Image processing device and method, image transmission/receptor system and method, and providing medium

[0002] This invention relates to an apparatus and a method for processing images and a system and a method for transmitting and receiving images as well as a providing medium that are particularly adapted to carry out color signal processing operations that may vary as a function of individual image display apparatus in order to coordinate the colors of images to be displayed there so as to eliminate apparatus-dependency of the colors of images.

[0003] As a result of the rapid spread of DTP (desk top publishing) and the Internet in recent years, color images are manipulated more often than ever on the display screens of CRT (cathode ray tube) displays and liquid crystal displays.

[0004] For example, operations of drawing pictures by means of painting tools are being replaced by those of drawing computer graphics by means of personal computers. Consumers place orders by seeing images of products displayed on the display screen as electronic advertisements that are transmitted by way of the Internet.

[0005] In any of such cases, it is necessary that the colors of the original picture (which may be a picture drawn by an artist or a photographic picture) and those of the facsimile image of the picture output by an apparatus (which may be the monitor screen of a display apparatus or a color printer) agree with each other.

[0006] Thus, it is highly desirable that, for a same picture, the image displayed on the display screen of a personal computer and the image output by a printer appear same in terms of their colors.

[0007] In the case of an electronic advertisement, if the image of an article (e.g., a jacket or a painting) displayed on the display screen of the personal computer of a consumer appears differently from the actual commodity, a trouble may arise between the commodity provider and the consumer when the consumer buys the commodity.

[0008] Thus, it is necessary to provide an arrangement in which a picture appears exactly the same on all the image display apparatus displaying an image of the picture particularly in terms of colors.

[0009] A system referred to as CMS (color management system) is known for correcting the differences of colors of images of the same picture among different image display apparatus displaying it.

[0010] FIG. 1 of the accompanying drawings schematically illustrate a CMS. Referring to FIG. 1, with a CMS, the color signals of a picture input through an input device (e.g., camera 1, scanner 2, monitor 3) are converted into common color space signals (e.g., CIE/XYZ, CIE/L*a*b*) that are not dependent on the characteristics of the device and then output through an output device (e.g., monitor 3, printer 4).

[0011] A conversion formula or a conversion table that is referred to as “profile” and specific to each device is used when converting a signal into that of a common color space. For examples, the color signals of a picture taken by camera 1 are converted into common color space signals by the profile specific to the camera 1. To output the signals through monitor 3, the common color space signals are then converted into color signals that reflect the characteristics of the monitor 3 by the profile specific to the monitor 3 and an image of the picture formed by the obtained color signals will be displayed on the monitor.

[0012] Such a profile is determined by means of the signal values input to the device and the color values (XYZ values or L*a*b* values) obtained by observing the colors of the image output according to the signal values typically through a calorimeter.

[0013] FIG. 2 of the accompanying drawings a chart showing the flow of data when the image on the monitor 3 is output to printer 4. Referring to FIG. 2, the image on the monitor 10 is converted into signals of a common color space by the profile specific to the monitor 3 (monitor profile 20). In other words, the image data (RGB data) of the monitor 3 are converted respectively into corresponding quantities of light by means of TRCs (tone reproduction curve, which will be described hereinafter) generated by TRC generator section 20-1. The quantities of light for RGB reflect the colors of the image viewed by the user on the monitor 3.

[0014] The data (on the quantities of light for RGB) generated by the TRC generator section 20-1 are then processed for conversion using a matrix representing the linear relationship between the quantities of light output to the monitor 3 and the CIE/XYZ values (or L*a*b* values) to obtain a series of values (CIE/XYZ values or L*a*b* values), which are then output as common color space signals 30.

[0015] The common color space signals 30 obtained by the monitor profile are then processed for conversion by the profile specific to the printer 4 (printer profile 40) to reflect the printing characteristics of the printer 4 and the obtained color signals for the printer, or CMY50, are printed and output.

[0016] Apparatus of a same type can show disparity, if slightly, in the characteristics depending on individual apparatus. Then, the profile is preferably calibrated for each apparatus.

[0017] The profiles of the monitors marketed by a same manufacturer can be calibrated typically by means of a monitor calibration tool or characterization tool provided by the manufacturer.

[0018] The monitor profile 20 is prepared by such a tool. FIG. 3 of the accompanying drawings is a flow chart of the operation of preparing a monitor profile. Referring to FIG. 3, firstly in Step S1, TRCs (g-curves) representing the non-linear relationship between the RGB data to be input to the monitor and the quantities of light of RBG of the monitor is prepared. Such TRCs can be obtained by observing the XYZ3-stimulus values of more than ten tones (e.g., 16 tones) sampled at regular intervals from the full range of tones (e.g., 256 tones) for each of the primary colors of red (R), green (G) and blue (B) of the RGB data (or RGBW data) and applying them to the g equation out of equations (1) shown below by non-linear regression (a TRC is obtained by linear interpolation or a conversion table if the number of samples is large). $\begin{array}{cc}\begin{array}{c}r=\frac{X_r}{X_{r,max}}={\left\{K_{r,\mathrm{gain}}\left(\frac{\mathrm{dr}}{2^N-1}\right)+K_{r,\mathrm{offset}}\right\}}^{{\gamma }_r}\\ g=\frac{Y_g}{Y_{g,max}}={\left\{K_{g,\mathrm{gain}}\left(\frac{dg}{2^N-1}\right)+K_{g,\mathrm{offset}}\right\}}^{{\gamma }_g}\\ b=\frac{Z_b}{Z_{b,max}}={\left\{K_{b,\mathrm{gain}}\left(\frac{\mathrm{db}}{2^N-1}\right)+K_{b,\mathrm{offset}}\right\}}^{{\gamma }_b}\end{array}& \left(1\right)\end{array}$

[0019] In the above equations (1), variables dr, dg and db respectively represent the input signal values for red, green and blue and variable N represent the number of bits of each input signal. Coefficient k_gainrepresents the gain of each of the colors (e.g., k_r.gainrepresents the gain of red) and coefficient k_offsetrepresent the offset of each of the colors (e.g., k_r.offsetrepresents the offset of red). Additionally, variables X_r, Y_gand Z_brespectively represent the 3-stimulus values of the three colors and variable X_r.max, Y_g.maxand Z_b.maxrespectively represent the 3-stimulus values of the three colors when the input signal values are maximal. Thus, variables r, g and b are obtained by normalizing X_r, Y_gand Z_brespectively by the maximum values X_r.max, Y_g.maxand Z_b.maxto take a value between 0 and 1.

[0020] FIG. 4 is a flow chart illustrating the operation of preparing a TRC corresponding to an input digital signal for red in Step S1 of FIG. 3. Referring to FIG. 4, in Step S21, XYZ_rvalues (including maximum value XYZ_r.max) are observed for the sampled several tones from the input signal corresponding to red. Then, in Step S22, the input signal values dr are normalized by dividing them by 2^N−1 and, in Step S23, the output brightness values are normalized by dividing X_rvalues by the maximum value X_r.max. In Step S24, a process of non-linear interpolation is conducted by means of equations (1). Finally, in Step S25, the values of coefficients k_r.offset, k_r.gainand γ_rare determined. Note that operations of preparing TRCs corresponding to input digital signals dg and db for green and blue will be conducted similarly.

