Patent Publication Number: US-2022227126-A1

Title: Estimation method, printing method and printing apparatus

Description:
BACKGROUND OF THE INVENTION 
     Field of the Invention 
     The present invention relates to a technique for estimating the expansion/contraction state of an elongated strip-shaped base material in a printing apparatus that ejects ink onto a surface of the base material while transporting the base material in a longitudinal direction thereof. 
     Description of the Background Art 
     An inkjet printing apparatus for printing an image on an elongated strip-shaped base material by ejecting ink from a plurality of heads while transporting the base material in a longitudinal direction thereof has heretofore been known. The inkjet printing apparatus ejects inks of different colors from the respective heads. Then, the inkjet printing apparatus prints a multi-color image on a surface of the base material by superimposing single-color images formed by the respective inks of the different colors. Such a conventional printing apparatus is disclosed, for example, in Japanese Patent Application Laid-Open No. 2004-268361. 
     In the printing apparatus of this type, the base material expands or contracts slightly when the base material absorbs the inks or when the inks on the base material become dry. As a result, a printed image formed on the surface of the base material is distorted. Also, there are cases in which the position of the inks ejected from the heads is improper due to the expansion and contraction of the base material. In conventional techniques, various parameters for the printing apparatus have been set to minimize the degradation in print quality resulting from the expansion and contraction of the base material. 
     Unfortunately, the amount of expansion/contraction of the base material varies depending on various conditions such as the tension applied to the base material, the type of base material, and the type of ink. In addition, there are cases in which the amount of expansion/contraction of the base material varies between printing apparatuses of the same type due to differences between machines. For these reasons, it has been difficult to set the aforementioned parameters uniquely. Also, the expansion/contraction state of the base material, which varies depending on image data to be printed, cannot be known prior to printing in conventional techniques. 
     SUMMARY OF THE INVENTION 
     In view of the foregoing, it is therefore an object of the present invention to provide a technique capable of estimating the expansion/contraction state of a base material in accordance with submitted data prior to printing. 
     To solve the aforementioned problem, a first aspect of the present invention is intended for a method of estimating the expansion/contraction state of an elongated strip-shaped base material in a printing apparatus that ejects ink onto a surface of the base material while transporting the base material in a longitudinal direction thereof. According to the first aspect of the present invention, the method comprises: a) a data acquisition step for acquiring submitted data that is image data to be printed; and b) an estimation step for outputting an estimation result indicating the expansion/contraction state of the base material resulting from ink, based on the submitted data, prior to printing of the submitted data. 
     A second aspect of the present invention is intended for the method of the first aspect, which further comprises c) a learning step for generating an estimation model that is able to estimate the expansion/contraction state of the base material by means of machine learning using learning data that is image data for learning as an input variable and the expansion/contraction state of the base material at the time of printing of the learning data in the printing apparatus as teacher data, wherein the submitted data is inputted to the estimation model, and the expansion/contraction state outputted from the estimation model is used as the estimation result in the estimation step (the step b)). 
     A third aspect of the present invention is intended for the method of the second aspect, wherein the learning data in the step c) is image data in which a plurality of marks arranged in spaced apart relation are incorporated, and wherein the expansion/contraction state that becomes the teacher data is measured in the learning step (the step c)) based on the positions of the marks on the base material at the time of printing of the learning data in the printing apparatus. 
     A fourth aspect of the present invention is intended for the method of the third aspect, wherein each of the marks includes: a base figure of a first color; and a mark figure of a second color different from the first color, the mark figure being in a position overlaid on the base figure. 
     A fifth aspect of the present invention is intended for the method of the fourth aspect, wherein the first color is white, and the second color is black. 
     A sixth aspect of the present invention is intended for the method of any one of the third to fifth aspects, wherein the teacher data indicates a change in distance between adjacent ones of the marks. 
     A seventh aspect of the present invention is intended for the method of any one of the third to fifth aspects, wherein the teacher data indicates the amount of displacement of each of the marks. 
     An eighth aspect of the present invention is intended for the method of any one of the second to seventh aspects, wherein the learning data is image data including a plurality of regions different in density value or coverage rate. 
     A ninth aspect of the present invention is intended for a method of printing using the estimation method as recited in any one of the first to eighth aspects. According to the ninth aspect of the present invention, the method further comprises d) a printing step for ejecting ink onto the surface of the base material while correcting the ejection position of ink onto the base material, based on the estimation result, the step d) being performed after the data acquisition step (the step a)) and the estimation step (the step b)). 
