Patent Publication Number: US-2011069334-A1

Title: Printing apparatus and printing method

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims priority to Japanese Patent Application No. 2009-219602 filed on Sep. 24, 2009. The entire disclosure of Japanese Patent Application No. 2009-219602 is hereby incorporated herein by reference. 
     BACKGROUND 
     1. Technical Field 
     The present invention relates a printing apparatus and a printing method adapted to be used with a certification system, a print operator terminal and a certifier terminal. 
     2. Related Art 
     There is proposed an on-demand printing system in which when printing is needed, a customer requests as much printing as is needed and a price is charged corresponding to the amount of printing (refer to JP-A-2006-146687). 
     SUMMARY 
     However, it is problematic in that the quality of a quantity of printed matter may not satisfy the requirements of a consumer, and the consumer has to purchase a quantity of printed matter of an unintended quality. Particularly, when an art object such as a picture is reproduced using a quantity of printed matter, the requirements for the reproducibility of the art object are high and the requirements of the consumer may not be satisfied. In addition, as a further demand, the provider that provides the reproduced art object desires to prevent duplicates of low reproducibility from being exhibited or distributed. 
     An advantage of some aspects of the invention is to provide a certification system capable of guaranteeing the reproducibility of a reproduced image, a print operator terminal and a certifier terminal. 
     According to one aspect of the present invention, a printing apparatus includes an obtaining unit, a printing unit and a consideration request unit. The obtaining unit is configured and arranged to obtain image data of an object and spectral characteristics information relating to the object. The printing unit is configured and arranged to print an image of the object according to the image data, and to print at least one color patch using the spectral characteristics information while the color patch is associated with the image. The consideration request unit is configured and arranged to transmit a consideration request for printing of the image based on a comparison result between the spectral characteristics information and spectral characteristics information obtained by color measurement of the color patch that was printed. 
     According to another aspect of the present invention, a printing method using a printer includes obtaining image data of an object and spectral characteristics information relating to the object, printing an image of the object according to the image data, and printing at least one color patch using the spectral characteristics information while the color patch is associated with the image, and transmitting a consideration request for printing of the image based on a comparison result between the spectral characteristics information and spectral characteristics obtained by color measurement of the color patch that was printed. 
     According to yet another aspect of the present invention, a recording medium recording a computer-readable program that prompts a computer to execute functions of: obtaining image data of an object and spectral characteristics information relating to the object; printing an image of the object according to the image data, and printing at least one color patch using the spectral characteristics information while the color patch is associated with the image; and transmitting a consideration request for printing of the image based on a comparison result between the spectral characteristics information and spectral characteristics information obtained by color measurement of the color patch that was printed. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Referring now to the attached drawings which form a part of this original disclosure: 
       The invention will be described with reference to the accompanying drawings, wherein like numbers reference like elements. 
         FIG. 1  is an overall configuration diagram of a certification system. 
         FIG. 2  is a block diagram showing the hardware configuration of a computer. 
         FIG. 3  is a block diagram showing the software configuration of a certification system. 
         FIG. 4  is a flowchart of an overall procedure performed by a certification system. 
         FIG. 5  is a flowchart of an image input process. 
         FIG. 6  is a schematic diagram showing the configuration for generating correction data. 
         FIG. 7  is a diagram showing the configuration for measuring the spectral reflectance of a picture. 
         FIG. 8  is a flowchart showing a printing process. 
         FIG. 9  is a layout of patch data (image data) for certification. 
         FIG. 10  is a diagram showing a 3D-LUT. 
         FIG. 11  is a schematic diagram showing a printing scheme of a printer. 
         FIG. 12  is a flowchart of a measurement process. 
         FIG. 13  is a flowchart of a certification process. 
         FIG. 14  is a flowchart of a request and settlement process. 
         FIG. 15  is a diagram showing a spectral reflectance database. 
         FIGS. 16A and 16B  are diagrams showing a spectral Neugebauer model. 
         FIGS. 17A to 17C  are diagrams showing a cellular Yule-Nielsen Spectral Neugebauer Model. 
         FIG. 18  is a schematic diagram of a spectral reflectance-ink amount table. 
         FIG. 19  is a flowchart of a creating process of a spectral reflectance-ink amount table. 
         FIG. 20  is a diagram showing the software configuration of a certification system in accordance with a modified example. 
     
    
    
     DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS 
     Hereinafter, an embodiment of the present invention will be described according to the following sequence: A. Overall Configuration; B. Image Input Process; C. Printing Process; D. Measurement Process; E. Certification Process; F. Request and Settlement Process; G. Spectral Printing Model; H. Modified Example (H1. First Modified Example and H2. Second Modified Example); and I. Features of Embodiments. 
     A. Overall Configuration 
       FIG. 1  is a diagram schematically showing computers and a network constituting a certification system in accordance with this embodiment of the invention. Referring to  FIG. 1 , this embodiment of the invention includes at least a computer  10  of an art gallery A, a computer  20  of a print operator, and a computer  30  of an art gallery B, and the computers  10 ,  20  and  30  are communicably connected to one another through an Internet INT. In this embodiment, the computers  10 ,  20  and  30  are connected to one another through the Internet INT. However, for example, another communication medium (a communication protocol) such as a wired/wireless phone line may be interposed into the whole or a part of a communication line. 
       FIG. 2  shows one example of the hardware configuration of each of the computers  10 ,  20  and  30 . The computers  10 ,  20  and  30  in accordance with this embodiment have a substantially identical hardware configuration. The computer  10  includes a CPU  11 , a RAM  12 , a ROM  13 , a hard disk drive (HDD)  14 , a communication interface (I/F)  15 , a video interface (I/F)  16 , an input device interface (I/F)  17 , a general purpose interface (I/F)  18 , and a bus  19 . The computer  20  includes a CPU  21 , a RAM  22 , a ROM  23 , a HDD  24 , a communication I/F  25 , a video I/F  26 , an input device I/F  27 , a general purpose I/F  28 , and a bus  29 . The computer  30  includes a CPU  31 , a RAM  32 , a ROM  33 , a HDD  34 , a communication I/F  35 , a video I/F  36 , an input device I/F  37 , and a bus  39 . The CPUs  11 ,  21  and  31  develop program data stored in the ROMs  13 ,  23  and  33  and the HDDs  14 ,  24  and  34  to the RAMs  12 ,  22  and  32 , and perform an operation for executing processes or functions which will be described later, respectively. The communication I/Fs  15 ,  25  and  35  provide mediation for connecting the computers  10 ,  20  and  30  to the Internet INT, respectively. The video I/Fs  16 ,  26  and  36  perform a process for outputting an image on external displays  16   a ,  26   a  and  36   a . The input device I/Fs  17 ,  27  and  37  receive an operation through external keyboards  17   a ,  27   a  and  37   a  and external mice  17   b ,  27   b  and  37   b , and transmit signals based on the operation to the CPUs  11 ,  21  and  31 , respectively. 
     The general purpose I/F  18  of the computer  10  of the art gallery A provides an interface for connecting the computer to an external spectral reflectometer  18   b . The general purpose I/F  28  of the computer  20  of the print operator provides an interface for connecting the computer  20  to an external printer (a printing apparatus)  28   a  and an external spectral reflectometer  28   b . These elements  11  to  18 ,  21  to  28  and  31  to  37  are communicably connected to one another through the buses  19 ,  29  and  39 , and can perform a collaborative process by communicating with one another. The art gallery B exhibits a reproduced image PI of a picture D (an object) owned by the art gallery A for a constant period through an “art gallery A exhibition”, and the picture D owned by the art gallery A corresponds to a target object to be reproduced in accordance with this embodiment of the invention. In addition, the computer  10  of the art gallery A, the computer  20  of the print operator, and the computer  30  of the art gallery B are provided in a single number. However, there may be more than one art gallery A, print operator, and art gallery B, and the computers  10 ,  20  and  30  may be provided in a plural number in correspondence with the number of the art galleries A, the number of the print operators, and the number of the art galleries B, respectively. 
       FIG. 3  shows the software configuration and main data controlled by the computers  10 ,  20  and  30 . In the computer  10  of the art gallery A, an image data input unit M 1 , a calibration unit M 2 , a measurement data reception unit M 3 , a certification unit M 4 , a payment request unit M 5 , and a notification unit M 6  are controlled. In the computer  20  of the print operator, an image data obtaining unit M 7 , a printing unit M 8 , a measurement data obtaining unit M 9 , a measurement data transmission unit M 10 , a reception unit M 11 , and a consideration request unit M 12  are controlled. In the computer  30  of the art gallery B, a settlement unit M 13  is controlled. Processes performed by each of the software modules M 1  to M 13  will be described in detail later. 
     B. Image Input Process 
       FIG. 4  schematically shows the flow of an overall procedure performed by the certification system in accordance with this embodiment of the invention. In this embodiment, first, the computer  10  of the art gallery A performs the image input process (step S 100 ), thereby obtaining image data ID. Next, the computer  20  of the print operator performs the printing process (step S 200 ) of printing the reproduced image PI and certification patches CC, and further performs the measurement process (step S 300 ) of measuring the spectral characteristics of the certification patches CC. Then, the computer  30  of the art gallery B performs the certification process (step S 400 ). Last, the request and settlement process (step S 500 ) is performed among the computer  10  of the art gallery A, the computer  20  of the print operator, and the computer  30  of the art gallery B. Before the certification system performs each process which will be described later, the art gallery B places an order with the art gallery A and the print operator for the reproduced image PI of the picture D owned by the art gallery A. This order may be electronically transmitted to the art gallery A, or may also be transmitted to the art gallery A by a letter and the like. In relation to the order, information for specifying the picture D, the size of the reproduced image PI, a light source (a designated light source) when the art gallery B exhibits the reproduced image PI, and information for specifying a reproduction mode of the reproduced image PI are transmitted to the art gallery A and the print operator. As the reproduction mode of the reproduced image PI, any one of a spectral reflectance mode and a color value mode is designated. When the order is electronically transmitted to the art gallery A, order data including the above-described information is transmitted to the computer  10  of the art gallery A and the computer  20  of the print operator from the computer  30  of the art gallery B. Hereinafter, the overall procedure will be sequentially described starting from the image input process (step S 100 ). 
       FIG. 5  shows the flow of the image input process. The image input process is performed by the computer  10  of the art gallery A having received the order, specifically, by the image data input unit M 1  and the calibration unit M 2 . In step S 110 , the spectral reflectometer  18   b  measures the spectral reflectances R(λ) of a reference sample. The spectral reflectances R(λ) obtained by measuring the reference sample are written as confirmation spectral reflectances R c (λ). In addition, the spectral reflectances R(λ) represent a reflectance group when irradiating lights having a plurality of wavelength sections in a visible wavelength band. The spectral reflectances R(λ) of the reference sample are written as reference spectral reflectances R i (λ). The reference spectral reflectances R i (λ) have been previously determined, and reference data  14   a  including the reference spectral reflectances R i (λ) is stored in the HDD  13 . In step S 120 , the calibration unit M 2  generates correction data  14   b.    
       FIG. 6  schematically shows the configuration for generating the correction data  14   b . Herein, correction values R m (λ), which are obtained by subtracting the confirmation spectral reflectances R c (λ) from the reference spectral reflectances R i (λ) with respect to each wavelength section, are stored as the correction data  14   b . In addition, the generation dates of the correction data  14   b  are appended to the correction data  14   b . In step S 130 , the image data input unit M 1  measures the spectral reflectances R(λ) of the picture D as a target object to be reproduced, thereby generating the image data ID. In addition, in relation to the correction data  14   b  of this embodiment, the correction values R m (λ) are provided for each wavelength section. However, in relation to the correction data  14   b , the correction values R m (λ) may also be provided for each combination of each wavelength section and each spectral reflectance R(λ). In addition, tilt levels (primary differential values) obtained by differentiating the spectral reflectances R(λ) by wavelengths or secondary differential values obtained by differentiating the tilt levels by the wavelengths are combined with each combination of each wavelength section and each spectral reflectance R(λ), and the correction values R m (λ) are provided for each of these combinations, so that the correction data  14   b  may also be created as 3D to 4D-LUTs. 
       FIG. 7  is a diagram showing the configuration for measuring the spectral reflectance R(λ) of the picture D and generating the image data ID. As shown in  FIG. 7 , the spectral reflectometer  18   b  has a stage  18   b   1 , and the picture D is loaded on the stage  18   b   1 . The stage  18   b   1  can be driven along an XY axis in the horizontal direction and the driving amount of the stage  18   b   1  is obtained with respect to the XY direction. Whenever portions of the picture D facing a fixed measurement probe  18   b   2  are changed little by little as the stage  18   b   1  moves in the XY direction, the spectral reflectometer  18   b  measures the spectral reflectances R(λ) of each portion. The spectral reflectances R(λ) of each portion are sequentially stored in each pixel associated with the driving amount of the stage  18   b   1 , thereby completing the generation of the image data ID in which each pixel existing in coordinates of the XY direction specified by the driving amount has the spectral reflectance R(λ). By reducing the pitch of the driving amount in the XY direction of the stage  18   b   1 , the resolution of the image data ID can be increased. 
     In step S 140 , the calibration unit M 2  calculates the difference between the current date and the generation date of the correction data  14   b  and determines whether the difference exceeds a predetermined threshold value (e.g., 10 days). When the difference exceeds the threshold value, step S 110  is performed and the correction data  14   b  is generated anew. When the difference does not exceed the threshold value, step S 150  is performed. In step S 150 , the calibration unit M 2  corrects the spectral reflectances R(λ) by adding the correction values R m (λ) to the spectral reflectances R(λ) of each pixel of the image data ID. Thus, the spectral reflectances R(λ) of the image data ID are corrected. In addition, the calibration unit M 2  appends a certification flag to the image data ID (step S 160 ), wherein the certification flag indicates that correction based on appropriate correction data  14   b  has been performed. That is, it is certified that the image data ID has been corrected based on new correction data  14   b . Furthermore, the calibration unit M 2  appends reference light source information to the image data ID (step S 170 ), wherein the reference light source information specifies a light source (a reference light source) under which the picture D is exhibited in the art gallery A. After the image data ID is generated as described above, the image data input unit M 1  transmits the image data ID to the computer  20  of the print operator (step S 180 ). 
     C. Printing Process 
       FIG. 8  is a flowchart showing the printing process. The printing process is performed in the computer  20  of the print operator, which has received the order, specifically, by the image data obtaining unit M 7  and the printing unit M 8 . In step S 205 , the image data is received. In step S 210 , the image data obtaining unit M 7  determines whether the certification flag has been appended to the image data ID. That is, it is confirmed whether the correction based on the appropriate correction data  14   b  has been performed with respect to the image data ID. When the certification flag has not been appended to the image data ID, the printing process is ended. In this way, it is possible to prevent the reproduction image PI from being printed based on the image data ID in which the spectral reflectances R(λ) have not been appropriately corrected. In this embodiment, correction of the image data ID based on new correction data  14   b  serves as certification conditions of the image data ID. When the certification flag has been appended to the image data ID, step S 220  is performed. In step S 220 , the image data obtaining unit M 7  obtains the image data ID transmitted from the computer  10  of the art gallery A. In step S 230 , the printing unit M 8  converts the image size of the image data ID. In the above-described order, the size of the reproduction image PI is transmitted to the print operator, and the image size of the image data ID is converted based on the magnification of the size of the reproduction image PI and the print resolution of the printer  28   a . In the case of reducing the size, thinning-out and the like are performed. In the case of enlarging the size, pixels are inserted into the image data ID. The inserted pixels also include spectral reflectances R(λ) similarly to other pixels, but the spectral reflectances R(λ) are determined by an interpolation operation based on spectral reflectances R(λ) of adjacent pixels. In step S 235 , the image data ID is laid out together with patch data  24   b  for certification. 
