount w n  calculated in step SA 7  before performing the process in step SA 9 . For example, the controller  101  may correct the total displacement amount w n  in the case where the difference between the total displacement amount w n  and the total displacement amount w n−1  exceeds a threshold determined in advance. In another example, the controller  101  may derive a function for estimating the next total displacement amount w on the basis of plural total displacement amounts w calculated in the past, and correct the total displacement amount w n  in the case where the difference between a value estimated on the basis of the function and the total displacement amount w n  exceeds a threshold determined in advance. The correction of the total displacement amount w n  is performed by calculating the average value of the total displacement amount w n−1  and the total displacement amount w n+1 . In another example, a value estimated on the basis of the function discussed above may be used as the total displacement amount w n . 
     A part of a region in the principal scanning direction occupied by the block Ba extracted in step SA 5  may overlap, or may not overlap, the block Ba obtained in the preceding extraction. 
     One reference point may be provided for each line. In this case, the controller  101  may correct a captured image for one line, when a displacement amount d 1  and a displacement amount d 2  are calculated, using the displacement amounts d 1  and d 2 . 
     The process in  FIG. 7  may not be performed for each line in the principal scanning direction. The process in  FIG. 7  may be performed for every plural lines in the principal scanning direction. In this case, the RAM includes a line buffer that stores an image for plural lines. 
     A control program executed by the image reading apparatus  1  in the exemplary embodiment may be provided as stored in a computer readable recording medium such as a magnetic recording medium (such as a magnetic tape and a magnetic disk (such as an HDD and a flexible disk (FD))), an optical recording medium (such as an optical disk (such as a compact disk (CD) and a digital versatile disk (DVD))), a magneto-optical recording medium, and a semiconductor memory (such as a flash ROM). Alternatively, the program may be downloaded by way of a network such as the Internet. 
     The foregoing description of the exemplary embodiment of the present invention has been provided for the purposes of illustration and description. It is not intended to be exhaustive or to limit the invention to the precise forms disclosed. Obviously, many modifications and variations will be apparent to practitioners skilled in the art. The embodiment was chosen and described in order to best explain the principles of the invention and its practical applications, thereby enabling others skilled in the art to understand the invention for various embodiments and with the various modifications as are suited to the particular use contemplated. It is intended that the scope of the invention be defined by the following claims and their equivalents.