     A tenth aspect of the present invention is intended for a printing apparatus, which comprises: a data acquisition part for acquiring submitted data that is image data to be printed; a transport mechanism for transporting an elongated strip-shaped base material along a predetermined transport path in a longitudinal direction thereof; a head for ejecting ink onto a surface of the base material being transported by the transport mechanism, based on the submitted data; and an estimation part for outputting an estimation result indicating the expansion/contraction state of the base material resulting from the ink, based on the submitted data, prior to printing of the submitted data. 
     An eleventh aspect of the present invention is intended for the printing apparatus of the tenth aspect, which further comprises: a camera for photographing a printing surface of the base material in a position downstream from the head along the transport path; an expansion/contraction state measurement part for measuring the expansion/contraction state of the base material, based on a photographic image from the camera; and a learning part for generating an estimation model that is able to estimate the expansion/contraction state of the base material by means of machine learning using learning data that is image data for learning as an input variable and the expansion/contraction state at the time of printing of the learning data as teacher data, wherein the estimation part inputs the submitted data to the estimation model, and uses the expansion/contraction state outputted from the estimation model as the estimation result. 
     A twelfth aspect of the present invention is intended for the printing apparatus of the tenth or eleventh aspect, which further comprises: a correction value calculation part for calculating a correction value, based on the estimation result; and an operation control part for controlling the transport mechanism and the head so as to eject the ink onto the surface of the base material while correcting the ejection position of the ink onto the base material, based on the correction value. 
     According to the first to twelfth aspects of the present invention, the expansion/contraction state of the base material resulting from the ink is estimated, based on the submitted data, prior to the printing. This provides the estimation result of the expansion/contraction state in accordance with the submitted data. Thus, the submitted data is printed in consideration of the estimation result of the expansion/contraction state. 
     In particular, according to the second and eleventh aspects of the present invention, the use of the machine learning makes it easy to respond to changes in conditions, as compared with the process of calculating the estimation result of the expansion/contraction state based on a formula or table indicating a relationship between the image data and the expansion/contraction state. 
     In particular, according to the third aspect of the present invention, the plurality of marks incorporated in the learning data make it easy to obtain the expansion/contraction state of the base material that becomes the teacher data. 
     In particular, according to the fourth aspect of the present invention, the mark figure is recognizable regardless of the color of the image serving as a background. 
     In particular, according to the sixth aspect of the present invention, the teacher data represents the local amount of expansion/contraction for each region. The teacher data, which does not represent the accumulated amount of displacement, is easy to handle in the machine learning. 
     In particular, according to the seventh aspect of the present invention, the teacher data represents changes in coordinate position of each portion of the base material. In this case, the estimation result outputted from the estimation model also represents changes in coordinate position of each portion of the base material. Thus, the coordinate position of the ink for ejection onto the base material is easily corrected based on the estimation result. 
     In particular, according to the eighth aspect of the present invention, the amount of expansion/contraction of the base material in accordance with the density value or the coverage rate is learned. 
     These and other objects, features, aspects and advantages of the present invention will become more apparent from the following detailed description of the present invention when taken in conjunction with the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a diagram showing a configuration of a printing apparatus; 
         FIG. 2  is a partial top view of the printing apparatus in the vicinity of a printing part; 
         FIG. 3  is a block diagram showing connections between components of the printing apparatus and a computer; 
         FIG. 4  is a block diagram conceptually showing functions of the computer; 
         FIG. 5  is a flow diagram showing a procedure for a learning process; 
         FIG. 6  is a view showing an example of learning data; 
         FIG. 7  is an enlarged view of one part of the learning data; 
         FIG. 8  is a view showing an example of a method of measuring the expansion/contraction state of a base material; 
         FIG. 9  is a view showing another example of the method of measuring the expansion/contraction state of the base material; and 
         FIG. 10  is a flow diagram showing a procedure for a printing process. 
     
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     A preferred embodiment according to the present invention will now be described with reference to the drawings. 