       FIG. 9  shows the configuration of the layout in step S 235 . Herein, the image data ID having the converted size is allocated to an area of a printing paper having a predetermined size on which printing is performed, and the patch data  24   b  for certification stored in the HDD  23  is allocated to a blank space to which the image data ID is not allocated. The patch data  24   b  for certification is image data in which each pixel has spectral reflectance R(λ) similarly to the image data ID. In relation to the patch data  24   b  for certification, pixels having the same spectral reflectance R(λ) are distributed in an area having a rectangular shape. Thus, it is possible to reproduce color patches (certification patches CC) having a rectangular shape. Spectral reflectances R(λ) designated for each certification patch CC are obtained by measuring spectral reflectances R(λ) of a sample coated with pigments used for drawing the picture D. Usually, since pigments with a plurality of colors are used, a plurality of certification patches CC are formed. Since repairs are carried out in the case of an old picture D, the spectral reflectances R(λ) may be obtained by measuring a sample coated with pigments used at the time of the repair. Image data, to which the image data ID and the patch data  24   b  for certification are allocated, is written as print image data. 
     In step S 240 , the printing unit M 8  performs the following diverging branched processes according to the reproduction mode of the reproduction image PI. When the reproduction mode of the reproduction image PI is a spectral reflectance mode, the printing unit M 8  performs a color conversion process of converting the spectral reflectances R(λ) of each pixel into ink amount sets φ which are a combination of ink amounts of CMYKlclm inks, which are ejected onto a printing paper by the printer  28   a , in step S 250 . Herein, the ink amount sets φ, with which the spectral reflectances R(λ) of each pixel are reproducible, are calculated using a spectral printing model which will be described later. According to the spectral printing model, as any ink amount set φ is input, spectral reflectances R(λ) are output which are predicted to be reproduced on a printing paper when the printer  28   a  performs printing based on the ink amount set φ. Using the spectral printing model, the ink amount sets φ may not be calculated in reverse from the spectral reflectances R(λ) with which each pixel is reproducible. In this regard, in this embodiment, the printing unit M 8  performs the following color conversion process, thereby sequentially obtaining the ink amount sets φ with which the spectral reflectances R(λ) of each pixel are reproducible. 
     First, target pixels, for example, are selected in a pixel arrangement sequence, and the spectral reflectances R(λ) of the target pixels are obtained as target spectral reflectances R t (λ) (step S 250   a ). Next, an appropriate ink amount set φ is initially set in the spectral printing model (step S 250   b ), and spectral reflectances R(λ) calculated by the initial setting are obtained as prediction spectral reflectances R s (λ) (step S 250   c ). The printing unit M 8  determines whether an error (e.g., a Euclidean distance in spaces separated by wavelength sections) between the target spectral reflectances R t (λ) and the prediction spectral reflectances R s (λ) is smaller than a predetermined threshold value (step S 250   d ). In addition, the threshold value is small to the extent that the target spectral reflectances R t (λ) may be regarded to be equal to the prediction spectral reflectances R s (λ). When the error is larger than the threshold value, the ink amount set φ is updated (step S 250   e ), and the printing unit M 8  returns to step S 250   c . That is, the printing unit M 8  determines whether the error is smaller than the threshold value with respect to the updated ink amount set φ. When the error is equal to or less than the threshold value, the current ink amount set φ is employed as a solution and the ink amount set φ is stored in the target pixel (step S 2500 . After the ink amount set φ, is stored in the target pixel, the printing unit M 8  determines whether all pixels have been selected as the target pixel (step S 250   g ). In the event that not all the pixels have been selected, the printing unit M 8  returns to step S 250   a  and performs a process of obtaining a solution of an ink amount set φ with respect to the next target pixel. In addition, since it is highly probable that adjacent pixels have similar target spectral reflectances R t (λ), a solution of an ink amount set φ with respect to a just previous pixel may be initially set with respect to the current target pixel in step S 250   b . In this way, the number of updates of an ink amount set φ can be reduced. When all the pixels have been selected as the target pixel, the color conversion process is ended. In relation to the update of the ink amount set φ in step S 250   e , for example, it may also be possible to update the ink amount set φ by using Newton&#39;s method using the Jacobian matrix having matrix elements obtained by partially differentiating each wavelength component of spectral reflectances R(λ) by means of each component of the ink amount set φ. 
     Meanwhile, when the reproduction mode of the reproduction image PI is a color value mode, the printing unit M 8  performs a color conversion process based on color values in step S 260 . Herein, an ink amount set φ is calculated, with which color values when observing an object of spectral reflectances R(λ) of each pixel under a reference light source are reproducible under a designated light source. First, a target pixel is selected and spectral reflectances R(λ) of the target pixel are obtained (step S 260   a ). Next, color values (target color values TCV) from the object when irradiating light of the reference light source onto the object of the obtained spectral reflectances R(λ) are calculated (step S 260   b ). In detail, the spectral reflectances R(λ) are multiplied by spectral energy of the reference light source, and a color-matching function corresponding to a tristimulus value of a cone is further convoluted to the spectral reflectances R(λ), so that XYZ values are calculated. The XYZ values are converted into L*a*b values of a CIELAB color space, so that the L*a*b values are calculated as the target color values TCV. The target color value TCV represents a color value recognized by an observer when the picture D is exhibited in the art gallery A under the reference light source. After the target color values TCV are calculated, ink amount sets φ, with which the target color values TCV are reproducible under the designated light source, are obtained (step S 260   c ). Herein, the ink amount sets φ corresponding to the target color values TCV are obtained with reference to a 3D-LUT  24   a  in which the correspondence relation between the target color values TCV and the ink amount sets φ is provided for a plurality of lattice points. In addition, this embodiment uses the image data ID in which each pixel has the spectral reflectances R(λ) of the picture D. However, in the case of the color value mode, it may be possible to use image data ID in which each pixel has color values (target color values TCV) of the picture D under the reference light source. 
       FIG. 10  shows the 3D-LUT  24   a . The 3D-LUT  24   a  indicates table data in which the correspondence relation between the target color values TCV and the ink amount sets φ is provided for lattice points substantially uniformly existing in the CIELAB color space serving as an input color space. An interpolation operation is performed with respect to peripheral lattice points based on the correspondence relation between the target color values TCV and the ink amount sets φ, so that ink amount sets φ corresponding to any target color values TCV are calculated. The 3D-LUT  24   a  is stored in the HDD  24 , and is individually prepared for each of a plurality of designated light sources. This is because an ink amount set φ for reproducing the same target color value TCV varies depending on the designated light source. For example, when the designated light source is a light source D 50 , a 3D-LUT  24   a  created by measuring colors of color patches or estimating a reproduction color under the light source D 50  is used. After the ink amount set φ is calculated as described above, the ink amount set φ is stored in the target pixel (step S 260   d ). After the ink amount set φ is stored in the target pixel, the printing unit M 8  determines whether all pixels have been selected as the target pixel (step S 260   e ). In the event that not all the pixels have been selected, the printing unit M 8  returns to step S 260   a  and performs a process of obtaining an ink amount set φ with respect to the next target pixel. When all the pixels have been selected as the target pixel, the color conversion process is ended. In this way, the print image data, in which each pixel has spectral reflectances R(λ), can be converted into ink amount image data in which each pixel has an ink amount set φ. 
     In step S 270 , the printing unit M 8  performs a halftone process with respect to the ink amount image data. For example, ink amount sets φ of 255 grayscale are made into low-level grayscales (grayscales indicating whether dots of a single size or dots of a plurality of sizes can be ejected) by using a dither method or an error diffusion method. In addition, in step S 280 , a rasterization process is performed to allocate the halftone data obtained through the halftone process to each path or each nozzle of a print head provided in the printer  28   a . In this way, print control data available for the printer  28   a  can be created. In step S 290 , the printer  28   a  performs printing based on the print control data. Consequently, the reproduction image PI and the certification patches CC can be printed on the printing paper previously set in the printer  28   a.    
       FIG. 11  schematically shows a printing scheme of the printer  28   a  in this embodiment. The printer  28   a  includes a print head HD provided with a plurality of nozzles Nz for each ink of CMYKlclm, and control is performed based on print data PD to employ ink amounts of each ink of CMYKlclm ejected from the nozzles Nz as amounts designated by the above-described ink amount sets φ (d c , d m , d y , d k , d lc  and d lm ). Ink droplets ejected from each nozzle Nz adhere to the printing paper as fine dots, and a printed image having ink area coverage according to the ink amount sets φ (d c , d m , d y , d k , d lc  and d lm ) resulting from the collection of a plurality of dots is formed on the printing paper. 
     The printing result of the reproduction image PI and the certification patches CC based on the image data ID and the patch data  24   b  for certification is equal to the layout shown in  FIG. 9 . In this embodiment, the reproduction image PI and the certification patches CC are printed on the same printing paper, so that the reproduction image PI and the certification patches CC are associated with each other. However, the reproduction image PI and the certification patches CC are not always printed on the same printing paper. For example, it may be possible to print a common and unique identification number or barcode on the reproduction image PI and the certification patches CC. However, since color reproduction characteristics of the printer  28   a  change as time passes, it is preferable that a printing interval between the reproduction image PI and the certification patches CC is as short as possible. When the reproduction mode of the reproduction image PI is the spectral reflectance mode, spectral reflectances R(λ) identical to those of the picture D are reproduced on the reproduction image PI, and spectral reflectances R(λ) equal to those of coating surfaces of pigments used for drawing the picture D are reproduced on the certification patches CC. Meanwhile, when the reproduction mode of the reproduction image PI is the color value mode, if the reproduction image PI and the certification patches CC are observed under the designated light source of the art gallery B, a color value is obtained which is equal to the color value recognized when observing the picture D and the coating surfaces of the pigments used for drawing the picture D under the reference light source of the art gallery A. If the printing process is ended, the measurement process is subsequently performed by the computer  20  of the print operator. 
     D. Measurement Process 
       FIG. 12  is a flowchart of the measurement process. The measurement data obtaining unit M 9  measures the spectral reflectances R(λ) of each printed certification patch CC by using the spectral reflectometer  28   b  (step S 310 ). When the reproduction mode of the reproduction image PI is the spectral reflectance mode (step S 315 ), measurement data MD including spectral reflectances R(λ) obtained by measuring the certification patches CC is generated (step S 320 ). In step S 330 , the measurement data obtaining unit M 9  appends the target spectral reflectances R t (λ) when performing the color conversion process with respect to pixels corresponding to each certification patch CC to the measurement data MD as target data TD (the target spectral characteristics information). The spectral reflectances R(λ) stored in the patch data  24   b  for certification are used as the target spectral reflectances R t (λ) in this step. Meanwhile, when the reproduction mode of the reproduction image PI is the color value mode, color values when irradiating light of the designated light source with the spectral reflectances R(λ) obtained by measuring the certification patches CC are calculated (step S 335 ), and measurement data MD including the calculated color values is generated (step S 340 ). By the use of calculation equivalent to the calculation of the target color value TCV in step S 260   b , the color values can be calculated. However, spectral energy of the designated light source may be used instead of spectral energy of the reference light source. In addition, in this embodiment, the spectral reflectances R(λ) are measured and the color values under the designated light source are indirectly obtained. However, it may be possible to directly obtain color values through color measurement of a colorimeter after irradiating light of the designated light source onto the reproduction image PI. In step S 350 , the measurement data obtaining unit M 9  appends the target color value TCV when performing the color conversion process with respect to the pixels corresponding to each certification patch CC to the measurement data MD as the target data TD (the target spectral characteristics information). In step S 360 , the measurement data transmission unit M 10  transmits the measurement data MD to the computer  10  of the art gallery A, and ends the measurement process. 
