Abstract:
In color matching among media having different white points or different black points, how to address gray balances among media poses a problem. To solve this problem, upon converting a colorimetric value onto a color space that connects profiles, gray-balance correction is made on the human color perception space on the basis of a media white point and gray-balance black point.

Description:
BACKGROUND OF THE INVENTION  
         [0001]    The present invention relates to a color processing method and image processing apparatus and, more particularly, to a color process for implementing color matching in correspondence with different observation conditions and media.  
         FIELD OF THE INVENTION  
         [0002]    [0002]FIG. 1 shows an outline of general color matching among different devices.  
           [0003]    Input data as RGB data is converted into XYZ data on a device-independent color space by an input profile  1 . Since colors that fall outside the color gamut of an output device cannot be expressed by the output device, the input data which has been converted into the XYZ data on the device-independent color space undergoes color space compression so that all colors fall within the color gamut of the output device. After color space compression, the input data is converted from the device-independent color space into CMYK data on a color space which depends on the output device.  
           [0004]    In color matching, a reference white point and environmental light are fixed. For example, in a profile defined by ICC (International Color Consortium), the PCS (Profile Connection Space) used to connect profiles has XYZ values and Lab values relative to D50. For this reason, correct color reproduction of an input document and printout is guaranteed when they are observed under a light source with D50 characteristics. However, correct color reproduction is not guaranteed under a light source with other characteristics.  
           [0005]    Upon observing an identical sample (e.g., an image) under different light sources, XYZ values relative to the sample observed under the different light sources look different from each other. In order to predict XYZ values under different light sources, transform methods such as (1) scaling, (2) Von Kries transform, (3) a prediction formula based on a color perception model, and the like can be used.  
           [0006]    The scaling is a method of implementing W2/W1 scaling so as to convert XYZ values under reference white point W1 into those under reference white point W2. When this method is applied to an Lab uniform color space, Lab values under W1 match those under W2. For example, let (X1, Y1, Z1) be the XYZ values of a sample under W1 (Xw1, Yw1, Zw1), and (X2, Y2, Z2) be the XYZ values of a sample under W2(Xw2, Yw2, Zw2). Then, according to the scaling, we have:  
             X 2=( Xw 2/ Xw 1)· X 1  
             Y 2=( Yw 2/ Yw 1)· Y 1  
             Z 2=( Zw 2/ Zw 1)· Z 1  (1)  
           [0007]    The Von Kries transform is a method of implementing W2′/W1′ scaling on human color perception space PQR so as to convert XYZ values under W1 into those under W2. When this method is applied to an Lab uniform color space, Lab values under W1 do not match those under W2. According to the Von Kries transform, we have:  
                   [         X2           Y2           Z2         ]     =           [     M     -   1       ]          [           P2   /   P1         0       0           0         Q2   /   Q1         0           0       0         R2   /   R1           ]            [   M   ]            [         X1           Y1           Z1         ]              
            where        
     [         P1           Q1           R1         ]     =           [   M   ]          [         Xw1           Yw1           Zw1         ]            [         P2           Q2           R2         ]       =           [   M   ]          [         Xw2           Yw2           Zw2         ]            
     [   M   ]     =         [         0.40024       0.70760         -   0.08081               -   0.22630         1.16532       0.04570           0       0       0.91822         ]          
     [     M     -   1       ]     =     [         1.85995         -   1.12939         0.21990           0.36119       0.63881       0           0       0       1.08906         ]                    
             (   2   )                               
 