     &lt;1. Configuration of Printing Apparatus&gt; 
       FIG. 1  is a diagram showing a configuration of a printing apparatus  1  according to a preferred embodiment of the present invention. The printing apparatus  1  is an apparatus for printing an image on a surface of an elongated strip-shaped base material  9  by ejecting ink droplets from a plurality of heads  21  to  24  toward the base material  9  while transporting the base material  9 . The base material  9  may be printing paper or a resin film. The base material  9  may also be metal foil or a glass base material. As shown in  FIG. 1 , the printing apparatus  1  includes a transport mechanism  10 , a printing part  20 , a camera  30 , and a computer  40 . 
     The transport mechanism  10  is a mechanism for transporting the base material  9  in a transport direction extending along the length of the base material  9 . The transport mechanism  10  of the present preferred embodiment includes an unwinder  11 , a plurality of transport rollers  12 , and a winder  13 . The base material  9  is unwound from the unwinder  11 , and is transported along a transport path formed by the transport rollers  12 . Each of the transport rollers  12  rotates about an axis extending in a direction perpendicular to the transport direction to guide the base material  9  downstream along the transport path. The transported base material  9  is wound and collected on the winder  13 . The base material  9  is tensioned in the transport direction. This suppresses slack and wrinkles in the base material  9  during the transport. 
     The printing part  20  is a processing part for ejecting droplets of inks (ink droplets) toward the base material  9  being transported by the transport mechanism  10 . The printing part  20  of the present preferred embodiment includes a first head  21 , a second head  22 , a third head  23 , and a fourth head  24 . The first head  21 , the second head  22 , the third head  23 , and the fourth head  24  are arranged in spaced apart relation in the transport direction of the base material  9 . The base material  9  is transported under the four heads  21  to  24 , with a printing surface thereof facing upward. 
       FIG. 2  is a partial top view of the printing apparatus  1  in the vicinity of the printing part  20 . As indicated by broken lines in  FIG. 2 , each of the heads  21  to  24  has a lower surface provided with a plurality of nozzles  201  arranged parallel to the width direction of the base material  9 . The first, second, third, and fourth heads  21 ,  22 ,  23 , and  24  eject ink droplets of four colors, i.e., K (black), C (cyan), M (magenta), and Y (yellow), respectively, which serve as color components of a multi-color image from the nozzles  201  toward an upper surface of the base material  9 . 
     The first head  21  ejects K-color ink droplets toward the upper surface of the base material  9  in a first printing position P 1  lying on the transport path. The second head  22  ejects C-color ink droplets toward the upper surface of the base material  9  in a second printing position P 2 . The second printing position P 2  is downstream from the first printing position P 1 . The third head  23  ejects M-color ink droplets toward the upper surface of the base material  9  in a third printing position P 3 . The third printing position P 3  is downstream from the second printing position P 2 . The fourth head  24  ejects Y-color ink droplets toward the upper surface of the base material  9  in a fourth printing position P 4 . The fourth printing position P 4  is downstream from the third printing position P 3 . 
     A fixing part for fixing the inks on the printing surface of the base material  9  may be further provided downstream of the heads  21  to  24  as seen in the transport direction. The fixing part, for example, blows a heated gas toward the base material  9  to dry the inks adhering to the base material  9 . The fixing part may be of the type which irradiates UV-curable inks with UV light to cure the inks. 
     The camera  30  is an imaging device for photographing the printing surface of the base material  9  having passed the printing part  20 . The camera  30  is disposed in opposed relation to the printing surface of the base material  9  in a photographing position P 5  downstream from the four heads  21  to  24  along the transport path. For example, a line sensor including a plurality of imaging elements, such as CCD, CMOS, and other imaging elements, arranged in the width direction is used as the camera  30 . The camera  30  photographs the printing surface of the base material  9  to thereby acquire a photographic image. Then, the camera  30  sends the acquired photographic image to the computer  40 . 
     The computer  40  is an information processing device for controlling the printing apparatus  1 .  FIG. 3  is a block diagram showing connections between the computer  40  and the components of the printing apparatus  1 . As conceptually shown in  FIG. 3 , the computer  40  includes a processor  401  such as a CPU, a memory  402  such as a RAM, and a storage part  403  such as a hard disk drive. A computer program  404  for execution of a learning process and a printing process to be described later is stored in the storage part  403 . 