     E. Certification Process 
       FIG. 13  is a flowchart of the certification process performed by the certification unit M 4  of the computer  10  of the art gallery A. In step S 410 , the measurement data reception unit M 3  receives the measurement data MD. In step S 420 , the certification unit M 4  determines the reproduction mode of the reproduction image PI based on the target data TD appended to the measurement data MD. That is, if the measurement data MD includes the target spectral reflectances R t (λ), the certification unit M 4  determines that the reproduction mode of the reproduction image PI is the spectral reflectance mode. If the measurement data MD includes the target color value TCV, the certification unit M 4  determines that the reproduction mode of the reproduction image PI is the color value mode. When the reproduction mode of the reproduction image PI is the spectral reflectance mode, the certification unit M 4  calculates an error (e.g., a Euclidean distance in spaces separated by wavelength sections) between the target spectral reflectances R t (λ) included in the target data TD and measured spectral reflectances R(λ) with respect to each certification patch CC (step S 430 ). Then, the certification unit M 4  decides whether certification is possible based on the errors of each certification patch CC (step S 440 ). Herein, the possibility of the certification may be decided based on the comparison of the target spectral reflectances R t (λ) included in the target data TD and the measured spectral reflectances R(λ), and various certification criteria may be used. For example, it may be possible to calculate an average value of the errors of each certification patch CC and decide that the certification is possible when the average value is less than a predetermined threshold value. Instead of a simple average value, the possibility of the certification may also be decided based on a value obtained by multiplying each certification patch CC by different weights and linearly combining the certification patches CC with one another. A hue (pigments), on which reproducibility is considered, is designated by the art gallery A, and a large weight may be applied to the error of the certification patch CC corresponding to the designated pigment. Furthermore, when the maximum value of the error is less than a predetermined threshold value, it may be decided that the certification is possible. In addition, when a standard deviation of the errors of each certification patch CC is less than the predetermined threshold value, it may also be decided that the certification is possible. 
     Meanwhile, when the reproduction mode of the reproduction image PI is the color value mode, the certification unit M 4  calculates an error (e.g., color difference of a CIE1976) between the target color value TCV included in the target data TD and a measured color value with respect to each certification patch CC (step S 450 ). Then, in step S 440 , the certification unit M 4  decides whether certification is possible based on the errors of each certification patch CC. Herein, basically, when the error is small, it is decided that the certification is possible, and various certification criteria may be used. When it is decided that the certification is impossible, the notification unit M 6  provides a notification, which indicates that the certification is impossible, to the computer  20  of the print operator and the computer  30  of the art gallery B (step S 460 ). After receiving the notification, the computer  20  of the print operator performs calibration of the printer  28   a , and performs the printing process again. Meanwhile, when it is decided that the certification is possible, the request and settlement process is performed. 
     F. Request and Settlement Process 
       FIG. 14  is a flowchart of the request and settlement process. If the certification unit M 4  of the computer  10  of the art gallery A decides that the certification is possible in step S 440 , the notification unit M 6  provides a notification, which indicates that the certification is possible, to the computer  20  of the print operator and the computer  30  of the art gallery B (step S 510 ). In step S 520 , the payment request unit M 5  generates and transmits a payment request for the license fee required when the art gallery B exhibits the reproduction image PI. That is, the art gallery A provides the art gallery B with the opportunity of obtaining the license required when exhibiting the reproduction image PI only when the accuracy of reproducibility of the reproduction image PI is certified. The payment request includes at least permission for the exhibition of the reproduction image PI in the art gallery B and the amount of a consideration (compensation) for the certification. The amount of the consideration depends on the reproduction mode of the reproduction image PI, and a large amount is set in the spectral reflectance mode as compared with the color value mode. Furthermore, the payment request may include particulars such as a permitted exhibition period of the reproduction image PI, a designated light source under which the reproduction image PI is to be exhibited and the like. In addition, in the case of providing an indefinite exhibition period, it may be possible to clearly define a period, in which identification of the reproducibility can be ensured, by taking the difference between discoloration of the picture D and discoloration of the reproduction image PI into consideration. The payment request is transmitted to the computer  30  of the art gallery B. The payment request and the notification indicating that the certification is possible may also be simultaneously transmitted to the computer  30  of the art gallery B. 
     In the computer  20  of the print operator, the reception unit M 11  receives the notification indicating that the certification is possible (step S 530 ). Then, the consideration request unit M 12  generates a consideration request of the reproduction image PI and transmits the consideration request to the computer  30  of the art gallery B (step S 540 ). Furthermore, after receiving the notification indicating that the certification is possible, the computer  20  of the print operator transmits the reproduction image PI to the art gallery B. It may be possible to print a verification mark, which indicates that the certification has been completed, on the rear surface or blank space of the reproduction image PI. In addition, it may also be possible to set the amount of the consideration according to the reproduction mode. The computer  30  of the art gallery B receives the payment request from the computer  10  of the art gallery A and the consideration request from the computer  20  of the print operator (step S 550 ), and the settlement unit M 13  performs a settlement process with respect to the payment request and the consideration request (step S 560 ). For example, the settlement unit M 13  accesses a server (not shown) that manages bank accounts of the print operator and the art gallery A, and remits the money to the bank accounts. In this way, the request and settlement process is ended. 
     In accordance with this embodiment as described above, the art gallery B can exhibit the reproduction image PI of the picture D owned by the art gallery A. The spectral characteristics of the reproduction image PI are guaranteed by the certification of the art gallery A based on the measurement data MD. Thus, the reputation of the picture D can be prevented from being damaged due to the exhibition of a degraded reproduction image PI from the art gallery A&#39;s collection, and a faithful exhibition can be made in the art gallery B&#39;s exhibition. Meanwhile, the print operator prints the reproduction image PI with high accuracy, thereby obtaining the consideration for the printing of the reproduction image PI. When the reproduction mode is the spectral reflectance mode, the spectral reflectances R(λ) of the picture D are reproduced, and even if the reproduction image PI is exhibited under certain light sources, the reproduction image PI has color values equal to those of the picture D under the light sources. Meanwhile, when the reproduction mode is the color value mode, the reproduction image PI exhibited under the designated light source has color values equal to those of the picture D under the reference light source. The spectral reflectance mode is better than the color value mode from the standpoint of the realization of complete reproducibility. However, in the state in which the art gallery B has to exhibit the reproduction image PI under a designated light source different from the reference light source of the art gallery A, it is preferable to select the color value mode after designating the designated light source different from the reference light source. In any case, the certification is performed based on the reproduction accuracy of a certification patch CC corresponding to pigments used for drawing or repairing the picture D, so that the entire reproduction accuracy of the picture D drawn using the pigment can be guaranteed with high reliability. 
     G. Spectral Printing Model 
     A prediction model (the spectral printing model) used by the printing unit M 8  is for estimating spectral reflectances R(λ), which are obtained when printing is performed at any ink amount sets φ (d c , d m , d y , d k , d lc  and d lm ) available for the printer  28   a  of this embodiment, as the prediction spectral reflectances R s (λ), and corresponds to the function PM(φ) of Equation 1 above. In the spectral printing model, a color patch is actually printed by a standard machine (the printer  28   a ) as to a plurality of representative points on an ink amount space, and a spectral reflectance database RDB obtained by measuring spectral reflectances R(λ) thereof by using a spectral reflectometer is prepared. Then, prediction using a cellular Yule-Nielsen Spectral Neugebauer model employing the spectral reflectance database RDB is performed, so that the spectral reflectance R(λ) is accurately predicted when the printing is performed at any ink amount sets φ (d c , d m , d y , d k , d lc  and d lm ). 
       FIG. 15  shows the spectral reflectance database RDB. As shown in  FIG. 15 , the spectral reflectance database RDB is a look-up table including the spectral reflectances R(λ) (the spectral reflectance sets), which is obtained when printing and measurement are actually performed regarding the ink amount sets φ (d c , d m , d y , d k , d lc , and d lm ) of a plurality of lattice points on the ink amount space (six dimensions in this embodiment, but only a CM surface is illustrated for the simplification of the drawing). For example, lattice points of 5 grids dividing each ink amount axis are generated. Herein, 5 13  lattice points are generated, and a vast amount of the color patches are necessarily printed and measured. However, since the printer  28   a  actually has limitations on the number of the inks capable of being mounted at the same time or the amount of inks capable of being ejected at the same time, the number of the lattice points used in the printing and the measurement is reduced. 
     In addition, only a part of the lattice points is used for the printing and the measuring, and the spectral reflectances R(λ) of the other lattice points are predicted based on the spectral reflectances R(λ) of the lattice points which are actually used to perform the printing and the measurement, so that the number of the color patches on which the printing and the measurement are actually performed may be reduced. The spectral reflectance database RDB needs to be prepared for each printing paper with which the printer  28   a  can perform printing. Strictly speaking, this is because the spectral reflectances R(λ) are determined by the spectral transmittance and the reflectance of the printing paper which are caused by an ink film (dot) formed on the printing paper, and are strongly influenced by the surface property (the dot shape depends thereon) or the reflectance of the printing paper. Next, the prediction by the cellular Yule-Nielsen Spectral Neugebauer Model in which the spectral reflectance database RDB is used will be described. 
     The printing unit M 8  performs the prediction by the cellular Yule-Nielsen Spectral Neugebauer Model in which the spectral reflectance database RDB is used. In this prediction, the printing paper (the glossy paper in this embodiment) and the ink amount set φ are set as print conditions. When the prediction is performed on the glossy paper as the printing paper, the spectral reflectance database RDB created by printing the color patch on the glossy paper is set. 
     If the setting of the spectral reflectance database RDB is possible, the ink amount set φ (d c , d m , d y , d k , d lc , and d lm ) output from the ink amount set φ calculating module or the correction amount calculating module is applied to the spectral printing model. The cellular Yule-Nielsen Spectral Neugebauer Model is based on the spectral Neugebauer model and the Yule-Nielsen model, which are well known. Furthermore, in the following description, a model in which 3 kinds of inks of CMY are used will be described for simple description. The same model is easily extended to a model using any ink amount set including the CMYKlclm according to this embodiment. In addition, the cellular Yule-Nielsen Spectral Neugebauer Model is discussed, for example, in the following articles: “A Critical Review of Spectral Models Applied to Binary Color Printing”, by David R. Wyble et al., COLOR research and application, Volume 25, Number 1, pages 4-19 (February 2000), and “Optimization of the spectral Neugebauer model for printer characterization”, by Raja Balasubramanian, Journal of Electronic Imaging 8(2), pages 156-166 (April 1999). 
       FIGS. 16A and 16B  are diagrams showing the spectral Neugebauer model. In the spectral Neugebauer model, the prediction spectral reflectances R s (λ) of a printed matter when the printing is performed at any ink amount set φ (d c , d m , d y ) is given by Equation 1 below. 
     