           [0008]    The prediction formula based on a color perception model is a method of exploiting human color perception space QMH (or JCH) like CIE CAM97s so as to convert XYZ values under observation condition VC1 (including W1) into those under observation condition VC2 (including W2). Note that Q of QMH represents the brightness; M, the colorfulness; and H, the huequadrature or hueangle. Also, J of JCH represents the lightness; C, the chroma, and H huequadrature or hueangle. When this transform method is applied to an Lab uniform color space, Lab values under W1 do not match those under W2 as in the Von Kries transform. The color perception model can implement:  
           (X1, Y1, Z1)→[CIE CAM97s forward transform] 
           →(Q, M, H) or (J, C, H)  
           →[CIE CAM97s inverse transform] 
           →(x2, Y2, Z2)  (3)  
           [0009]    The above discussions are true when the sample is expressed on an ideal medium, i.e., on a media on which a white point corresponds to perfect reflection, and a black point corresponds to perfect absorption. However, we encounter different situations on media used in practice.  
           [0010]    For example, since a monitor has light source colors, a white point on a medium corresponding to R=G=B=255 can be considered as a relative brightness=100%, but a black point on a medium corresponding to R=G=B=0 does not match Y=100%. Also, since a print has object colors, C=M=Y=K=0% (paper white) has some reflectance Y, and does not match Y=100%. Furthermore, C=M=Y=K=100% considered as the darkest color does not match Y=0%.  
           [0011]    Moreover, since paper white of a print is not perfect reflection, it does not match a white point (e.g., D50) of a light source to be irradiated, and has a certain color. Likewise, device black (C=M=Y=K=100%) does not exist on the gray axis (the same chromaticity as the light source) of the light source to be irradiated.  
           [0012]    In the following description, as shown in FIG. 7, a white point expressed on media by respective devices (a color corresponding to R=G=B=255 in an 8-bit RGB device or to C=M=Y=K=0% in a CMYK device) will be defined as a “media white point”, and a black point expressed on media by respective devices (a color corresponding to R=G=B=0 in an RGB device or to C=M=Y=K=100% in a CMYK device, or a color corresponding to black based on an allowable ink dot formation amount specified depending on devices) will be defined as a “media black point”. That is, the media white and black points indicate white and black points that a device can reproduce on media.  
           [0013]    In this manner, as a “light source white point” and the “media white point”, and a “light source black point” and the “media black point” are different from each other, images on different media compared under an identical light source often give different impressions. For example, when media have different white points like white paper and newspaper (recycled paper), if these media are juxtaposed and compared, a person perceives that their paper white appearances are obviously different. However, if these media are independently compared, a person perceives the white points of both the newspaper and white paper as “white”. Such phenomenon occurs since the human eye accommodates itself to white.  
           [0014]    By simply matching XYZ values under an identical light source, those of print colors may match, but paper white appearances on the backgrounds remain different, and the white background may be tinged with another color in some cases.  
           [0015]    Likewise, as for black points of media, black points that can be expressed on media are different depending on devices. If respective media are independently compared, even when these media have different black points a person perceives these black points as “black”, and the human eye also accommodates itself to black.  
           [0016]    Among devices having different color gamuts, differences in color gamuts can be avoided by the color space compression technique. However, as for a dark part near the black point, shadows may totally look black even when the color space compression technique is used.  
           [0017]    In order to solve these problems, color matching must be done in consideration of the media white and black points in addition to matching XYZ values under an identical light source.  
           [0018]    Conventional white point correction and black point correction on media use a simple method for correcting the XYZ values of a sample on the basis of the black point, and then scaling the corrected values on the basis of the brightness (or reflectance) (WinColor specification). That is, let MW1 (Xmw1, Ymw1, Zmw1) be the media white point, and MK1 (Xmk1, Ymk1, Zmk1) be the media black point. Then, the relationship between a sample (X1, Y1, Z1) and corrected sample (X2, Y2, Z2) on media (white point correction and black point correction on media) is expressed by:  