     As shown in  FIG. 3 , the computer  40  is connected to the transport mechanism  10 , the four heads  21  to  24 , and the camera  30  for communication therewith. The computer  40  is also connected to a server  2  that is an external storage device for communication therewith. Submitted data D 1  is stored in the server  2 . The submitted data D 1  is image data to be printed in the printing apparatus  1  for obtainment of a printed product. The computer  40  acquires the submitted data D 1  from the server  2 , and controls the operations of the transport mechanism  10  and the four heads  21  to  24 , based on the submitted data D 1 . Thus, the printing process in the printing apparatus  1  proceeds. A large number of learning data D 2  for use in the learning process to be described later are also stored in the server  2 . 
     &lt;2. Functions of Computer&gt; 
     In this printing apparatus  1 , each of the four heads  21  to  24  ejects ink droplets to thereby print a single-color image on the upper surface of the base material  9 . A multi-color image is formed on the upper surface of the base material  9  by superimposing the four single-color images. If the ink droplets ejected from the four heads  21  to  24  are out of position relative to each other on the base material  9 , the image quality of a printed product is lowered. Controlling such misalignment (misregistration) between the single-color images on the base material  9  within an allowable range is an important factor for obtainment of high-quality printed products. 
     The base material  9  expands and contracts non-uniformly when the inks are absorbed by the base material  9  or when the inks on the base material  9  become dry. The occurrence of such expansion and contraction of the base material  9  distorts a printed image formed on the printing surface. The occurrence of such expansion and contraction of the base material  9  also makes the aforementioned misregistration prone to occur. To overcome these disadvantages, the computer  40  of the printing apparatus  1  has the function of estimating the expansion/contraction state of the base material  9  prior to printing based on the submitted data D 1  to perform printing while correcting the ejection positions of the ink droplets through the use of the estimation result.  FIG. 4  is a block diagram conceptually showing functions of the computer  40 . 
     As shown in  FIG. 4 , the computer  40  includes a data acquisition part  41 , an expansion/contraction state measurement part  42 , a learning part  43 , an estimation part  44 , a correction value calculation part  45 , and an operation control part  46 . Functions of the data acquisition part  41 , the expansion/contraction state measurement part  42 , the learning part  43 , the estimation part  44 , the correction value calculation part  45 , and the operation control part  46  are implemented by the processor  401  of the computer  40  operating in accordance with the computer program  404 . 
     The data acquisition part  41  is a processing part for acquiring the submitted data D 1  and the learning data D 2 . The data acquisition part  41  reads the submitted data D 1  and the learning data D 2  from the server  2 . The data acquisition part  41  inputs the read learning data D 2  to the learning part  43  and the operation control part  46 . The data acquisition part  41  also inputs the read submitted data D 1  to the estimation part  44  and the operation control part  46 . 
     The expansion/contraction state measurement part  42  is a processing part for measuring the expansion/contraction state of the base material  9 , based on a photographic image D 3  sent from the camera  30 . A method of measuring the expansion/contraction state of the base material  9  will be described later. The expansion/contraction state measurement part  42  inputs a measured expansion/contraction state D 4  of the base material  9  to the learning part  43 . 
     The learning part  43  is a processing part for learning a relationship between image data and the expansion/contraction state of the base material  9  which will result when the image data is printed. This printing apparatus  1  performs the learning process by means of the learning part  43  prior to the printing of the submitted data D 1  for obtainment of a printed product. During the learning process, the learning data D 2  is inputted to the aforementioned operation control part  46  and the learning part  43 . The operation control part  46  controls the operations of the transport mechanism  10  and the printing part  20 , based on the learning data D 2 . Thus, the learning data D 2  is printed on the printing surface of the base material  9 . During the learning process, the camera  30  photographs the base material  9  subjected to the printing. 
     The learning part  43  uses the learning data D 2  as an input variable and the expansion/contraction state D 4  measured by the expansion/contraction state measurement part  42  as teacher data to perform the learning process by means of a supervised machine learning algorithm. The learning part  43  repeats such a learning process until a predetermined termination condition is satisfied. Thus, the learning part  43  generates an estimation model M. The estimation model M outputs an estimation result indicating the expansion/contraction state of the base material  9 , based on the inputted image data. The details on the learning process will be described later. 
     The learning part  43  uses, for example, deep learning (a multi-layer neural network) as the machine learning algorithm. However, the machine learning algorithm used by the learning part  43  is not limited to the deep learning. Other machine learning algorithms such as Markov random fields (MRFs) and Boltzmann machines may be used in place of the deep learning. 