[0021] FIGS. 5A through 5C are exemplary TRCs for red, green and blue prepared in a manner as described above.

[0022] Generally, γ values for a monitor refers to those of γs in equations (1). Note that most of the currently available tools utilizes k_gain=1.0 and k_offset=0 in equations (1).

[0023] Returning to FIG. 3, in Step S2, a matrix representing the linear relationship between the quantities of light of RGB and the monitor and the CIE/XYZ values are determined. If, for example, the monitor in question is of the self-emission type and the law of addition approximately holds true for the quantities of light (r, g, b) when mixing colors, then the CIE/XYZ3-stimulus values (X_CRT, Y_CRT, Z_CRT) can be obtained from the quantities of light of RGB corrected in Step S1 (normalized values) and a 3×m matrix as described below. For the purpose of simplification, a matrix of 3×3 which is of the most simple form, is shown below. $\begin{array}{cc}\left[\begin{array}{c}{X}_{\mathrm{CRT}}\\ Y_{\mathrm{CRT}}\\ Z_{\mathrm{CRT}}\end{array}\right]=\left[\begin{array}{ccc}{X}_{r,max}& X_{g,max}& X_{b,max}\\ Y_{r,max}& Y_{g,max}& Y_{b,max}\\ Z_{r,max}& Z_{g,max}& Z_{b,max}\end{array}\right]\left[\begin{array}{c}r\\ g\\ b\end{array}\right]& \left(2\right)\end{array}$

[0024] Such a matrix can be obtained by observing the XYZ3-stimulus values of each of the three primary colors for the highest brightness.

[0025] Note that, in most of the known tools of the type under consideration, the TRCs and the matrix are determined on an assumption that the monitor is not affected by ambient light and used in the dark and the monitor profile is obtained and the TRCs are corrected on the basis of them.

[0026] Thus, as shown in FIG. 6, when ambient light is present, the values (CIE/XYZ values) obtained from the image on the monitor will be those of the colors of the self-emission type monitor (X_CRT, Y_CRT, Z_CRT) plus those of the colors of ambient light reflected by the surface of the tube of the monitor (R_bk×(X_Amb, Y_Amb, Z_Amb)) because ambient light is reflected by the surface of the tube of the monitor so that consequently they may be different from those observed when the profile was prepared (in the dark). Thus, there is a problem accompanying such known tools that the colors of the images on the monitor cannot be accurately corrected when ambient light exists.

[0027] Additionally, as seen from FIG. 7A, the TRC brightness will increase (shift from curve a to curve b) when ambient light is present. In FIG. 7A, the horizontal axis represents the value of the normalized input digital signal (or the value of the input digital signal divided by the value of the maximum input digital signal of the monitor) and the vertical axis represent the output brightness of the monitor.

[0028] FIG. 7B is a graph obtained by normalizing the vertical axis of FIG. 7A by the value of the maximum brightness. As seen from FIG. 7B, the monitor shows a narrower dynamic range (D2<D1) when ambient light is present (and its performance reflects curve b′ with a dynamic range of D2) than when ambient light is not found (and its performance reflects curve a′ with a dynamic range of D1).

[0029] Thus, the dynamic range is narrowed when ambient light exists so that consequently the image on the monitor lacks sharp contrast to the viewer because of the partly lost dynamic range.

[0030] Now, the monitor is provided with a function that allows the user to arbitrarily regulate the contrast, the brightness and the reference white (neutral) point of the monitor. If the function is used to change the contrast, the brightness and the reference white point, the TRC characteristics measured when the profile is prepared (the relationship between the values of the input digital signals and the quantities of light of RGB output to the monitor) will also have to be changed. If such is the case, the characteristics of the monitor will have to be measured once again to update the TRCs in order to accurately correct the colors. However, it is practically impossible to measure the characteristics of the monitor each time the above function is used and hence there exits a problem of a difficulty with which the colors are accurately corrected on the monitor.

[0031] Thus, it is necessary to maintain the conditions under which the profile is prepared (that the monitor is used in the dark and the contrast, the brightness and the reference white point at the time of shipment are kept unchanged) in order to accurately correct the colors on the monitor. If this requirement is not met and the conditions have been altered, the characteristics of the monitor have to be measured once again under the current conditions.

[0032] It is a first object of the present invention to provide an apparatus and a method for processing images as well as a providing medium that are adapted to properly correct the colors of images.

[0033] According to a first aspect of the invention, the chromatic profile of a monitor to be used for outputting an image is adapted to update the profile depending on the information obtained on the viewing environment. Thus, if ambient light changes, the monitor profile will be automatically updated to realize color matching without measuring the operating characteristics of the monitor once again.

[0034] It is a second object of the present invention to provide an apparatus and a method for processing images as well as a providing medium that are adapted to automatically update the chromatic profile of a monitor for color matching.

[0035] According to a second aspect of the invention, information on the setting of a monitor to be used for outputting an image is obtained and input and the chromatic profile of the monitor is updated according to the obtained input information so that the updated profile is stored in the monitor. Thus, if the user arbitrarily change the setting of the monitor, the operating characteristics of the monitor do not have to be measured after the change because the monitor profile is automatically updated for color matching.

[0036] It is a third object of the invention to provide a system and a method for transmitting/receiving images as well as a providing medium that are adapted to make the appearance of the image at the transmitter agree with that of the image at the receiver in terms of colors.

[0037] According to a third aspect of the invention, the chromatic profile of the input device, information on the initial operating conditions of the input device when the profile is prepared and information on the current operating conditions of the input device are added in the transmitter to the image data to be transmitted and sent to the receiver which, upon receiving the transmitted image data, extracts the profile, the information on the initial operating conditions and the information on the current operating conditions from the received image data and performs a processing operation of correcting the colors for the image data. Thus, when an image input through the input device of the transmitter is output to the output device of the receiver by way of the internet, for example, and the transmitted cannot update the profile in response to ambient light and the information on the setting of the input device, the output device of the receiver can perform the updating operation for the transmitter in order to make the appearance of the image at the transmitter agree with that of the image at the receiver in terms of colors.

[0038] It is a fourth object of the invention to provide an apparatus and a method for processing images as well as a providing medium that are adapted to accurately calibrate the chromatic profile of a monitor with a minimal amount of data obtained by measurement if the black level is isolated.

[0039] According to a fourth aspect of the invention, a 3×4 matrix containing elements for offsetting the light emitting components of the display section in a state where the image data is equal to 0 will be generated to obtain color signals that are not dependent on the device in response to the outcome of detecting the emission of light of the display section in a state where the image data is equal to 0 and that of detecting if the law of addition holds true for mixed colors. Thus, the chromatic profile of the monitor can be accurately calibrated with a minimal amount of data obtained by measurement if the black level is isolated.