             X 2=( X 1− Xmk 1)/( Ymw 1− Ymk 1)  
             Y 2=( Y 1− Ymk 1)/( Ymw 1− Ymk 1)  
             Z 2=( Z 1− Zmk 1)/( Ymw 1 −Ymk 1)  (4)  
           [0019]    The ICC profile recommends that XYZ values with respect to a sample on media are expressed on the PCS(D50) relative to the media white point. However, such transform method has not been established yet, and the following simple method is used (ICC specification). That is, let MW2 (Xmw2, Ymw2, Zmw2) be the media white point, and IW3 (Xiw3, Yiw3, Ziw3) be the white point of a light source on the PCS. Then, the relationship between a sample (X2, Y2, Z2) and corrected sample (X3, Y3, Z3) on media (correction from the media white point to the PCS(D50)) is expressed by:  
             X 3=( Xiw 3/ Xmw 2)· X 2  
             Y 3=( Yiw 3/ Ymw 2)· Y 2  
             Z 3=( Ziw 3/ Zmw 2)· Z 2  (5)  
           [0020]    However, equations (4) and (5) do not match human color perception since they are based on the scaling on an XYZ color space. Also, equations (4) have disadvantages that the chromaticity of the white point changes depending on the XYZ values of the black point.  
           [0021]    That is, color matching among media having different white points or different black points confronts the following problems:  
           [0022]    (1) how to address color matching among media having different white points;  
           [0023]    (2) how to address color matching among media having different black points; and  
           [0024]    (3) how to address color matching among media having different white points and gray-balance black points.  
         SUMMARY OF THE INVENTION  
         [0025]    The present invention has been made to solve the aforementioned problems individually or together, and has as its object to satisfactorily match gray balances in color matching among media having different white and black points.  
           [0026]    In order to achieve the above objects, a preferred embodiment of the present invention discloses an image processing method of generating conversion data, which is used in conversion between data on a device-dependent color space and data on a device-independent color space, from a calorimetric value, comprising steps of:  
           [0027]    acquiring media white and black points;  
           [0028]    calculating a gray-balance black points from the media white and black points;  
           [0029]    converting the calorimetric value using the media white point and the gray-balance black point; and  
           [0030]    calculating the conversion data using the converted calorimetric value to perform gray-balance correction,  
           [0031]    wherein the gray-balance black point is calculated by changing lightness of the media white point to lightness of the media black point.  
           [0032]    Also, a preferred embodiment of the present invention discloses an image processing method comprising steps of:  
           [0033]    converting color data dependent on a source-side device to color data in a device-independent color space;  
           [0034]    correcting the converted color data on the basis of a media white point and gray-balance black point on the source side, and a media white point and gray-balance black point on the destination side to perform gray-balance correction; and  
           [0035]    converting the corrected color data to color data dependent on a destination-side device,  
           [0036]    wherein the gray-balance black point on the source side is calculated from the media white point and gray-balance black point on the source side, and  
           [0037]    the gray-balance black point on the destination side is calculated from the media white point and gray-balance black point on the destination side.  
           [0038]    Other features and advantages of the present invention will be apparent from the following description taken in conjunction with the accompanying drawings, in which like reference characters designate the same or similar parts throughout the figures thereof.  
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0039]    [0039]FIG. 1 is a schematic diagram showing general color matching among different devices;  
         [0040]    [0040]FIG. 2A is a view for explaining the result of correction based on media white points;  
         [0041]    [0041]FIG. 2B is a view for explaining the result of correction based on media white and black points;  
         [0042]    FIGS.  3  to  6  show a user interface;  
         [0043]    [0043]FIG. 7 is a view for explaining the media white point, black point, and gray-balance black point; and  
         [0044]    [0044]FIG. 8 is a block diagram showing the arrangement of an image processing apparatus. 
     