     The estimation part  44  is a processing part for estimating the expansion/contraction state of the base material  9  which will result when the submitted data D 1  is printed, based on the submitted data D 1 . The estimation part  44  uses the estimation model M generated by the learning part  43  to perform an estimation process. The estimation part  44  inputs the submitted data D 1  acquired by the data acquisition part  41  to the estimation model M. Then, the expansion/contraction state of the base material  9  corresponding to the submitted data D 1  is outputted from the estimation model M. The estimation part  44  uses the expansion/contraction state outputted from the estimation model M as an estimation result D 5 . 
     The correction value calculation part  45  is a processing part for calculating a correction value D 6 , based on the estimation result D 5 . The correction value calculation part  45  calculates the correction value D 6  in a direction for canceling the amount of expansion/contraction of the base material  9  indicated by the estimation result D 5 . The calculated correction value D 6  is inputted to the operation control part  46 . 
     The operation control part  46  is a processing part for controlling the operations of the transport mechanism  10  and the four heads  21  to  24 . When printing the aforementioned learning data D 2 , the operation control part  46  outputs a command value based on the learning data D 2  to the transport mechanism  10  and the four heads  21  to  24 . Thus, the operation control part  46  brings the transport mechanism  10  and the four heads  21  to  24  into operation to print the learning data D 2  on the printing surface of the base material  9 . When printing the submitted data D 1 , on the other hand, the operation control part  46  corrects a command value based on the submitted data D 1  with the use of the correction value D 6 . Then, the operation control part  46  outputs the corrected command value to the transport mechanism  10  and the four heads  21  to  24 . Thus, the operation control part  46  brings the transport mechanism  10  and the four heads  21  to  24  into operation to correct and print the submitted data D 1  on the printing surface of the base material  9 . 
     &lt;3. Learning Process&gt; 
     Next, the learning process for execution in the aforementioned printing apparatus  1  will be described.  FIG. 5  is a flow diagram showing a procedure for the learning process. This learning process is performed prior to the printing of the submitted data D 1  for obtainment of a printed product. 
     For the learning process, the data acquisition part  41  initially reads the learning data D 2  from the server  2 , as shown in  FIG. 5 . Then, the data acquisition part  41  inputs the learning data D 2  to the learning part  43  and the operation control part  46  (Step S 1 ). 
       FIG. 6  is a view showing an example of the learning data D 2 . As shown in  FIG. 6 , the learning data D 2  is image data in which a plurality of grid marks  52  are incorporated in an image  51  such as a picture or a pattern. The multiple learning data D 2  have respective images  51  different from each other. The amount of expansion/contraction of the base material  9  varies depending on the amounts of inks ejected onto the base material  9 . It is hence desirable that the image  51  of the learning data D 2  is an image including a plurality of regions different in density value or coverage rate. This allows the learning of the amount of expansion/contraction of the base material  9  in accordance with the density value or the coverage rate. 
     Each of the grid marks  52  is a mark indicating a predetermined coordinate position in the learning data D 2 . The grid marks  52  are arranged over the entire learning data D 2 . The grid marks  52  are also arranged in spaced apart relation in the transport direction and the width direction of the base material  9 . In the learning data D 2 , the grid marks  52  are disposed on the front side of the image  51 . 
       FIG. 7  is an enlarged view of one part of the learning data D 2 . As shown in  FIG. 7 , such a grid mark  52  of the present preferred embodiment is comprised of a base  figure 521  and a mark  figure 522 . The base  figure 521  is a rectangular figure filled in with white (0% density value). The mark  figure 522  is a black (100% density value) cross-shaped figure overlaid on the front side of the base  figure 521 . In an upper region of  FIG. 7 , the grid mark  52  is placed on a black background. In such a case, the mark  figure 522  is recognizable because the mark  figure 522  is on the white base  figure 521  while the background and the mark  figure 522  are of the same black color. In a lower region of FIG.  7 , the grid mark  52  is placed on a white background. In such a case, a boundary between the base  figure 521  and the background which are of the same white color is not recognizable, but the black mark  figure 522  is recognizable. 
     In the present preferred embodiment, the grid mark  52  is comprised of the white base  figure 521  and the black mark  figure 522  that is overlaid on the front side of the base  figure 521  in this manner. This makes the mark  figure 522  recognizable regardless of the color of the image  51  serving as the background. 