[0040] It is a fifth object of the invention to provide an apparatus and a method for processing images as well as a providing medium that are adapted to accurately carry out an operation of chromatic calibration with a minimal amount of data obtained by measurement.

[0041] According to a fifth aspect of the invention, a total of nine tone reproduction curves will be generated in response to the outcome of detecting if the law of proportion holds true or not and then formulas will be generated to obtain color signals that are not device-dependent from the nine tone reproduction curves and the 3-stimulus values for the black level. Thus, the chromatic profile of the monitor can be accurately with a minimal amount of data obtained by measurement.

[0042] FIG. 1 is a schematic illustration of a CMS.

[0043] FIG. 2 is a flow chart showing the flow of data when the image on the monitor 3 of FIG. 1 is output to the printer 4.

[0044] FIG. 3 is a flow chart of the operation of preparing a monitor profile.

[0045] FIG. 4 is a flow chart illustrating a conventional operation of preparing a TRC corresponding to an input digital signal.

[0046] FIGS. 5A through 5C are exemplary graphs of TRCs for the three primary colors of RGB.

[0047] FIG. 6 is a schematic illustration showing how the measured color values change when ambient light exists.

[0048] FIGS. 7A and 7B are graphs illustrating how the dynamic range is modified when ambient light exists.

[0049] FIG. 8 is a schematic block diagram of an embodiment of the invention, showing the configuration thereof.

[0050] FIG. 9 is a schematic block diagram of the embodiment of FIG. 8, showing the configuration in greater detail.

[0051] FIG. 10 is a schematic block diagram of a displayed GUI that can be used for the ambient light input section 101 of the embodiment of FIG. 8.

[0052] FIGS. 11A through 11C are graphs showing exemplary TRC characteristics that may be obtained when ambient light exists.

[0053] FIG. 12 is a schematic block diagram of the embodiment of FIG. 8, showing the configuration in greater detail.

[0054] FIG. 13 is a schematic block diagram of a monitor, illustrating an model of operation.

[0055] FIG. 14 is a schematic block diagram of another embodiment of the invention, showing the configuration thereof.

[0056] FIG. 15 is a schematic block diagram of still another embodiment of the invention, showing the configuration thereof.

[0057] FIG. 16 is a schematic block diagram of still another embodiment of the invention, showing the configuration thereof.

[0058] FIG. 17 is a flow chart, illustrating the operation of the embodiment of FIG. 16.

[0059] FIG. 18 is a flow chart for the processing operation of a GOG model when no isolated black exists.

[0060] FIG. 19 is a flow chart for the processing operation of a GOGO model when isolated black exists.

[0061] Now, the present invention will be described in greater detail by referring to the accompanying drawings that illustrate preferred embodiments of the invention.

[0062] FIG. 8 is a schematic block diagram of an embodiment of the invention, showing the configuration thereof.

[0063] Referring to FIG. 8, the image processing section 100 of the embodiment comprises a viewing environment converting section 100a, a profile updating section 100b, a monitor specific values converting section 100cand a contrast correcting section 100dand is adapted to update the profile according to the information it acquires with regard to ambient light and the information specific to the monitor 103.

[0064] The viewing environment converting section 100acalculate the XYZ_Ambvalues of ambient light and determines by computation the XYZ_CRTvalues and the TRC of the monitor taking the influence of ambient light into consideration. The profile updating section 100bgenerates a monitor profile that reflects ambient light and the information set and displayed on the display section of the embodiment and stores it in memory section 104.

[0065] The monitor specific values converting section 100cprepares TRCs on the basis of the contrast and the brightness selected for the monitor 103 and generates a matrix from the reference white point also selected for the monitor 103. The contrast correcting section 100dcorrects the contrast for the TRC1 stored in the memory 104aof the memory section 104 and supplies the obtained TRC2 to the profile updating section 100b. It also generates drive values and bias values for the monitor 103.

[0066] Note that the drive values and the bias values respectively represent the gains and the biases of the three colors of red (R), green (G) and blue (B) of the RGB data input to the monitor 103.

[0067] The ambient light input section 101 in FIG. 8 typically comprises one or more than one photosensor and is adapted to detect information on the chromaticity and the brightness of ambient light and supplies the obtained information to the image processing section 100 as information on the viewing environment. Note that the ambient light input section 101 may be so arranged that the user may manually input necessary information by way of a GUI (graphical user interface) which will be described hereinafter.

[0068] The monitor control section 102 in FIG. 8 automatically alters the TRC characteristics of the monitor 103 according to ambient light and the information selected for it. It also supply the information on the monitor 103 including the values selected for the reference white point, the contrast and the brightness to the image processing section 100.

[0069] The monitor 103 is fed with image data (RGB data) that have been processed by the profile stored in the memory section 104 and then outputs and displays the supplied image data.

[0070] The memory section 104 comprises memory 104aand memory 104b. The memory 104astores the monitor profile whereas the memory 104bstores information on the reference white point, the contrast and the brightness of the monitor 103.

[0071] The embodiment having the above described configuration operates in a manner as described below.

[0072] The embodiment of FIG. 8 is configured as to (1) generate an optimal monitor profile in response to the viewing environment and also (2) generate an optimal monitor profile in response to alteration(s) made on the selected values (on the contrast, the brightness and the reference white point) for the monitor 103. These operations will be discussed sequentially hereinafter.

[0073] FIG. 9 is a schematic block diagram of the embodiment of FIG. 8, showing the configuration adapted to generate an optimal monitor profile in response to the viewing environment. In this configuration, the monitor specific values converting section 100cis not taken into consideration. Otherwise, the configuration is identical with that of FIG. 8.

[0074] The ambient light input section 101 detects information on ambient light (in terms of the CIE/xy chromaticity and illuminance of ambient light) of the monitor 103 by means of one or more than one photosensors mounted typically on the top of the monitor 103 and supplies it to the image processing section 100-1 as viewing environment information.

[0075] Note that a GUI as shown in FIG. 10 may be displayed on the monitor 103 to input the viewing environment information in place of inputting the information on ambient light (viewing environment) obtained by the photosensors. In the example of FIG. 10, three different light sources of incandescent light, fluorescent light and natural light are available and an appropriate light source can be selected by checking the inside of a check box arranged for them. Additionally, it is so arranged that a predetermined value may be directly input by the user by way of a keyboard (not shown) for the illuminance of the light source. The data input by the user are then converted into the CIE/xy chromaticity and illuminance of ambient light typically by means of a data table.