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS  
       [0045]    An image process according to an embodiment of the present invention will be described in detail hereinafter with reference to the accompanying drawings.  
         [0046]    An image process to be described below is implemented by programs and data that implement white point correction, black point correction, gray-balance correction, and a user interface to be described later to an image processing apparatus  1  shown in FIG. 8, i.e., a computer device such a personal computer or the like. As such programs, driver software that receives an image from an image input device  2  or the like, image edit software used to edit an image, driver software such as a so-called printer driver or display driver that outputs an image to image output devices  3  and  4 , color matching programs (profile builder or color matching module (CMM)), and the like are assumed.  
         [0047]    The image process to be described later can be executed not only by a computer device but also by an image input device or image output device. Especially, when the image input device  2  such as a digital camera or the like is directly connected to the image output device  3  such as an ink-jet printer or the like, and an image sensed by the digital camera is to be printed, the image process to be described below is preferably executed by the image input device  2  or image output device  3 .  
         [0048]    [0048]FIG. 8 is a block diagram showing the arrangement of the image processing apparatus  1  that executes the image process of this embodiment. A CPU  11  controls other building components and executes an image process to be described later via a system bus  14  using a RAM  13  as a work memory in accordance with programs such as an OS, application programs, various device drivers, and the like, and data stored in a ROM  12  and hard disk (HD)  15 . The HD  15  stores the aforementioned driver software, image edit software, driver software such as a printer driver, display driver, and the like, color matching programs (profile builder and color matching module (CMM)), and the like.  
         [0049]    Various user interfaces to be described later are displayed on a monitor  4  by the CPU  11 . The user inputs various instructions and data to the image processing apparatus  1  by operating a keyboard and mouse  20  in accordance with the user interface displayed on the monitor  4 . The input various instructions and data are sent to the CPU  11  via the system bus  14 .  
         [0050]    Interfaces (I/Fs)  16  and  17  interposed between an image input device  2  and printer  3 , and the system bus  14  can adopt serial buses such as USB, IEEE1394, and the like, parallel interfaces such as IEEE1284, SCSI, GPIB, and the like, or serial interfaces such as RS232C, RS422, and the like. Also, an I/F  18  interposed between the monitor  4  and system bus  14  can adopt an analog video interface such as VGA or the like, or a digital video interface such as DVI or the like. An I/F  18  interposed between the keyboard and mouse  20 , and the system bus  14  can adopt a versatile keyboard interface and USB.  
         [0051]    [Outline] 
         [0052]    The image process of this embodiment implements white point correction and black point correction to make color matching among different media close to human color perception by making color transform so that grayscales (color sequences that couple white and black points) on different media match on the human color perception space in consideration of media white and black points.  
         [0053]    It is natural to translate a problem about media white point correction to that of human color perception accommodation to a media white point rather than to a light source white point.  
         [0054]    Also, a problem about a media black point can be translated to that of human eye accommodation not only to a white point but also to a black point.  
         [0055]    Likewise, the image process of this embodiment allows gray-balance correction to make color matching among different media close to human color perception by making color transform so that gray balances (gray chromaticity levels at respective lightness levels match the “chromaticity of a white point”) on the human color perception space match in consideration of media white and gray-balance black points.  
         [0056]    Characteristic features of the image process of this embodiment are as follows:  
         [0057]    Assume that the media gray-balance black point is a point which has the same lightness (brightness) as that of the media black point, and has the same color appearance (chromaticity) as that of the media white point, as shown in FIG. 7.  
         [0058]    (1) Using a chromatic adaptation model of the Von Kries transform or the like or that of CIE CAM97s or the like in white point correction among media, color matching closer to human color perception can be implemented among media having different white points.  
         [0059]    (2) Since not only white point correction but also black point correction are made on the human color perception space, the color reproduction of a dark part can be improved.  
         [0060]    (3) The gray color reproduction can be improved in consideration of a gray balance.  
         [0061]    [Image Process With Intervention of PCS] 
         [0062]    [0062]FIG. 2A shows the result of correction based on media white points, and FIG. 2B is a view for explaining the result of correction based on media white and black points. The left side in FIGS. 2A and 2B indicates the source side, and the right side indicates the destination side.  
         [0063]    In order to implement color matching that considers media white and black points on an ICC profile, measured values (X, Y, Z) obtained by a measurement unit undergo white point correction and black point correction, and the ICC profile is generated using corrected measured values (X′, Y′, Z′).  
         [0064]    In a method of converting a media white point to the PCS (D50), a chromatic adaptation model is applied under the assumption that the human eye accommodates itself to a media white point. Let MW2 (Xmw2, Ymw2, Zmw2) be the media white point, and IW3(Xiw3, Yiw3, Ziw3) be a D50 white point of a light source on the PCS. Then, if the Von Kries transform is used as a chromatic adaptation model, the relationship between a sample (X2, Y2, Z2) on a medium and sample (X3, Y3, Z3) on the PCS is expressed by:  
                 [         X3           Y3           Z3         ]     =           [     M     -   1       ]          [             P3   /   P2                      0       0           0         Q3   /   Q2         0           0       0         R3   /   R2           ]            [   M   ]            [         X2           Y2           Z2         ]              
            where        
     [         P2           Q2           R2         ]     =           [   M   ]          [         Xmw2           Ymw2           Zmw2         ]            [         P3           Q3           R3         ]       =       [   M   ]          [         Xiw3           Yiw3           Ziw3         ]                   (   6   )                               
 