       
         
           
             
               
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     1 
                   
                    
                   
                     
 
                   
                    
                   
                     
                       
                         R 
                         s 
                       
                        
                       
                         ( 
                         λ 
                         ) 
                       
                     
                     = 
                     
                       
                         
                           a 
                           w 
                         
                          
                         
                           
                             R 
                             w 
                           
                            
                           
                             ( 
                             λ 
                             ) 
                           
                         
                       
                       + 
                       
                         
                           a 
                           c 
                         
                          
                         
                           
                             R 
                             c 
                           
                            
                           
                             ( 
                             λ 
                             ) 
                           
                         
                       
                       + 
                       
                         
                           a 
                           m 
                         
                          
                         
                           
                             R 
                             m 
                           
                            
                           
                             ( 
                             λ 
                             ) 
                           
                         
                       
                       + 
                       
                         
                           a 
                           y 
                         
                          
                         
                           
                             R 
                             y 
                           
                            
                           
                             ( 
                             λ 
                             ) 
                           
                         
                       
                       + 
                       
                         
                           a 
                           r 
                         
                          
                         
                           
                             R 
                             r 
                           
                            
                           
                             ( 
                             λ 
                             ) 
                           
                         
                       
                       + 
                       
                         
                           a 
                           g 
                         
                          
                         
                           
                             R 
                             g 
                           
                            
                           
                             ( 
                             λ 
                             ) 
                           
                         
                       
                       + 
                       
                         
                           a 
                           b 
                         
                          
                         
                           
                             R 
                             b 
                           
                            
                           
                             ( 
                             λ 
                             ) 
                           
                         
                       
                       + 
                       
                         
                           a 
                           k 
                         
                          
                         
                           
                             R 
                             k 
                           
                            
                           
                             ( 
                             λ 
                             ) 
                           
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       a 
                       w 
                     
                     = 
                     
                       
                         ( 
                         
                           1 
                           - 
                           
                             f 
                             c 
                           
                         
                         ) 
                       
                        
                       
                         ( 
                         
                           1 
                           - 
                           
                             f 
                             m 
                           
                         
                         ) 
                       
                        
                       
                         ( 
                         
                           1 
                           - 
                           
                             f 
                             y 
                           
                         
                         ) 
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       a 
                       c 
                     
                     = 
                     
                       
                         
                           f 
                           c 
                         
                          
                         
                           ( 
                           
                             1 
                             - 
                             
                               f 
                               m 
                             
                           
                           ) 
                         
                       
                        
                       
                         ( 
                         
                           1 
                           - 
                           
                             f 
                             y 
                           
                         
                         ) 
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       a 
                       m 
                     
                     = 
                     
                       
                         ( 
                         
                           1 
                           - 
                           
                             f 
                             c 
                           
                         
                         ) 
                       
                        
                       
                         
                           f 
                           m 
                         
                          
                         
                           ( 
                           
                             1 
                             - 
                             
                               f 
                               y 
                             
                           
                           ) 
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       a 
                       y 
                     
                     = 
                     
                       
                         ( 
                         
                           1 
                           - 
                           
                             f 
                             c 
                           
                         
                         ) 
                       
                        
                       
                         ( 
                         
                           1 
                           - 
                           
                             f 
                             m 
                           
                         
                         ) 
                       
                        
                       
                         f 
                         y 
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       a 
                       r 
                     
                     = 
                     
                       
                         ( 
                         
                           1 
                           - 
                           
                             f 
                             c 
                           
                         
                         ) 
                       
                        
                       
                         f 
                         m 
                       
                        
                       
                         f 
                         y 
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       a 
                       g 
                     
                     = 
                     
                       
                         
                           f 
                           c 
                         
                          
                         
                           ( 
                           
                             1 
                             - 
                             
                               f 
                               m 
                             
                           
                           ) 
                         
                       
                        
                       
                         f 
                         y 
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       a 
                       b 
                     
                     = 
                     
                       
                         f 
                         c 
                       
                        
                       