[0076] The viewing environment converting section 100aof the image processing section 100-1 determines by computation the XYZ values of ambient light by substituting the viewing environment information M and the reflectivity R_bkof the surface of the tube of the monitor 103 in equation (3) below by the respective values input through the ambient light input section 101: $\begin{array}{cc}\left[\begin{array}{c}{X}_{\mathrm{Amb}}\\ Y_{\mathrm{Amb}}\\ Z_{\mathrm{Amb}}\end{array}\right]=R_{\mathrm{bk}}·\frac{M}{\pi }·\frac{1}{y_{\mathrm{Amb}}}\left[\begin{array}{c}{x}_{\mathrm{Amb}}\\ y_{\mathrm{Amb}}\\ 1-x_{\mathrm{Amb}}-y_{\mathrm{Amb}}\end{array}\right]& \left(3\right)\end{array}$

[0077] where X_Amband Y_Ambrespectively represent the x, y chromaticity points of ambient light and M represents the illuminance of ambient light.

[0078] Subsequently, the viewing environment converting section 100areads out the XYZ values (XYZ_CRTvalues) of the monitor 103 corresponding to the input signals values dr, dg and db from the memory 104a(and hence the values obtained by using equations (1) and (2) above) and adds the XYZ values (XYZ_Ambvalues) of light reflected by the surface of the tube as determined by equation (3) above to the above values according to equation (4) below to determine the XYZ values when ambient light exists: $\begin{array}{cc}{\left[\begin{array}{c}X\\ Y\\ Z\end{array}\right]}_{\mathrm{measured}}=\left[\begin{array}{c}{X}_{\mathrm{CRT}}\\ Y_{\mathrm{CRT}}\\ Z_{\mathrm{CRT}}\end{array}\right]+\left[\begin{array}{c}{X}_{\mathrm{Amb}}\\ Y_{\mathrm{Amb}}\\ Z_{\mathrm{Amb}}\end{array}\right]=\left[\begin{array}{c}{X}_{\mathrm{CRT}}\\ Y_{\mathrm{CRT}}\\ Z_{\mathrm{CRT}}\end{array}\right]+R_{\mathrm{bk}}·\frac{M}{\pi }·\frac{1}{y_{\mathrm{Amb}}}\left[\begin{array}{c}{x}_{\mathrm{Amb}}\\ y_{\mathrm{Amb}}\\ 1-x_{\mathrm{Amb}}-y_{\mathrm{Amb}}\end{array}\right]& \left(4\right)\end{array}$

[0079] Note that equation (4) above is based on the assumption that the measured values of the colors of the monitor can be expressed as the quantity of light emitted by the monitor itself and the quantity of ambient light reflected by the surface of the tube of the monitor.

[0080] The XYZ values obtained for a situation where ambient light exists are then fed to the profile updating section 100b.

[0081] With the above processing operation, it is now possible to generate XYZ values for a situation where ambient light exists. However, as described above by referring to FIGS. 6 and 7, as the illuminance of ambient light rises, the apparent dynamic range of the image on the monitor screen is narrowed to lose its sharp contrast. The contrast correcting section 100dcompensates the loss of contrast due to the raised illuminance of ambient light by means of a processing operation as described below.

[0082] This processing operation for correction is carried out by modifying the coefficient k_offsetfor the offset of any of the TRCs of the monitor profile generated from the XYZ3-stimulus values of the monitor 103 that is obtained in the dark in the negative direction (and the coefficient k_gainfor the gain in the direction of making it greater than 1).

[0083] For example, if the curve a of FIG. 11A is one of the TRCs for the monitor 103 obtained when no ambient light exists (in the dark), the TRC is shifted to curve b in FIG. 11B when the monitor 103 is placed in an environment where ambient light exists. Thus, in this embodiment, a processing operation will be performed so as to make the TRC (curve c) obtained after the correction to be found closer to the TRC (curve a) obtained in the dark as shown in FIG. 11C.

[0084] While the above processing operation for correction is performed independently for each color, or for each of the signals of RGB data, all the operations are identical. Therefore, only the operation for G (green) will be described hereinafter.

[0085] Firstly, the TRC obtained for G in the dark (representing the relationship between the quantity of green light g and the input digital signal dg for green) is expressed by equation (5) below: $\begin{array}{cc}g=\frac{Y_g}{Y_{\mathrm{gm}ax}}={\left\{k_{g,\mathrm{gain}}\left(\frac{dg}{2^N-1}\right)+k_{g,\mathrm{offset}}\right\}}^{{\gamma }_g}& \left(5\right)\end{array}$

[0086] where Y_g, Y_gmaxrepresent respectively the brightness and the maximum brightness of G observed in the dark.

[0087] Now, assume that ambient light is reflected by the surface of the tube of the monitor 103. Then, the brightness Y_gAmbin the presence of ambient light is expressed by equation (6) below: $\begin{array}{cc}\begin{array}{c}{Y}_{\mathrm{gAmb}}=Y_g+R_{\mathrm{bk}}·Y_{\mathrm{Amb}}\\ =Y_{gmax}{\left\{k_{g,\mathrm{gain}}\left(\frac{dg}{2^N-1}\right)+k_{g,\mathrm{offset}}\right\}}^{{\gamma }_g}+R_{\mathrm{bk}}·Y_{\mathrm{Amb}}\end{array}& \left(6\right)\end{array}$

[0088] where R_bkrepresents the reflectivity of the surface of the tube of the monitor 103 and Y_Ambrepresents the brightness of ambient light.

[0089] A TRC as shown below (TRC in the presence of ambient light) is obtained by normalizing equation (6). $\begin{array}{cc}\begin{array}{c}{g}_{\mathrm{Amb}}=\frac{Y_{\mathrm{gAmb}}}{Y_{\mathrm{gAmb}max}}=\frac{\left(Y_g+R_{\mathrm{bk}}·Y_{\mathrm{Amb}}\right)}{\left(Y_{gmax}+R_{\mathrm{bk}}·Y_{\mathrm{Amb}}\right)}\\ =\frac{1}{\left(Y_{gmax}+R_{\mathrm{bk}}·Y_{\mathrm{Amb}}\right)}[Y_{gmax}·\{k_{g,\mathrm{gain}}\left(\frac{dg}{2^N-1}\right)+\\ {k_{g,\mathrm{offset}}\}}^{{\gamma }_g}+R_{\mathrm{bk}}·Y_{\mathrm{Amb}}]\end{array}& \left(7\right)\end{array}$

[0090] The curve to be corrected for contrast is the TRC obtained in the dark has to meet the requirement expressed by formula below.