         [0065]    Color space PQR converted by the 3×3 matrix [M] corresponds to a human cone response to a white point.  
         [0066]    When white point correction alone is made, as shown in FIG. 2A, since media white point MW2 is converted into D50, the lightness of black point IK3 on the PCS(Lab) becomes higher as a result of correction. This result does not pose any problem if the white point brightness (or reflectance) of the source-side medium is nearly equal to that of the destination-side medium. However, if their difference is large, the above result may cause black to unnaturally stand out.  
         [0067]    On the other hand, when white point correction and black point correction are made, as shown in FIG. 2B, since white points IW3 and black points IK3 on the source and destination sides match, a visible dynamic range can be assured, and black can be prevented from unnaturally standing out.  
         [0068]    Let (Pw, Qw, Rw) be a cone response to a white point under light source IA, and (P, Q, R) be a cone response to arbitrary color N under light source IA. In the Von Kries transform, a cone response (Pw′, Qw′, Rw′) to a white point under light source IB and a cone response (P′, Q′, R′) to arbitrary color N under light source IB have a relationship expressed by:  
         
       P/Pw=P′/Pw′ 
     
         
       Q/Qw=Q′/Qw′ 
     
           R/Rw=R′/Rw′   (7)  
         [0069]    In consideration of a cone response (Pk, Qk, Rk) to a black point under light source IA and a cone response (Pk′, Qk′, Rk′) to a black point under light source IB, the above relationship is rewritten as:  
         ( P−Pk )/( Pw−Pk )=( P′−Pk′ )/( Pw′−Pk′ )  
         ( Q−Qk )/( Qw−Qk )=( Q′−Qk′ )/( Qw′−Qk′ )  
         ( R−Rk )/( Rw−Rk )=( R′−Rk′ )/( Rw′−Rk′ )  (8)  
         [0070]    When this relationship is applied to the method of converting media white and black points to the PCS(D50), a chromatic adaptation model in which the human eye accommodates itself to the media white and black points can be derived. That is, let MW1 (Xmw1, Ymw1, Zmw1) be the media white point, MK1 (Xmk1, Ymk1, Zmk1) be the media black point, IW2 (Xiw2, Yiw2, Ziw2) be a D50 white point of a light source on the PCS, and IK2(Xik2, Yik2, Zik2) be a black point (0, 0, 0) of the light source on the PCS. Then, the relationship between a sample (X1, Y1, Z1) on a medium and a sample (X2, Y2, Z2) on the PCS is expressed, using, e.g., the Von Kries transform as a chromatic adaptation model, by:  
                 [         X2           Y2           Z2         ]     =       [     M     -   1       ]          [               (     P2w   -   P2k     )            (     P   -   P1k     )     /     (     P1w   -   P1k     )         +   P2k                   (     Q2w   -   Q2k     )            (     Q   -   Q1k     )     /     (     Q1w   -   Q1k     )         +   Q2k                   (     R2w   -   R2k     )            (     R   -   R1k     )     /     (     R1w   -   R1k     )         +   R2k           ]              
            where        
     [         P           Q           R         ]     =           [   M   ]          [         X1           Y1           Z1         ]            
     [         P1w           Q1w           R1w         ]     =           [   M   ]          [         Xmw1           Ymw1           Zmw1         ]            [         P1k           Q1k           R1k         ]       =           [   M   ]          [         Xmk1           Ymk1           Zmk1         ]            
     [         P2w           Q2w           R2w         ]     =           [   M   ]          [         Xiw2           Yiw2           Ziw2         ]            [         P2k           Q2k           R2k         ]       =       [   M   ]          [         Xik2           Yik2           Zik2         ]                                 Also   ,                equation                   (   9   )                   can                 be                 modified                 as        :                 (   9   )                     [         X2           Y2           Z2         ]     =             [     M     -   1       ]          [     N   G     ]            [   M   ]            [           X1   -   Xmk1               Y1   -   Ymk1               Z1   -   Zmk1           ]            [         Xik2           Yik2           Zik2         ]              
            where        
     [     N   G     ]     =         [             P2w   -   P2k       P1w   -   P1k           0       0           0           Q2w   -   Q2k       Q1w   -   Q1k           0           0       0           R2w   -   R2k       R1w   -   R1k             ]          
     [         P1w           Q1w           R1w         ]     =           [   M   ]          [         Xmw1           Ymw1           Zmw1         ]            [         P1k           Q1k           R1k         ]       =           [   M   ]          [         Xmk1           Ymk1           Zmk1         ]            
     [         P2w           Q2w           R2w         ]     =           [   M   ]          [         Xiw2           Yiw2           Ziw2         ]            [         P2k           Q2k           R2k         ]       =       [   M   ]          [         Xik2           Yik2           Zik2         ]                        
             (   10   )                               
 