     After Step S 1 , the operation control part  46  controls the operations of the transport mechanism  10  and the four heads  21  to  24 , based on the learning data D 2 . This prints the learning data D 2  on the printing surface of the base material  9  (Step S 2 ). Specifically, the plurality of grid marks  52  together with the image  51  are printed on the printing surface of the base material  9 . Also, the camera  30  photographs the printing surface of the base material  9  on which the learning data D 2  is printed (Step S 3 ). The photographic image D 3  obtained by the photographing is sent from the camera  30  to the computer  40  and inputted to the expansion/contraction state measurement part  42 . 
     The expansion/contraction state measurement part  42  measures the expansion/contraction state of the base material  9 , based on the photographic image D 3  sent from the camera  30  (Step S 4 ). Specifically, the expansion/contraction state measurement part  42  extracts the positions of the grid marks  52  on the base material  9  from the photographic image D 3 . Then, the expansion/contraction state measurement part  42  measures the expansion/contraction state of the base material  9 , based on the positions of the grid marks  52 . As mentioned above, each of the grid marks  52  is comprised of the white base  figure 521  and the black mark  figure 522 . This makes the positions of all of the grid marks  52  recognizable regardless of the color and density of the image  51  serving as the background. Thus, the expansion/contraction state of the base material  9  is measured with accuracy. 
       FIG. 8  is a view showing an example of a method of measuring the expansion/contraction state of the base material  9 . In the example of  FIG. 8 , the expansion/contraction state measurement part  42  measures a distance between adjacent ones of the grid marks  52  in the photographic image D 3 . Then, the expansion/contraction state measurement part  42  calculates a difference between the measured distance between the grid marks  52  and the distance between the grid marks  52  in the learning data D 2  as the amount of expansion/contraction. In other words, a change in the distance between the adjacent grid marks  52  is measured as the amount of expansion/contraction in the method of  FIG. 8 . The expansion/contraction state measurement part  42  performs such a measurement of the amount of expansion/contraction for all of the adjacent grid marks  52  in the photographic image D 3 . As a result, a heat map showing a distribution of the amounts of expansion/contraction on the base material  9  is provided. 
     When the base material  9  expands or contracts, the amount of displacement of each region on the base material  9  is influenced not only by the amount of expansion/contraction of that region but also by the amount of expansion/contraction of other regions, and becomes the accumulation value of these amounts of expansion/contraction. However, the heat map provided by the measurement method of  FIG. 8  represents the local amount of expansion/contraction for each region of the base material  9 . Thus, this heat map is easy to handle as teacher data in Step S 5  to be described below. 
       FIG. 9  is a view showing another example of the method of measuring the expansion/contraction state of the base material  9 . In the example of  FIG. 9 , the expansion/contraction state measurement part  42  measures the position of each of the grid marks  52  in the photographic image D 3 . Specifically, the expansion/contraction state measurement part  42  uses a specific grid mark  52  in the photographic image D 3  as an origin to measure the coordinate position of each of the remaining grid marks  52  with respect to the origin. Then, the expansion/contraction state measurement part  42  calculates a difference between the measured coordinate position and the coordinate position of each of the grid marks  52  in the learning data D 2  as the amount of expansion/contraction. In other words, the amount of displacement of each of the grid marks  52  on the base material  9  is measured as the amount of expansion/contraction in the method of  FIG. 9 . The expansion/contraction state measurement part  42  performs such a measurement of the amount of expansion/contraction for all of the grid marks  52  in the photographic image D 3 . As a result, a vector map showing a distribution of the amounts of expansion/contraction on the base material  9  is provided. 
     The vector map provided by the measurement method of  FIG. 9  represents the amount of displacement of the coordinate position of each portion of the base material  9 . In this case, the estimation result outputted from the estimation model M to be described later also represents the amount of displacement of the coordinate position of each portion of the base material  9 . Thus, the use of the measurement method of  FIG. 9  makes it easy to use the estimation result during the correction of the coordinate positions of the inks for ejection onto the base material  9  in the correction value calculation part  45 . 
     The expansion/contraction state measurement part  42  inputs the provided heat map or vector map as the expansion/contraction state D 4  of the base material  9  to the learning part  43 . 