[0091] g_Amb≈g  (8)

[0092] γ_gin equation (7) represents a (constant) value specific to the monitor 103 so that the values of k_g.gainand k_g.offsethave to be determined to meet the requirement of (8). If the values of k_g.gainand k_g.offsetsatisfying the requirement of (8) are k_g.Amb.gainand k_g.Amb.offset, equation (9) below can be drawn. $\begin{array}{cc}\frac{1}{\left(Y_{gmax}+R_{\mathrm{bk}}·Y_{\mathrm{Amb}}\right)}[Y_{gmax}·{\left\{k_{g,\mathrm{Amb}·\mathrm{gain}}\left(\frac{dg}{2^N-1}\right)+k_{g,\mathrm{Amp}·\mathrm{offset}}\right\}}^{{\gamma }_g}+R_{\mathrm{bk}}·Y_{\mathrm{Amb}}]\approx g& \left(9\right)\end{array}$

[0093] Formula (9) can be modified to become formula (10) below. $\begin{array}{cc}{\left\{k_{g,\mathrm{Amb}·\mathrm{gain}}\left(\frac{dg}{2^N-1}\right)+k_{g,\mathrm{Amp}·\mathrm{offset}}\right\}}^{{\gamma }_g}\approx \frac{1}{Y_{gmax}}\left\{g\left(Y_{gmax}+R_{\mathrm{bk}}·Y_{\mathrm{Amb}}\right)-R_{\mathrm{bk}}·Y_{\mathrm{Amb}}\right\}& \left(10\right)\end{array}$

[0094] Thus, k_g.Amb.gainand k_g.Amb.offsetsatisfying the requirement of formula (10) above are then supplied to the contrast correcting section 100dand the monitor control section 102 as drive signal and bias signal so that the contrast and the brightness of the monitor 103 are regulated according to these values. Meanwhile, the new TRC determined by equation (7) is supplied from the contrast correcting section 100dto the profile updating section 100bas TRCB.

[0095] Thus, the contrast correcting section 100dreads out the TRCA from the profile A (a profile prepared without taking ambient light into consideration) stored in the memory 104aand inputs the XYZ values output from the viewing environment converting section 100ato determine k_g.Amb.gainand k_g.Amb.offsetthat satisfy the requirement of formula (10) by means of non-linear recurrence. It then outputs these values to the monitor control section 102 respectively as a drive signal and a bias signal.

[0096] Additionally, the contrast correcting section 100doutputs the new TRC obtained by substituting k_g.gainand k_g.offsetof equation (7) with k_g.Amb.gainand k_g.Amb.offsetrespectively (or TRC prepared by taking ambient light into consideration) as TRCB to the profile updating section 100b. As a result, the profile updating section 100bstores both the XYZ values fed from the viewing environment converting section 100aand the profile B generated from the TRCB fed from the contrast correcting section 100d(or profile prepared by taking ambient light into consideration) into the memory 104a.

[0097] Thus, it is possible to compensate the loss of contrast by the above processing operation for correcting the contrast.

[0098] However, as a result of the above contrast compensating operation, there can be occasions where the image displayed on the monitor 103 can appear dark. If such is the case, it is desirable that the determined values of k_g.Amb.gainand k_g.Amb.offsetare multiplied by an appropriate constant of proportion.

[0099] If the monitor 103 is a broadcast monitor, values such as γ=2.2, k_gain=1.0 and k_offset=0 will be used in the dark. If such a monitor is used in an office, the above problem of the displayed image that appears dark can be alleviated by selecting a value between 1.0 and 1.4 for k_gainand a value between −0.4 and 0.0 for k_offset.

[0100] As described above, the operation of correcting the measured color values of the viewing environment converting section 100ais an operation of updating the relationship between the CIE/XYZ values that are not device-dependent and the RGB data of the monitor 103 and hence in line with the concept of CMS as discussed earlier.

[0101] The contrast correcting section 100dcorrects the contrast of the image displayed on the monitor in order to reproduce the desired colors in the presence of ambient light.

[0102] Thus, with the above processing operation, it is possible to generate an optimal profile B for a viewing environment where ambient light exists from the profile A prepared for a completely dark viewing environment without determining the characteristics of the monitor 103 for another time.

[0103] Now, the configuration (2) of the embodiment adapted to generate an optimal profile when the user modifies the setting of the monitor 103 (in terms of contrast, brightness and reference white point) will be described by referring to FIG. 12.

[0104] In FIG. 12, the viewing environment converting section 100aand the contrast correcting section 100dare omitted from the configuration of FIG. 8. Otherwise, the configuration is identical with that of FIG. 8. Before describing the operation of this configuration, a model of operation of monitor 103 will be discussed by referring to FIG. 13.

[0105] FIG. 13 is a schematic block diagram of a monitor, illustrating an model of operation. Referring to FIG. 13, computer system 200 comprises a host computer 200aand a DA (Digital to Analog) converter 200band is adapted to output video signals corresponding to a requested image.

[0106] On the other hand, CRT display system 300 comprises a video amplifier 300a, a CRT electron gun 300band a fluorescent body 300cas well as other components.

[0107] The model operates in a manner as described below. For the simplicity of explanation, only signals for R (red) will be described.

[0108] Of the RGB data output from the host computer 200a, the input digital signal dr for red color is linearly converted into a video signal voltage V_rby the DA converter 200b, using equation (11) below: $\begin{array}{cc}{V}_r=\mathrm{Cont}·\left(\frac{dr}{2^N-1}\right)+\mathrm{Brt}& \left(11\right)\end{array}$

[0109] where Cont and Brt respectively correspond to the information on the contrast and the one on the brightness selected for the monitor 103 and determine the video voltage of the white level and that of the black level of the monitor 103.

[0110] The video signal voltage V_robtained by the DA converter 200bis amplified by the video amplifier 300aof the CRT display system 300, using equation (12) below and then supplied to the electron gun 300b:

[0111] V_G,r=drive_r·V_r+bias_r  (12)

[0112] where driver represents the gain of the video amplifier 300aand bias_rrepresents the offset of the video amplifier 300a.

[0113] The rate at which an electron beam is shot from the CRT electron gun 300bis a function of the voltage different of the control grid voltage (V_Gr) and the cutoff voltage (V_Cr) at which an electron beam starts to be emitted from the gun and the electric current (j_r) gushes out from the electron gun 300bis expressed by known equation (13) below:

[0114] j_r=ρ(V_G,r−V_C,r)^γ(V_G,r−V_C,r≧0)  (13)

[0115] where ρ represents the coefficient of the current efficiency of the electric current discharged from the electron gun 300band is referred to as perveance.

[0116] The electrons discharged from the electron gun 300bcollide with the fluorescent body 300capplied to the inner surface of the CRT panel to make it emit light. The radiant quantity of light L_rfrom the fluorescent body 300cis expressed by equation (14) below:

[0117] L_r=k_r·j_r  (14)

[0118] where k_ris a constant indicating the extent of influence on the light emitting efficiency of the fluorescent body and the radiant quantity of the CRT glass panel.

[0119] Now, equation (15) can be derived from equations (11) through (14). $\begin{array}{cc}{L}_r=k_r·\rho {\left\{{\mathrm{drive}}_r\left[\mathrm{Cont}·\left(\frac{dr}{2^N-1}\right)+\mathrm{Brt}\right]+{\mathrm{bias}}_r-V_{c,r}\right\}}^{{\gamma }_r}& \left(15\right)\end{array}$

[0120] If bias_r−V_c,rin equation (15) is replaced by bias_r, or if bias_r−V_c,r=bias_r, then equation (16) below is obtained. $\begin{array}{cc}{L}_r=k_r·\rho {\left\{{\mathrm{drive}}_r\left[\mathrm{Cont}·\left(\frac{dr}{2^N-1}\right)+\mathrm{Brt}\right]+{\mathrm{bias}}_r\right\}}^{{\gamma }_r}& \left(16\right)\end{array}$

[0121] From equation (16), the radiant quantity L_r.maxwhen the input digital signal (dr) for red shows the maximum value (dr=2^N−1) is obtained by equation (17) below.