                         
                           f 
                           m 
                         
                          
                         
                           ( 
                           
                             1 
                             - 
                             
                               f 
                               y 
                             
                           
                           ) 
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       a 
                       k 
                     
                     = 
                     
                       
                         f 
                         c 
                       
                        
                       
                         f 
                         m 
                       
                        
                       
                         f 
                         y 
                       
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
     In Equation 1, a i  is an area ratio of the i th  region, and R i (λ) is the spectral reflectance of the i th  region. The suffix ‘i’ means a region (w) of no ink, a region (c) of the cyan ink only, a region (m) of the magenta ink only, a region (y) of the yellow ink only, a region (r) on which the magenta ink and the yellow ink are ejected, a region (g) on which the yellow ink and the cyan ink are ejected, a region (b) on which the cyan ink and the magenta ink are ejected, and a region (k) on which 3 colors of the CMY inks are ejected. In addition, f c , f m  and f y  are the proportions of the areas (called as “ink area coverage”), each of which is covered with the ink when only one kind of the CMY inks is ejected. 
     The ink area coverage f c , f m  and f y  are given by the Murray-Davies model shown in  FIG. 16B . In the Murray-Davies model, for example, the ink area coverage f c  of the cyan ink is a nonlinear function of the ink amount d c  of the cyan ink. For example, the ink amount d c  can be converted into the ink area coverage f c  by a one-dimensional lookup table. The reason that ink area coverage f c , f m  and f y  are a nonlinear function of the ink amounts d c , d m  and d y  is that when a small amount of ink is ejected onto a unit area, the ink spreads sufficiently, whereas when a large amount of ink is ejected, the inks overlap with each other so that there is not much increase in the covered area. The other kinds of the MY inks are also the same. 
     When the Yule-Nielsen model is applied in relation to the spectral reflectance, Equation 1 above is rewritten as Equation 2a or Equation 2b below. 
     
       
         
           
             
               
                 
                   
                     Equation 
                      
                     
                         
                     
                      
                     2 
                   
                    
                   
                       
                   
                    
                   
                     
 
                   
                    
                   
                     
                       
                         
                           
                             
                               
                                 R 
                                 s 
                               
                                
                               
                                 ( 
                                 λ 
                                 ) 
                               
                             
                             
                               1 
                               / 
                               n 
                             
                           
                           = 
                           
                             
                               
                                 a 
                                 w 
                               
                                
                               
                                 
                                   
                                     R 
                                     w 
                                   
                                    
                                   
                                     ( 
                                     λ 
                                     ) 
                                   
                                 
                                 
                                   1 
                                   / 
                                   n 
                                 
                               
                             
                             + 
                             
                               
                                 a 
                                 c 
                               
                                
                               
                                 
                                   
                                     R 
                                     c 
                                   
                                    
                                   
                                     ( 
                                     λ 
                                     ) 
                                   
                                 
                                 
                                   1 
                                   / 
                                   n 
                                 
                               
                             
                             + 
                             
                               
                                 a 
                                 m 
                               
                                
                               
                                 
                                   
                                     R 
                                     m 
                                   
                                    
                                   
                                     ( 
                                     λ 
                                     ) 
                                   
                                 
                                 
                                   1 
                                   / 
                                   n 
                                 
                               
                                
                               
                                 a 
                                 y 
                               
                                
                               
                                 
                                   
                                     R 
                                     y 
                                   
                                    
                                   
                                     ( 
                                     λ 
                                     ) 
                                   
                                 
                                 
                                   1 
                                   / 
                                   n 
                                 
                               
                             
                             + 
                           
                         
                       
                     
                     
                       
                         
                           
                             
                               a 
                               r 
                             
                              
                             
                               
                                 
                                   R 
                                   r 
                                 
                                  
                                 
                                   ( 
                                   λ 
                                   ) 
                                 
                               
                               
                                 1 
                                 / 
                                 n 
                               
                             
                           
                           + 
                           
                             
                               a 
                               g 
                             
                              
                             
                               
                                 
                                   R 
                                   g 
                                 
                                  
                                 
                                   ( 
                                   λ 
                                   ) 
                                 
                               
                               
                                 1 
                                 / 
                                 n 
                               
                             
                           
                           + 
                           
                             
                               a 
                               b 
                             
                              
                             
                               
                                 
                                   R 
                                   b 
                                 
                                  
                                 
                                   ( 
                                   λ 
                                   ) 
                                 
                               
                               
                                 1 
                                 / 
                                 n 
                               
                             
                           
                           + 
                           
                             
                               a 
                               k 
                             
                              
                             
                               
                                 
                                   R 
                                   k 
                                 
                                  
                                 
                                   ( 
                                   λ 
                                   ) 
                                 
                               
                               
                                 1 
                                 / 
                                 n 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     2 
                      
                     a 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     
                       R 
                       s 
                     
                      
                     
                       ( 
                       λ 
                       ) 
                     
                   
                   = 
                   
                     
                       { 
                       
                         
                           
                             
                               
                                 
                                   a 
                                   w 
                                 
                                  
                                 
                                   
                                     
                                       R 
                                       w 
                                     
                                      
                                     
                                       ( 
                                       λ 
                                       ) 
                                     
                                   
                                   
                                     1 
                                     / 
                                     n 
                                   
                                 
                               
                               + 
                               
                                 
                                   a 
                                   c 
                                 
                                  
                                 
                                   
                                     
                                       R 
                                       c 
                                     
                                      
                                     
                                       ( 
                                       λ 
                                       ) 
                                     
                                   
                                   
                                     1 
                                     / 
                                     n 
                                   
                                 
                               
                               + 
                               
                                 
                                   a 
                                   m 
                                 
                                  
                                 
                                   
                                     
                                       R 
                                       m 
                                     
                                      
                                     
                                       ( 
                                       λ 
                                       ) 
                                     
                                   
                                   
                                     1 
                                     / 
                                     n 
                                   
                                 
                               
                               + 
                               
                                 
                                   a 
                                   y 
                                 
                                  
                                 
                                   
                                     
                                       R 
                                       y 
                                     
                                      
                                     
                                       ( 
                                       λ 
                                       ) 
                                     
                                   
                                   
                                     1 
                                     / 
                                     n 
                                   
                                 
                               
                               + 
                             
                           
                         
                         
                           
                             
                               
                                 
                                   a 
                                   r 
                                 
                                  
                                 
                                   
                                     
                                       R 
                                       r 
                                     
                                      
                                     
                                       ( 
                                       λ 
                                       ) 
                                     
                                   
                                   
                                     1 
                                     / 
                                     n 
                                   
                                 
                               
                               + 
                               
                                 
                                   a 
                                   g 
                                 
                                  
                                 
                                   
                                     
                                       R 
                                       g 
                                     
                                      
                                     
                                       ( 
                                       λ 
                                       ) 
                                     
                                   
                                   
                                     1 
                                     / 
                                     n 
                                   
                                 
                               
                               + 
                               
                                 
                                   a 
                                   b 
                                 
                                  
                                 
                                   
                                     
                                       R 
                                       b 
                                     
                                      
                                     
                                       ( 
                                       λ 
                                       ) 
                                     
                                   
                                   
                                     1 
                                     / 
                                     n 
                                   
                                 
                               
                               + 
                               
                                 
                                   a 
                                   k 
                                 
                                  
                                 
                                   
                                     
                                       R 
                                       k 
                                     
                                      
                                     
                                       ( 
                                       λ 
                                       ) 
                                     
                                   
                                   
                                     1 
                                     / 
                                     n 
                                   
                                 
                               
                             
                           
                         
                       
                       } 
                     
                     n 
                   
                 
               
               
                 
                   ( 
                   
                     2 
                      
                     b 
                   
                   ) 
                 
               
             
           
         
       
     