         [0071]    Likewise, upon application to a method of converting a media white point and gray-balance black point to the PCS(D50) upon correcting a gray balance, a chromatic adaptation model in which the human eye accommodates itself to the media white and gray-balance black points can be derived. That is, let MW1 (Xmw1, Ymw1, Zmw1) be the media white point, MK1 (Xmk1, Ymk1, Zmk1) be the media black point, IW2 (Xiw2, Yiw2, Ziw2) be a D50 white point of a light source on the PCS, and IK2 (Xik2, Yik2, Zik2) be a black point (0, 0, 0) of the light source on the PCS. Then, the relationship between a sample (X1, Y1, Z1) on a medium and a sample (X2, Y2, Z2) on the PCS is also expressed by equation (9) or (10).  
         [0072]    The gray-balance black point in this embodiment is obtained by the following calculations. That is, let (Xmw, Ymw, Zmw) be the media white point, and (Xmbk, Ymbk, Zmbk) be the media black point. Then, a corresponding gray-balance black point (Xmk, Ymk, Zmk) is calculated by:  
         
       Xmk=Ymbk·Xmw/Ymw  
     
         Ymk=Ymbk  
         
       Zmk=Ymbk·Zmw/Ymw  
     
         [0073]    [Image Process Without Intervention of PCS] 
         [0074]    Equations (6), (9), and (10) above indicate a case with the intervention of the PCS. Alternatively, the source-side white point and destination-side white point, and the source-side black point and destination-side black point can be associated with each other without the intervention of the PCS. Such process is used in a color matching module (CMM) which directly stores colorimetric values under respective observation conditions in a private tag or the like of an ICC profile in place of PCS values, and implements color matching using the information.  
         [0075]    In a method of converting a white point of the source-side medium to that of the destination-side medium, a chromatic adaptation model is applied under the assumption that the human eye accommodates itself to white points of respective media. That is, let MW1 (Xmw1, Ymw1, Zmw1) be a white point of the source-side medium, and MW2(Xmw2, Ymw2, Zmw2) be a white point of the destination-side medium. Then, the relationship between a sample (X1, Y1, Z1) on the source-side medium and a sample (X2, Y2, Z2) on the destination-side medium is expressed, using, e.g., the Von Kries transform as a chromatic adaptation model, by:  
                 [         X2           Y2           Z2         ]     =           [     M     -   1       ]          [           P2   /   P1         0       0           0         Q2   /   Q1         0           0       0         R2   /   R1           ]            [   M   ]            [         X1           Y1           Z1         ]              
            where             [         P1           Q1           R1         ]     =           [   M   ]          [         Xmw1           Ymw1           Zwm1         ]            [         P2           Q2           R2         ]       =       [   M   ]          [         Xmw2           Ymw2           Zmw2         ]                   (   11   )                               
 
         [0076]    In a method of converting white and black points of the source-side medium to those of the destination-side medium, a chromatic adaptation model is applied under the assumption that the human eye accommodates itself to white and black points of respective media. That is, let MW1 (Xmw1, Ymw1, Zmw1) be a white point of the source-side medium, MK1 (Xmk1, Ymk1, Zmk1) be a black point of the source-side medium, MW2 (Xmw2, Ymw2, Zmw2) be a white point of the destination-side medium, and MK2 (Xmk2, Ymk2, Zmk2) be a black point of the destination-side medium. Then, the relationship between a sample (X1, Y1, Z1) on the source-side medium and a sample (X2, Y2, Z2) on the destination-side medium is expressed, using, e.g., the Von Kries transform as a chromatic adaptation model, by:  
                 [         X2           Y2           Z2         ]     =       [     M     -   1       ]          [               (     P2w   -   P2k     )            (     P   -   P1k     )     /     (     P1w   -   P1k     )         +   P2k                   (     Q2w   -   Q2k     )            (     Q   -   Q1k     )     /     (     Q1w   -   Q1k     )         +   Q2k                   (     R2w   -   R2k     )            (     R   -   R1k     )     /     (     R1w   -   R1k     )         +   R2k           ]              
            where        
     [         P           Q           R         ]     =           [   M   ]          [         X1           Y1           Z1         ]            
     [         P1w           Q1w           R1w         ]     =           [   M   ]          [         Xmw1           Ymw1           Zmw1         ]            [         P1k           Q1k           R1k         ]       =           [   M   ]          [         Xmk1           Ymk1           Zmk1         ]            
     [         P2w           Q2w           R2w         ]     =           [   M   ]          [         Xmw2           Ymw2           Zmw2         ]            [         P2k           Q2k           R2k         ]       =       [   M   ]          [         Xmk2           Ymk2           Zmk2         ]                         (   12   )                               
 