     Subsequently, the learning part  43  uses the learning data D 2  inputted from the data acquisition part  41  in Step S 1  as an input variable and the expansion/contraction state D 4  of the base material  9  measured in Step S 4  as teacher data to perform machine learning using a supervised machine learning program. In this process, the learning part  43  prepares the estimation model M for estimating the expansion/contraction state of the base material  9 , based on the image data. The estimation model M outputs the estimation result of the expansion/contraction state, based on the inputted learning data D 2 . The learning part  43  adjusts parameters of the estimation model M so that the estimation result outputted from the estimation model M is closer to the expansion/contraction state D 4  that is the teacher data (Step S 5 ; a learning process). 
     Thereafter, the learning part  43  judges whether a predetermined termination condition is satisfied or not (Step S 6 ). The termination condition may be, for example, that a difference between the estimation result and the teacher data is less than a preset threshold value. Alternatively, the termination condition may be that the number of repetitions of Steps S 1  to S 5  reaches a preset threshold value. If the termination condition is not satisfied (No in Step S 6 ), the computer  40  repeats the process of Steps S 1  to S 5  described above. At this time, the learning data D 2  may be that from a different image  51 . 
     The estimation accuracy of the estimation model M is improved by repeating the learning process of Steps S 1  to S 5 . Then, when the termination condition is satisfied (Yes in Step S 6 ), the learning part  43  terminates the learning process. This generates a learned estimation model M with high estimation accuracy. In other words, the learned estimation model M is able to accurately estimate the expansion/contraction state of the base material  9  which will result when the inputted image data is printed, based on the inputted image data. The learning part  43  provides the generated estimation model M to the estimation part  44 . 
     A predetermined number of learning data D 2  may be used as a single learning data set. Then, the learning process may be performed on a plurality of learning data sets. In this case, while a predetermined number of learning data D 2  included in the single learning data set are printed, the process of Steps S 1  to S 5  may be repeated without judging the termination condition in Step S 6 . Then, when the process of Steps S 1  to S 5  is completed for all of the learning data D 2  included in the single learning data set, the judgment of the termination condition in Step S 6  may be made. If the termination condition is not satisfied in Step S 6 , the learning process of Steps S 1  to S 5  may be performed on another learning data set. 
     &lt;4. Printing Process&gt; 
     Next, the printing process for execution in the printing apparatus  1  will be described. The printing process is performed after the aforementioned learning process.  FIG. 10  is a flow diagram showing a procedure for the printing process. 
     For the printing process, the submitted data D 1  to be printed is initially acquired (Step S 7 ; a data acquisition step), as shown in  FIG. 10 . Specifically, the data acquisition part  41  reads the submitted data D 1  from the server  2 . Then, the data acquisition part  41  inputs the submitted data D 1  to the estimation part  44  and the operation control part  46 . 
     The estimation part  44  inputs the submitted data D 1  to the estimation model M generated by the learning part  43 . Then, the estimation model M outputs the estimation result D 5  of the expansion/contraction state of the base material  9  (Step S 8 ; an estimation step). The estimation result D 5  indicates an estimated value of the expansion/contraction state of the base material  9  resulting from inks when the submitted data D 1  is printed in the printing apparatus  1 . The estimation part  44  outputs the obtained estimation result D 5  to the correction value calculation part  45 . 
     The correction value calculation part  45  calculates the correction value D 6 , based on the estimation result D 5  outputted from the estimation part  44  (Step S 9 ). This correction value D 6  is a control value for fine adjustment of the ejection position of ink droplets onto the base material  9 . The correction value calculation part  45  sets the correction value D 6  in a direction for canceling the expansion/contraction state of the base material  9  indicated by the estimation result D 5 . For example, if a portion of the base material  9  is estimated to be displaced toward one side in the width direction thereof due to the expansion and contraction of the base material  9 , the correction value calculation part  45  calculates the correction value D 6  so that the ejection position of ink droplets is corrected toward the other side in the width direction. Then, the correction value calculation part  45  inputs the calculated correction value D 6  to the operation control part  46 . 
     Thereafter, the operation control part  46  controls the operations of the transport mechanism  10  and the four heads  21  to  24 , based on the submitted data D 1  acquired from the data acquisition part  41  and the correction value D 6  acquired from the correction value calculation part  45 . In this process, the operation control part  46  corrects the ink ejection position specified by the submitted data D 1  in accordance with the correction value D 6 . This correction is made, for example, for each pixel of the submitted data D 1 . Then, ink droplets are ejected at the corrected ejection position on the printing surface of the base material  9 . Thus, the submitted data D 1  is printed on the printing surface of the base material  9  (Step S 10 ; a printing step). 