     In Equation 2a and Equation 2b, n is a predetermined coefficient equal to or more than 1, and for example, n can be set to 10. Equation 2a and Equation 2b are equations representing the Yule-Nielsen Spectral Neugebauer Model. 
     The cellular Yule-Nielsen Spectral Neugebauer Model employed in this embodiment is obtained by dividing the ink color space of the Yule-Nielsen Spectral Neugebauer Model described above into plural cells. 
       FIG. 17A  shows an example of cell division in the cellular Yule-Nielsen Spectral Neugebauer Model. Herein, for simple description, the cell division is illustrated in a two-dimensional ink amount space including two axes of the ink amount d c  and d m  of the CM inks. Furthermore, since the ink area coverage f c  and f m  uniquely relate to the ink amount d c  and d m  in the Murray-Davies model described above, the ink area coverage f c  and f m  may be considered as the axes representing the ink area coverage f c  and f m . The white circles are the grid points (termed “lattice points”) in the cell division. The two-dimensional ink amount (coverage) space is divided into nine cells C 1  to C 9 . The ink amount set φ (d c , d m ) corresponding to each lattice point is the ink amount set φ corresponding to the lattice point defined in the spectral reflectance database RDB. That is, by referring to the spectral reflectance database RDB described above, the spectral reflectances R(λ) of each lattice point can be obtained. Therefore, the spectral reflectance R(λ)  00 , R(λ)  10 , R(λ)  20  . . . R(λ)  33  of each lattice point can be obtained from the spectral reflectance database RDB. 
     In practice, the cell division in this embodiment is also performed in the six-dimensional ink amount space of the CMYKlclm inks, and the coordinates of each lattice point also are expressed by the six-dimensional ink amount set φ (d c , d m , d y , d k , d lc  and d lm ). Then, the spectral reflectance R(λ) of each lattice point corresponding to the ink amount set (d c , d m , d y , d k , d lc  and d lm ) of each lattice point is obtained from the spectral reflectance database RDB (for example, the spectral reflectance database of the glossy paper). 
       FIG. 17B  shows the relationship between the ink area coverage f c  and the ink amount d c  which are used in the cell division model. Herein, the ink amount range 0 to d cmax  of one kind of ink is also divided into three sections, and the virtual ink area coverage f c  used in the cell division model is obtained by the nonlinear curve which increases monotonically from 0 to 1 in every section. The ink area coverage f m , and f y  are also obtained with respect to other inks in the same manner. 
       FIG. 17C  shows a calculation method of the prediction spectral reflectances R s (λ) when the printing is performed at any ink amount set φ (d c , d m ) in a cell C 5  located at the center position shown in  FIG. 17A . When the printing is performed at the ink amount set φ (d c , d m ), the spectral reflectances R(λ) are given by Equation 3 below. 
     
       
         
           
             
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   3 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       
                         
                           
                             
                               R 
                               s 
                             
                              
                             
                               ( 
                               λ 
                               ) 
                             
                           
                           = 
                           
                             
                               ( 
                               
                                 ∑ 
                                 
                                   
                                     a 
                                     i 
                                   
                                    
                                   
                                     
                                       
                                         R 
                                         i 
                                       
                                        
                                       
                                         ( 
                                         λ 
                                         ) 
                                       
                                     
                                     
                                       1 
                                       / 
                                       n 
                                     
                                   
                                 
                               
                               ) 
                             
                             n 
                           
                         
                       
                     
                     
                       
                         
                           = 
                           
                             
                               ( 
                               
                                 
                                   
                                     a 
                                     11 
                                   
                                    
                                   
                                     
                                       
                                         R 
                                         11 
                                       
                                        
                                       
                                         ( 
                                         λ 
                                         ) 
                                       
                                     
                                     
                                       1 
                                       / 
                                       n 
                                     
                                   
                                 
                                 + 
                                 
                                   
                                     a 
                                     12 
                                   
                                    
                                   
                                     
                                       
                                         R 
                                         12 
                                       
                                        
                                       
                                         ( 
                                         λ 
                                         ) 
                                       
                                     
                                     
                                       1 
                                       / 
                                       n 
                                     
                                   
                                 
                                 + 
                                 
                                   
                                     a 
                                     21 
                                   
                                    
                                   
                                     
                                       
                                         R 
                                         21 
                                       
                                        
                                       
                                         ( 
                                         λ 
                                         ) 
                                       
                                     
                                     
                                       1 
                                       / 
                                       n 
                                     
                                   
                                 
                                 + 
                                 
                                   
                                     a 
                                     22 
                                   
                                    
                                   
                                     
                                       
                                         R 
                                         22 
                                       
                                        
                                       
                                         ( 
                                         λ 
                                         ) 
                                       
                                     
                                     
                                       1 
                                       / 
                                       n 
                                     
                                   
                                 
                               
                               ) 
                             
                             n 
                           
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       
                         
                           
                             a 
                             11 
                           
                           = 
                           
                             
                               ( 
                               
                                 1 
                                 - 
                                 
                                   f 
                                   c 
                                 
                               
                               ) 
                             
                              
                             
                               ( 
                               
                                 1 
                                 - 
                                 
                                   f 
                                   m 
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             a 
                             12 
                           
                           = 
                           
                             
                               ( 
                               
                                 1 
                                 - 
                                 
                                   f 
                                   c 
                                 
                               
                               ) 
                             
                              
                             
                               f 
                               m 
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             a 
                             21 
                           
                           = 
                           
                             
                               f 
                               c 
                             
                              
                             
                               ( 
                               
                                 1 
                                 - 
                                 
                                   f 
                                   m 
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             a 
                             22 
                           
                           = 
                           
                             
                               f 
                               c 
                             
                              
                             