         [0077]    Equation (12) can be modified as:  
                 [         X2           Y2           Z2         ]     =             [     M     -   1       ]          [     N   G     ]            [   M   ]            [           X1   -   Xmk1               Y1   -   Ymk1               Z1   -   Zmk1           ]            [         Xmk2           Ymk2           Zmk2         ]              
            where        
     [     N   G     ]     =         [             P2w   -   P2k       P1w   -   P1k           0       0           0           Q2w   -   Q2k       Q1w   -   Q1k           0           0       0           R2w   -   R2k       R1w   -   R1k             ]          
     [         P1w           Q1w           R1w         ]     =           [   M   ]          [         Xmw1           Ymw1           Zmw1         ]            [         P1k           Q1k           R1k         ]       =           [   M   ]          [         Xmk1           Ymk1           Zmk1         ]            
     [         P2w           Q2w           R2w         ]     =           [   M   ]          [         Xmw2           Ymw2           Zmw2         ]            [         P2k           Q2k           R2k         ]       =       [   M   ]          [         Xmk2           Ymk2           Zmk2         ]                         (   13   )                               
 
         [0078]    Likewise, the gray balance on the source-side medium can be matched with that on the destination-side medium. Let MW1 (Xmw1, Ymw1, Zmw1) be a white point of the source-side medium, MK1 (Xmk1, Ymk1, Zmk1) be a black point of the source-side medium, MW2 (Xmw2, Ymw2, Zmw2) be a white point of the destination-side medium, and MK2 (Xmk2, Ymk2, Zmk2) be a gray-balance black point of the destination-side medium. Then, the relationship between a sample (X1, Y1, Z1) on the source-side medium and a sample (X2, Y2, Z2) on the destination-side medium is expressed by equation (12) or (13) above that considers the gray balance.  
         [0079]    Note that the gray-balance black points on the source and destination sides are obtained by the following calculations. As for the source side, let (Xmw1, Ymw1, Zmw1) be the media white point, and (Xmbk1, Ymbk1, Zmbk1) be the media black point. Then, a corresponding gray-balance black point (Xmk1, Ymk1, Zmk1) is calculated by:  
           Xmk 1 =Ymbk 1 ·Xmw 1 /Ymw 1  
         Ymk1=Ymbk1  
           Zmk 1= Ymbk 1· Zmw 1 /Ymw 1  
         [0080]    As for the destination side, let (Xmw2, Ymw2, Zmw2) be the media white point, and (Xmbk2, Ymbk2, Zmbk2) be the media black point. Then, a corresponding gray-balance black point (Xmk2, Ymk2, Zmk2) is calculated by:  
           Xmk 2 =Ymbk 2 ·Xmw 2/ Ymw 2  
         Ymk2=Ymbk2  
           Zmk 2 =Ymbk 2· Zmw 2/ Ymw 2  
         [0081]    [Bradford Transform] 
         [0082]    In the above description, the Von Kries transform is used as a chromatic adaptation model. Alternatively, the Bradford transform may be used.  
         [0083]    When the Bradford transform is used, 3×3 matrices [MB] and [MB −1 ] are applied in place of 3×3 matrices [M] and [M −1 ] in equations (6), (9), and (10) to (13).  
               [   MB   ]     =         [         0.8591       0.2664         -   0.1614               -   0.7502         1.7135       0.0367           0.0389         -   0.0685         1.0296         ]          
     [     MB     -   1       ]     =     [         0.9870         -   0.1471         0.1600           0.4323       0.5184       0.0493             -   0.0085         0.0400       0.9685         ]               (   14   )                               
 