[0122] L_r,max=k_r·ρ[drive_r(Cont+Brt)+bias_r]^γ  (17)

[0123] Then, equation (18) is obtained by normalizing L_rby L_r.max. $\begin{array}{cc}\frac{L_r}{L_{r,max}}={\left\{\frac{{\mathrm{drive}}_r\left[\mathrm{Cont}·\left(\frac{dr}{2^N-1}\right)+\mathrm{Brt}\right]+{\mathrm{bias}}_r}{{\mathrm{drive}}_r\left(\mathrm{Cont}+\mathrm{Brt}\right)+{\mathrm{bias}}_r}\right\}}^{{\gamma }_r}& \left(18\right)\end{array}$

[0124] The equation (18) can be modified to produce equation (19) below. $\begin{array}{cc}\frac{L_r}{L_{r,max}}=[\left(\frac{{\mathrm{drive}}_r·\mathrm{Cont}}{{\mathrm{drive}}_r\left(\mathrm{Cont}+\mathrm{Brt}\right)+{\mathrm{bias}}_r}\right)\left(\frac{d_r}{2^N-1}\right)+{\left(\frac{{\mathrm{drive}}_r·\mathrm{Brt}+{\mathrm{bias}}_r}{{\mathrm{drive}}_r\left(\mathrm{Cont}+\mathrm{Brt}\right)+{\mathrm{bias}}_r}\right)]}^{{\gamma }_r}& \left(19\right)\end{array}$

[0125] Assume here that gain coefficient K_r.gainand offset coefficient k_r.offsetof the normalization model are expressed by equations (20) below. $\begin{array}{cc}{k}_{r,\mathrm{gain}}=\frac{{\mathrm{drive}}_r·\mathrm{Cont}}{{\mathrm{drive}}_r\left(\mathrm{Cont}+\mathrm{Brt}\right)+{\mathrm{bias}}_r}& \left(20\right)\\ k_{r,\mathrm{offset}}=\frac{{\mathrm{drive}}_r·\mathrm{Brt}+{\mathrm{bias}}_r}{{\mathrm{drive}}_r\left(\mathrm{Cont}+\mathrm{Brt}\right)+{\mathrm{bias}}_r}& \end{array}$

[0126] Then, equation (21) is obtained by substituting equation (19) by equation (20). $\begin{array}{cc}\frac{L_r}{L_{r,max}}={\left[k_{r,\mathrm{gain}}\left(\frac{dr}{2^N-1}\right)+k_{r,\mathrm{offset}}\right]}^{{\gamma }_r}& \left(21\right)\end{array}$

[0127] The equation (21) represents the relationship between the radiant quantity of the fluorescent body for red and the input digital signal value dr. and is identical with equations (1) above to prove that the above model fits well to the actual monitor 103.

[0128] Thus, the TRC showing the relationship between the quantity of light of the monitor and the input digital signal value can also be expressed by equation (21) or (1). Since γ is a (constant) value specific to the monitor in either of these equations, if any of the values for the setting of the monitor 103 is changed, a new TRC can be obtained by modifying only _K.gainand K_r.offset.

[0129] Now, from equation (20), it will be appreciated that Cont and Brt contained in the two equations correspond respectively to the contrast and the brightness of the monitor. As a matter of fact, K_r.gainand K_r.offsetchange their values as the values of Cont. and Brt change.

[0130] Note that Cont and Brt are common to all R, G and B signals and hence the quantity of light corresponding to any of such signals change when these values are modified.

[0131] Now, an occasion where the user wants to modify the reference white point of the monitor 103 will be discussed below.

[0132] The reference white point of the monitor 103 is determined by the ratio of the quantities of light of RGB. Thus, the reference white point can be modified by modifying the gain (drive_rin the case of red) and the offset (bias_rin the case of red) of the video amplifier for each of the colors as expressed in equation (20) above.

[0133] Thus, if the user wants to modify the reference white point of the monitor 103, an optimal TRC can be generated in response to the modification by correcting the value of the gain and that of the offset (k_gain, k_offset) for each of the colors of the monitor profile.

[0134] Since the chromaticity value of white changes as the reference white point changes, the matrix of equation (2) showing the relationship between the quantities of light and the CIE/XYZ values of the monitor 103 will also change. Then, the modified matrix can be obtained in a manner as described below.

[0135] Firstly, r=1, g=0 and b=0 are used in equation (2) showing the relationship between the brightness values (CIE/XYZ values) and the quantities of light (r, g, b) to determine the CIE/XYZ values (X_r.max, Y_r.max, Z_r.max) for the maximal brightness of red.

[0136] Subsequently, the CIE/xyz chromaticity values (x_r, y_r, z_r) of red is obtained by means of equations (22) below showing the relationship between CIE/XYZ values and CIE/xyz values. $\begin{array}{cc}{x}_r=\frac{X_{r,max}}{X_{r,max}+Y_{r,max}+Z_{r,max}}& \left(22\right)\\ y_r=\frac{Y_{r,max}}{X_{r,max}+Y_{r,max}+Z_{r,max}}& \\ z_r=1-x_r-y_r& \end{array}$

[0137] Then, a similar operation will be conducted for both green and blue to determine the values of (x_g, y_g, z_g) and (x_b, y_b, z_b).

[0138] Note that the relationship between the color temperature and the chromaticity point of white of the monitor 103 may be expressed in the form of a data table so that chromaticity point data (x_w, y_w, z_w) corresponding to the modified color temperature may be read out from the table.

[0139] Then, the mixing ratio (h′_r, h′_g, h′_b) that provides a reference white point for the maximal quantities of light of R, G and B is determined from the data obtained in a manner as described above. Since the monitor 103 is a self-emission type device and the law of addition substantially holds true for mixed colors, equations (23) below can be drawn.

[0140] h′_rx_r+h′_gx_g+h′_bx_b=x_w

[0141] h′_ry_r+h′_gy_g+h′_by_b=y_w

[0142] h′_rz_r+h′_gz_g+h′_bz_b=z_w  (23)

[0143] Since the chromaticity data (x_w, y_w, z_w) are proportional to the stimuli of the colors, equations (24) below can be obtained through normalization by y_w, using h_r=h′_r/y_w, h_g=h′_g/y_wand h_bh′_b/y_w. $\begin{array}{cc}\left[\begin{array}{ccc}{x}_r& x_g& x_b\\ y_r& y_g& y_b\\ z_r& z_g& z_b\end{array}\right]\left[\begin{array}{c}{h}_r\\ h_g\\ h_b\end{array}\right]=\left[\begin{array}{c}{x}_w/y_w\\ 1\\ z_w/y_w\end{array}\right]& \left(24\right)\end{array}$

[0144] Thus, the mixing ratio (h_r, h_g, h_b) of the colors can be obtained by solving the equation (24) above. Then, CIE/XYZ values can be obtained from the values of r, g, b that are obtained through normalization using the maximum brightness values of R, G, B and equation (25) generated by using the mixing ratio. $\begin{array}{cc}\left[\begin{array}{ccc}{h}_r{x}_r& h_g{x}_g& h_b{x}_b\\ h_r{y}_r& h_g{y}_g& h_b{y}_b\\ h_r{z}_r& h_g{z}_g& h_b{z}_b\end{array}\right]\left[\begin{array}{c}r\\ g\\ b\end{array}\right]=\left[\begin{array}{c}{X}_{\mathrm{CRT}}\\ Y_{\mathrm{CRT}}\\ Z_{\mathrm{CRT}}\end{array}\right]& \left(25\right)\end{array}$

[0145] where 0<r, g, b<1 and 0<Y_CRT<1.