                               f 
                               m 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
     In Equation 3, the ink area coverage f c  and f m  are values given by the graph shown in  FIG. 17B . In addition, the spectral reflectances R(λ)  11 , (λ)  12 , (λ)  21 , and (λ)  22  corresponding to four lattice points surrounding the cell C 5  can be obtained by referring to the spectral reflectance database RDB. Therefore, all the values constituting the right side of Equation 3 can be confirmed, and as the calculation result, when the printing is performed at any ink amount set φ (d c , d m ), the prediction spectral reflectances R s (λ) can be calculated. The wavelength λ is sequentially shifted in the visible wavelength band, so that the prediction spectral reflectances R s (λ) can be obtained in the visible wavelength band. When the ink amount space is divided into plural cells, the prediction spectral reflectances R s (λ) can be calculated with high accuracy as compared with the case of no division. As described above, the printing unit M 8  can predict the prediction spectral reflectances R s (λ) according to the ink amount set φ sequentially updated. 
     H. Modified Example 
     H1. First Modified Example 
       FIG. 18  is a schematic diagram of a spectral reflectance-ink amount table used for a color conversion process in accordance with the first modified example. The spectral reflectance-ink amount table  24   c  is stored in the HDD  23 . The spectral reflectance-ink amount table  24   c  has an input space of a wavelength section number dimension, which employs spectral reflectances R(λ) of each wavelength section as an axis, and an output space is a space of an ink amount set φ. In the example of  FIG. 18 , spectral reflectances R(λ) of other wavelength sections are constant (e.g., 50%), and the section of the input space, in which only spectral reflectance R 400 (λ) of a wavelength section  400 ±20 nm and only spectral reflectance R 440 (λ) of a wavelength section  440 ±20 nm are changed, is shown. In the section, lattice points (indicated by circles) are provided on each intersection point of the orthogonal lattice, and an ink amount set φ for reproducing spectral reflectance R(λ) of each lattice point is set to correspond to the section. 
       FIG. 19  is a flowchart showing a creating sequence of the spectral reflectance-ink amount table  24   c . When creating the spectral reflectance-ink amount table  24   c , the above-described spectral printing model is used. Basically, it is equal to the process for calculating the ink amount set φ for reproducing the spectral reflectances R(λ) of each pixel in the above-described color conversion process. First, lattice points are generated on the orthogonal lattice points of the input space of the above-described spectral reflectances R(λ) (step S 600 ). Herein, the lattice points having the number, which is obtained by squaring the number of lattice points by the wavelength sections, are generated. After the lattice points are generated, any one of the lattice points is selected as a target lattice point, and spectral reflectances R(λ) of the target lattice point are obtained as target spectral reflectances R t (λ) (step S 610 ). Next, an appropriate ink amount set φ is initially set in the spectral printing model (step S 620 ), and spectral reflectances R(λ) calculated by the initial setting are obtained as prediction spectral reflectances R s (λ) (step S 630 ). It is determined whether an error between the target spectral reflectances R t (λ) and the prediction spectral reflectances R s (λ) is smaller than a predetermined threshold value (step S 640 ). 
     In addition, the threshold value is small to the extent that the target spectral reflectances R t (λ) may be regarded to be equal to the prediction spectral reflectances R s (λ). When the error is larger than the threshold value, the ink amount set φ is updated (step S 650 ), and step S 630  is performed. That is, it is determined whether the error is smaller than the threshold value with respect to the updated ink amount set φ. When the error is equal to or less than the threshold value, the current ink amount set φ is employed as a solution and this ink amount set φ is registered in the spectral reflectance-ink amount table  24   c  as an ink amount set φ corresponding to a target lattice point (step S 660 ). If the ink amount set φ is registered with respect to the target lattice point, it is determined whether all lattice points have been selected as the target lattice point (step S 670 ). When not all the lattice points have been selected, step S 610  is performed and a process is performed to obtain a solution of an ink amount set φ with respect to the next target lattice point. Also, in step S 620 , a solution of an ink amount set φ with respect to a just previous lattice point may be initially set with respect to the current target lattice point. Furthermore, the update of an ink amount set φ may also be performed using the Jacobian matrix. The registration of ink amount sets φ corresponding to all lattice points is completed, resulting in the completion of the spectral reflectance-ink amount table  24   c . In addition, as to all lattice points of the input space of the spectral reflectances R(λ), there exist no ink amount sets φ with which the spectral reflectances R(λ) of the lattice points are reproducible. Thus, when the error is not smaller than the threshold value even if the update of the ink amount set φ is repeated by the predetermined number of times, the lattice point is removed from the spectral reflectance-ink amount table  24   c . Therefore, a region where there exist the lattice points registered in the spectral reflectance-ink amount table  24   c  indicates the range of the spectral reflectances R(λ) which are reproducible by the printer  28   a.    
     An interpolation operation is performed with reference to the spectral reflectance-ink amount table  24   c  created as described above, so that the printing unit M 8  can obtain ink amount sets φ corresponding to the spectral reflectances R(λ) of each pixel. In addition, as to certain pixels, when spectral reflectances R(λ) out of the range of the spectral reflectances R(λ) which are reproducible by the printer  28   a  are input, the printing may be stopped because it may be determined that the inputted image data ID is not reproducible. Furthermore, as to the pixels, color conversion equal to that in the color value mode may also be performed. 
     H2. Second Modified Example 
       FIG. 20  shows a software configuration and main data which are controlled by the computers  10 ,  20  and  30 . In the computer  10  of the art gallery A, the measurement data reception unit M 3 , the certification unit M 4 , the payment request unit M 5 , and the notification unit M 6  are controlled. In the computer  20  of the print operator, the image data input unit M 1 , the calibration unit M 2 , the image data obtaining unit M 7 , the printing unit M 8 , the measurement data obtaining unit M 9 , the measurement data transmission unit M 10 , the reception unit M 11 , and the consideration request unit M 12  are controlled. In this modified example, the image data input unit M 1  and the calibration unit M 2  are executed in the computer  20  of the print operator instead of the computer  10  of the art gallery A, differently from the previous embodiment. Therefore, the image input process is performed in the computer  20  of the print operator. As described above, the print operator may be requested to perform the procedure from the generation of the image data ID to the printing of the reproduction image PI, and only the certification process may be performed by the computer  10  of the art gallery A. In the previous embodiment, the reproduction image PI destined to be exhibited is printed. However, even in the case of manufacturing goods (e.g., an underlay, a mouse pad and the like) having the reproduction image PI of the picture D owned by the art gallery A as a pattern, the certification process can be performed with respect to the reproduction image PI printed as a pattern. 
     I. Features of Embodiments 
     In a certification system in accordance with the illustrated embodiments, a print operator terminal, a certifier terminal, and a consumer terminal are communicably connected to one another. In the certification system, first, an image data obtaining unit provided in the print operator terminal obtains image data including pixels for which spectral characteristics of a target object to be reproduced have been designated. A printing unit provided in the print operator terminal prints a reproduction image based on the image data and a plurality of certification patches, for which the spectral characteristics have been designated, while associating them with each other. A measurement data obtaining unit provided in the print operator terminal obtains measurement data by measuring the spectral characteristics of the certification patches. Next, a measurement data transmission unit provided in the print operator terminal transmits the measurement data to the certifier terminal. 
     Then, a measurement data reception unit provided in the certifier terminal receives the measurement data. Next, a certification unit provided in the certifier terminal determines whether the certification of the reproduction image associated with the certification patches is possible on the basis of a comparison of the spectral characteristics of the measurement data and the spectral characteristics designated for the certification patches. When it is determined that the certification of the reproduction image is possible, a notification unit provided in the certifier terminal transmits a notification, which indicates that the certification of the reproduction image is possible, to the print operator terminal. In addition, a payment request unit provided in the certifier terminal transmits a payment request to the consumer terminal. Then, a reception unit provided in the print operator terminal receives the notification, which indicates that the certification of the reproduction image is possible, on the basis of the measurement data. Next, a consideration request unit provided in the print operator terminal transmits a consideration request for the printing of the reproduction image to the consumer terminal. Meanwhile, a settlement unit provided in the consumer terminal receives the payment request and the consideration request, and performs settlement with respect to the payment request and the consideration request. 
     With such a configuration, the certification of the reproduction image may be performed on the basis of the comparison of the spectral characteristics of the measurement data and the spectral characteristics designated for the certification patches, and reproducibility of the reproduction image may be guaranteed. Since the settlement is performed for the certifier terminal having performed the certification in response to the payment request, the certifier terminal may obtain the consideration for the certification (license). Meanwhile, since the settlement also is performed for the print operator terminal having performed the printing in response to the consideration request, the print operator terminal may obtain the consideration for the printing of the certified reproduction image. 
     Reproducibility of spectral reflectance is one example of the spectral characteristics evaluated in the certification. If the reproducibility of spectral reflectance of the target object to be reproduced may be certified in the reproduction image, it may be possible to guarantee that the reproduction image is obtained, such that a color equal to that of the target object to be reproduced is shown, even under certain light sources. A color value is one example of the spectral characteristics evaluated in the certification. If it is possible to certify that a color under a reference light source of the target object to be reproduced is reproduced by the reproduction image under a designated light source, it may be possible to guarantee color reproducibility with respect to the reproduction image under the designated light source. It is preferable that the certification patch has the distinctive spectral characteristics of the reproduction image. When the target object to be reproduced is a picture drawn using pigments, it may be considered that the spectral characteristics of the target object to be reproduced are distinctive due to the pigment. In such a case, the certification patch is given the spectral characteristics of the pigment, resulting in the realization of certification with high reliability. 
     There is an appropriate printing scheme when printing is performed by a printing apparatus that prints the reproduction image and the certification patch by allowing a plurality of inks to adhere to a recording medium. That is, the printing unit specifies the ink amount of the inks, which are adhered to the recording medium by the printing apparatus with respect to each pixel of the image data, by referring to a look-up table which defines the correspondence relation of the spectral characteristics and the ink amount of the inks adhering to the recording medium. Particularly, when the spectral characteristic is the spectral reflectance, the look-up table is a table in which the ink amount is specified for each spectral reflectance defined by a combination of reluctances in a plurality of wavelength sections. Meanwhile, as a scheme for performing printing without using the look-up table, the ink amount of the inks for reproducing the spectral characteristics of each pixel of the image data may be specified based on a spectral characteristic prediction model. In addition, since the reproduction image to be certified is reproduced based on the image data, it is preferable that certification is also performed for the image data. 
     Moreover, the technical scope of the invention can be realized by a detailed apparatus and a method performed by the apparatus. That is, the invention can be carried out as a certification method including processes corresponding to each unit performed by the above-described certification system. Of course, when the above-described certification apparatus reads a program and realizes the above-described units, it goes without saying that the technical scope of the invention can be realized by a program for executing functions corresponding to the units, or various recording media on which the program is recorded. 
     GENERAL INTERPRETATION OF TERMS 
     In understanding the scope of the present invention, the term “comprising” and its derivatives, as used herein, are intended to be open ended terms that specify the presence of the stated features, elements, components, groups, integers, and/or steps, but do not exclude the presence of other unstated features, elements, components, groups, integers and/or steps. The foregoing also applies to words having similar meanings such as the terms, “including”, “having” and their derivatives. Also, the terms “part,” “section,” “portion,” “member” or “element” when used in the singular can have the dual meaning of a single part or a plurality of parts. Finally, terms of degree such as “substantially”, “about” and “approximately” as used herein mean a reasonable amount of deviation of the modified term such that the end result is not significantly changed. For example, these terms can be construed as including a deviation of at least ±5% of the modified term if this deviation would not negate the meaning of the word it modifies. 
     While only selected embodiments have been chosen to illustrate the present invention, it will be apparent to those skilled in the art from this disclosure that various changes and modifications can be made herein without departing from the scope of the invention as defined in the appended claims. Furthermore, the foregoing descriptions of the embodiments according to the present invention are provided for illustration only, and not for the purpose of limiting the invention as defined by the appended claims and their equivalents.