         [0084]    [CIE CAM97s] 
         [0085]    A color perception model may be used in place of the chromatic adaptation model. When CIE CAM97s is applied as the color perception model, equations (16) are used in place of equations (15) in forward chromatic adaptation transform of CIE CAM97s  
           Rc={D (1.0/ Rw )+1 −D}R    
           Gc={D (1.0/ Gw )+1 −D}G    
           Bc={D (1.0/ Bw   p )+1 −D}|B|   P   (15)  
         [0086]    for  
           p= ( Bw/ 1.0) 0.0834    
           D=F−F/ (1+2· LA   1/4   +LA   2 /300)  
           Rc=[D{ 1.0/( Rw−Rk )}+1 −D] ( R−Rk )  
           Gc=[D{ 1.0/( Gw−Gk )}+1 −D] ( G−Gk )  
           Bc=[D{ 1.0/( Bw−Bk ) P }+1 −D]|B−Bk|   P   (16)  
         [0087]    for  
           p={ ( Bw−Bk )/1.0} 0.0834    
           D=F−F/ (1+2 ·LA   1/4   +LA   2 /300)  
         [0088]    where Rw, Gw, and Bw are R, G, and B corresponding to a media white point, and Rk, Gk, and Bk are R, G, and B corresponding to a media black point. A similar substitution is made in inverse chromatic adaptation transform of CIE CAM97s.  
         [0089]    Likewise, in consideration of the gray balance, Rw, Gw, and Bw are R, G, and B corresponding to a media white point, and Rk, Gk, and Bk are R, G, and B corresponding to a media gray-balance black point.  
         [0090]    [User Interface] 
         [0091]    Upon generating a profile, the user can select using check boxes  31  and  32  on a user interface shown in FIG. 3 whether or not white point correction and/or black point correction are/is made for a calorimetric value. That is, the user can select “white point correction=OFF, black point correction=OFF”, “white point correction=ON, black point correction=OFF”, “white point correction=OFF, black point correction=ON”, or “white point correction=ON, black point correction=ON”.  
         [0092]    Each correction exploits, e.g., equations (6), (9), and (10). The user can also select the types of chromatic adaptation models or color perception models to be applied to that correction using radio buttons on a transform option field  33 .  
         [0093]    Likewise, upon making color matching, the user can select using check boxes  41  and  42  on a user interface shown in FIG. 4 whether or not white and black points of the source-side medium and those of the destination-side medium undergo white point correction and/or black point correction. Also, the user can select the types of chromatic adaptation models or color perception models to be applied to that correction using radio buttons on a transform option field  43 .  
         [0094]    When gray-balance correction is made upon generating a profile or making color matching, the user selects one of the white point correction check box  41 /black point correction check box  42  and a gray-balance correction check box  44  on user interfaces shown in FIGS. 5 and 6. Of course, the user can select the type of chromatic adaptation model or color perception model to be applied to the gray-balance correction from those in the field  43 .  
         [0095]    Gray data corrected based on the type of correction and the type of model to be applied, which are selected in this way, may be visually displayed on a preview field  45 . An image including N patches is displayed in the preview field  45 . Each patch shows gray of each of gradations which divide a gray line equally with N. The gray line connects between the media white point, and a black point which is selected by a user who uses the user interface, such as the gray-balance black point. When the user operates the user interface to change the media black point and the gray-balance black point, the image displayed in the preview field  45  will be changed.  
         [0096]    In each of the above embodiments, the XYZ values are used, but Lab values may be used instead. When Lab values are used, a media gray-balance black point is a point which has the same lightness (L value) as that of the media black point, and has the same color appearance (a, b values) as that of the media white point.  
         [0097]    &lt;Other Embodiment&gt; 
         [0098]    The present invention can be applied to a system constituted by a plurality of devices (e.g., host computer, interface, reader, printer) or to an apparatus comprising a single device (e.g., copying machine, facsimile machine).  
         [0099]    Further, the object of the present invention can also be achieved by providing a storage medium storing program codes for performing the aforesaid processes to a computer system or apparatus (e.g., a personal computer), reading the program codes, by a CPU or MPU of the computer system or apparatus, from the storage medium, then executing the program.  
         [0100]    In this case, the program codes read from the storage medium realize the functions according to the embodiment/embodiments, and the storage medium storing the program codes constitutes the invention.  
         [0101]    Further, the storage medium, such as a floppy disk, a hard disk, an optical disk, a magneto-optical disk, CD-ROM, CD-R, a magnetic tape, a non-volatile type memory card, and ROM can be used for providing the program codes.  
         [0102]    Furthermore, besides aforesaid functions according to the above embodiment/embodiments are realized by executing the program codes which are read by a computer, the present invention includes a case where an OS (operating system) or the like working on the computer performs a part or entire processes in accordance with designations of the program codes and realizes functions according to the above embodiment/embodiments.  
         [0103]    Furthermore, the present invention also includes a case where, after the program codes read from the storage medium are written in a function expansion card which is inserted into the computer or in a memory provided in a function expansion unit which is connected to the computer, CPU or the like contained in the function expansion card or unit performs a part or entire process in accordance with designations of the program codes and realizes functions of the above embodiment/embodiments.  
         [0104]    As many apparently widely different embodiments of the present invention can be made without departing from the spirit and scope thereof, it is to be understood that the invention is not limited to the specific embodiments thereof except as defined in the appended claims.