[0146] As a result of the above operations, the matrix can be updated whenever the reference white point is modified.

[0147] Now, the operation of the embodiment of FIG. 12 will be described on the basis of the above explanation.

[0148] If the setting of the monitor 103 (in terms of contrast or brightness) is modified, the monitor control section 102 retrieves the values of Cont and Brt from the monitor 103 and supplies them to the monitor specific values converting section 100cof the image processing section 100-2.

[0149] Then, the monitor specific values converting section 100cgenerates a new TRCB by correcting the values of the gain and the offset (k_gain, k_offset) in equations (1), referring to the values of Cont and Brt fed from the monitor control section 102 and supplies the new TRCB to the profile updating section 100b.

[0150] If, on the other hand, the reference white point of the monitor 103 is modified, the monitor specific values converting section 100cretrieves the data on the chromaticity point corresponding to the modified color temperature from the data table stored in advance.

[0151] Then, it generates a new matrix by solving the equation (24) and determining the mixing ratio (h_r, h_g, h_b) and outputs it to the profile updating section 100bas matrix B.

[0152] The profile updating section 100bprepares a new profile, or profile B, on the basis of the TRCB output from the monitor specific values converting section 100cand the matrix B and stores it in a predetermined region of the memory 104a.

[0153] With the above operations, if the data on the setting of the monitor (contrast, brightness, reference white point) are modified by the user, it is now possible to generate a profile corresponding to the new setting of the monitor 103 by updating the (initial) profile prepared in the dark without measuring the values of the characteristics of the monitor 103 once again.

[0154] FIG. 14 is a schematic block diagram of another embodiment of the invention, showing the configuration thereof. Note that, in FIG. 14, the components same as or similar to those of FIG. 8 are denoted respectively by the same reference symbols and will not be described any further.

[0155] This embodiment is so designed that the appearance of colors is held unchanged if the image being displayed by it under a set of predetermined operating conditions, or conditions 1, is moved to a place with a different set of operating conditions, or conditions 2.

[0156] In FIG. 14, monitor 103-1 refers to the monitor when it is used in operating conditions C (conditions 1), which are represented by setting information C and ambient light information (viewing environment information) C.

[0157] Then, in FIG. 14, monitor 103-2 refers to the monitor when it is used in operating conditions D (conditions 2), which are represented by setting information D and ambient light information (viewing environment information) D. Thus, the monitor 103-aand the monitor 103-2 are a same and identical monitor.

[0158] The image processing section 100 comprises image processing section 101-1 and image processing section 101-2 respectively shown in FIGS. 9 and 12.

[0159] This embodiment operates in a manner as described below.

[0160] Under the operation conditions C, the RGB data C output to the monitor 103-1 are corrected by the profile C modified in response to the user-selected setting information C and the ambient light information C.

[0161] To display the RGB data C on the monitor 103-2 under the operating conditions D, firstly the original data (the data before corrected by the profile C in response to the user-selected setting information C and the ambient light information C) are restored by means of the TRCC and the matrix C contained in the profile for the operating conditions C.

[0162] The restored data are then corrected by the profile D for the operating conditions D before output to the monitor 103-2.

[0163] With the above processing operation, it is now possible to make the two monitors 103-1 and 103-2 to display a same image in terms of colors, contrast and brightness if the monitors are actually a same monitor 103 and only the operating conditions (including the user-selected setting values and the viewing environment) are changed.

[0164] FIG. 15 is a schematic block diagram of still another embodiment of the invention, showing the configuration thereof.

[0165] Note that, in FIG. 15, the components that are same as or similar to those of FIG. 8 are denoted respectively by the same reference symbols and will not be described any further.

[0166] This embodiment is so designed that the image displayed on monitor 103-1 is transferred to monitor 103-2 by way of internet 500 and displayed on the latter monitor.

[0167] The image processing section 600 comprises an image processing section 100 that receives the image transmitted by way of internet 500 and outputs the received image to the monitor 103-2 after carrying out predetermined processing operations on it.

[0168] This embodiment operates in a manner as described below.

[0169] The RGB data C displayed on the monitor 103-1 of the transmitter are transmitted to the receiver by way of internet 500 after the profile C stored in memory 104a-1, the information on the initial operating conditions (the operating conditions when the profile is generated) and the information C on the current operating conditions are added thereto by the monitor control section 102-1.

[0170] Since the monitor 103-1 of the transmitter is not provided with the functional feature of correcting the image data according to the operating conditions, the appearance of the colors of the image displayed on the monitor 103-1 is affected by the viewing environment and the setting of the monitor 103-1.

[0171] Then, the image processing section 600 of the receiver receives the information transmitted from the transmitter.

[0172] The image processing section 600 then extracts the profile C and the RGB data C from the transmitted information and performs an converting operation on the RGB data C by means of the obtained profile C to generate XYZC data.

[0173] The image processing section 100 carries out an operation of correcting the obtained XYZC data that reflects the operating conditions of the transmitter. More specifically, the image processing section 100 corrects the XYZC data by referring to the information on the initial operating conditions and the one on the operating conditions C. As a result, the XYZC data are converted to XYZD data that reflects the actual appearance of colors of the transmitter.

[0174] The obtained XYZD data are then converted to RGB data E by the profile E generated by the image processing section 100 to reflect the operating conditions E of the receiver and stored in the memory 104a-2 and then output to the monitor 103-2.

[0175] The above described embodiment is adapted to transmit the image displayed on the monitor 103-1 by way of the internet 500 and display it on the monitor 103-2. Thus, if the transmitter is not provided with a functional feature of correcting the profile according to the operating conditions, the image displayed on the transmitter and the one displayed on the receiver can be made to appear same and identical by transmitting the RGB data to which information on the operating conditions is added and correcting the transmitted data to reflect difference between the operating conditions of the transmitter and those of the receiver.

[0176] Now, if the monitor emits light if the input signals (dr, dg, db) shows values of (0, 0, 0) (which represents no substantive image data), the law of addition of colors (the sum of the 3-stimulus values of the individual colors of RGB #3-stimulus values when the three colors of RGB are emitted simultaneously) does not hold true. However, according to the invention, the colors can be calibrated accurately by minimally measuring the chromatic characteristics of the monitor. This function will be described in terms of two different occasions, when the law of proportion holds true for spectral distribution of light and when the law does not holds true.