     As described above, the printing apparatus  1  estimates the expansion/contraction state of the base material  9  resulting from inks, based on the submitted data D 1 , prior to the printing of the submitted data D 1 . Thus, the printing apparatus  1  is capable of ejecting ink droplets onto the printing surface of the base material  9  while correcting the ink ejection position in consideration of the estimation result. As a result, the printing apparatus  1  provides high-quality printed products with less distortion of the printed image and with less misregistration. 
     &lt;5. Modifications&gt; 
     While the one preferred embodiment according to the present invention has been described hereinabove, the present invention is not limited to the aforementioned preferred embodiment. 
     &lt;5-1. First Modification&gt; 
     In the aforementioned preferred embodiment, the grid marks  52  are arranged in equally spaced apart relation in the learning data D 2 . However, the grid marks  52  need not necessarily be equally spaced apart from each other. For example, the grid marks  52  may be arranged more densely in a portion of the image  51  where a change in density value or in coverage rate is larger than in other portions thereof. 
     &lt;5-2. Second Modification&gt; 
     In the aforementioned preferred embodiment, each of the grid marks  52  is comprised of the white base  figure 521  and the black mark  figure 522 . However, the color of the base  figure 521  is not necessarily limited to white. Also, the color of the mark  figure 522  is not necessarily limited to black. For example, the base  figure 521  may be black and the mark  figure 522  may be white. The base  figure 521  and the mark  figure 522  may also be of other colors. It is only necessary that each of the grid marks  52  is comprised of the base  figure 521  of a first color and the mark  figure 522  of a second color different from the first color. In addition, the shapes of the base  figure 521  and the mark  figure 522  may be different from those of the aforementioned preferred embodiment. 
     &lt;5-3. Third Modification&gt; 
     In the aforementioned preferred embodiment, the only information inputted to the estimation model M in the learning process is the learning data D 2 . However, additional information such as detected values from various sensors in the printing apparatus  1  and the type of the base material  9  in addition to the learning data D 2  may be inputted to the estimation model M. In that case, the aforementioned additional information in addition to the submitted data D 1  may be inputted to the estimation model M in the printing process. This allows the estimation model M to output the estimation result D 5  with higher accuracy in consideration of the additional information. 
     &lt;5-4. Fourth Modification&gt; 
     In the aforementioned preferred embodiment, the expansion/contraction state of the base material  9  is estimated based on the estimation model M generated by machine learning. However, the expansion/contraction state of the base material  9  may be estimated by other methods. For example, a relationship between the density value or coverage rate of each region included in the submitted data D 1  and the expansion/contraction state of the base material  9  may be formulated. Also, a correspondence relationship between the density value or coverage rate of each region included in the submitted data D 1  and the expansion/contraction state of the base material  9  may be specified using a table. Then, prior to the printing of the submitted data D 1 , an estimation result indicating the expansion/contraction state of the base material  9  may be outputted based on the submitted data D 1  and the aforementioned formula or table. 
     If the formula or table is used, it is necessary to modify the formula or table each time the state of the printing apparatus  1  or the type of the base material  9  is changed. This process of modifying the formula or table places a heavy burden on a user because consideration is required from various viewpoints. On the other hand, the use of machine learning as in the aforementioned preferred embodiment allows the estimation model M to be re-created by performing a certain learning process even when the state of the printing apparatus  1  or the type of the base material  9  is changed. Thus, the aforementioned preferred embodiment is capable of easily responding to changes in conditions. 
     &lt;5-5. Other Modifications&gt; 
     In the aforementioned preferred embodiment, the nozzles  201  are arranged in a line in the width direction in each of the heads  21  to  24 . However, the nozzles  201  may be arranged in two or more lines in each of the heads  21  to  24  as shown in  FIG. 2 . 
     The printing apparatus  1  of the aforementioned preferred embodiment includes the four heads  21  to  24 . However, the number of heads in the printing apparatus  1  may be in the range of one to three or not less than five. For example, the printing apparatus  1  may include a head for ejecting ink of a spot color in addition to those for K, C, M and Y. 
     The components described in the aforementioned preferred embodiment and in the modifications may be consistently combined together, as appropriate. 
     While the invention has been shown and described in detail, the foregoing description is in all aspects illustrative and not restrictive. It is therefore understood that numerous modifications and variations can be devised without departing from the scope of the invention.