[0177] When the law of proportion holds true for spectral distribution, the profile of spectral distribution (L_r,p, L_g,p, L_b,p) (P=λ) of the colors of RGB of the monitor is constant regardless of their intensities and equation (26) below applies.

[0178] L_r,λ=r·L_r,λ,max

[0179] L_g,λ=g·L_g,λ,max

[0180] L_b,λ=b·L_b,λ,max  (26)

[0181] Then, if only the emission of red light is measurable or if the emission of light other than red light can be isolated from the measured value typically by means of a technique of principal component analysis, the XYZ3-stimulus values (X_r, Y_r, Z_r) are expressed by equations (27) below on the basis of the physical properties of the monitor. $\begin{array}{cc}{X}_r={X_{r,max}\left(k_{r,\mathrm{gain}}·\frac{dr}{2^N-1}+k_{r,\mathrm{offset}}\right)}^{{\gamma }_r}& \left(27\right)\\ Y_r={Y_{r,max}\left(k_{r,\mathrm{gain}}·\frac{dr}{2^N-1}+k_{r,\mathrm{offset}}\right)}^{{\gamma }_r}& \\ Z_r={Z_{r,max}\left(k_{r,\mathrm{gain}}·\frac{dr}{2^N-1}+k_{r,\mathrm{offset}}\right)}^{{\gamma }_r}& \end{array}$

[0182] By normalizing the equations (27) by the maximum values of the 3-stimulus values (X_r.max, Y_r.max, Z_r.max), equations (28) are obtained. $\begin{array}{cc}{r}^{\prime }\left(X\right)=\frac{X_r}{X_{r,max}}={\left(k_{r,\mathrm{gain}}·\frac{dr}{2^N-1}+k_{r,\mathrm{offset}}\right)}^{{\gamma }_r}& \left(28\right)\\ r^{\prime }\left(Y\right)=\frac{Y_r}{Y_{r,max}}={\left(k_{r,\mathrm{gain}}·\frac{dr}{2^N-1}+k_{r,\mathrm{offset}}\right)}^{{\gamma }_r}& \\ r^{\prime }\left(Z\right)=\frac{Z_r}{Z_{r,max}}={\left(k_{r,\mathrm{gain}}·\frac{dr}{2^N-1}+k_{r,\mathrm{offset}}\right)}^{{\gamma }_r}& \end{array}$

[0183] As shown by equations (28), the formulas for the channel to be used for XYZ can alternatively be expressed by using a single formula. Note that equations (1) are realized by using the equation of r′(X) above. In the above equations, N represents the number of bits of the input signal and γ_rrepresents the number to be used for the tone characteristics of red. While the equations of (28) are produced for red, similar expressions can be produced for green and blue. Thus, the formulas for the channel to be used for expressing the tone characteristics representing the relationship between the input digital signal (dr, dg, db) and the quantity of light for any of RGB can alternatively be expressed by means of a single formula. In other words, only a total of three formulas may be used for the three colors of RGB. Then, all the colors displayed on the monitor can be expressed in terms of CIE122-1996, using XYZ values ((X, Y, Z)_measured) and equation (29) below. $\begin{array}{cc}{\left[\begin{array}{c}X\\ Y\\ Z\end{array}\right]}_{\mathrm{measured}}=\left[\begin{array}{ccc}{X}_{r,max}& X_{g,max}& X_{b,max}\\ Y_{r,max}& Y_{g,max}& Y_{b,max}\\ Z_{r,max}& Z_{g,max}& Z_{b,max}\end{array}\right]\left[\begin{array}{c}{r}^{\prime }\\ g^{\prime }\\ b^{\prime }\end{array}\right]& \left(29\right)\end{array}$

[0184] In the actual monitor, if the input signal is used only for a single color, it is difficult to accurately measure the emission of light of that color. In most cases, a slight emission of light of different colors will be picked up and measured due to the mutual effect of the channels and the regulated state of the black level. However, if the values of the RGB digital input signals of the monitor are (0, 0, 0), it is proved by experiments that the above theory holds true provided that the rate of light emission of the monitor is sufficiently low (and the black level is not isolated).

[0185] Nevertheless, once the user arbitrarily regulates the contrast and the brightness of the monitor to shift the black level, the monitor can emit light even (and the black level can become isolated) if the values of the RGB digital input signals of the monitor are (0, 0, 0). If such is the case, the offset coefficient k_offsetwill take a positive value and the quantities of light of RGB (r′, g′, b′) when the input signal values are (0, 0, 0) can be expressed by equations (30).

[0186] r′=(k_r,offset)^γ, g′=(k_g,offset)^γ, b′=(k_b,offset)^γ  (30)

[0187] Thus, the XYZ3-stimulus values Y_min, Y_min, Z_min) of the colors of RGB can be expressed by equations (31) for the black level. $\begin{array}{cc}\{\begin{array}{c}{X}_{r,min}=X_{r,max}·k_{r,{\mathrm{offset}}^{{\gamma }_r}}\\ Y_{r,min}=Y_{r,max}·k_{r,{\mathrm{offset}}^{{\gamma }_r}}\\ Z_{r,min}=Z_{r,max}·k_{r,{\mathrm{offset}}^{{\gamma }_r}}\end{array}& \left(31\right)\\ \{\begin{array}{c}{X}_{g,min}=X_{g,max}·k_{g,{\mathrm{offset}}^{{\gamma }_g}}\\ Y_{g,min}=Y_{g,max}·k_{g,{\mathrm{offset}}^{{\gamma }_g}}\\ Z_{g,min}=Z_{g,max}·k_{g,{\mathrm{offset}}^{{\gamma }_g}}\end{array}& \\ \{\begin{array}{c}{X}_{b,min}=X_{b,max}·k_{b,{\mathrm{offset}}^{{\gamma }_b}}\\ Y_{b,min}=Y_{b,max}·k_{b,{\mathrm{offset}}^{{\gamma }_b}}\\ Z_{b,min}=Z_{b,max}·k_{b,{\mathrm{offset}}^{{\gamma }_b}}\end{array}& \end{array}$

[0188] The XYZ3-stimulus values (X_k.min, Y_k.min, Z_k.min) of the black level can be expressed by equations (32) below. $\begin{array}{cc}\{\begin{array}{c}{X}_{k,min}=X_{r,min}+X_{g,min}+X_{b,min}\\ Y_{k,min}=Y_{r,min}+Y_{g,min}+Y_{b,min}\\ Z_{k,min}=Z_{r,min}+Z_{g,min}+Z_{b,min}\end{array}& \left(32\right)\end{array}$

[0189] Taking light of the three colors into consideration, if an input signal is applied only to the red channel, the measured 3-stimulus values (Y_r.measured, Y_r.measured, Z_r.measured) will be expressed by equations (33). Equations (34) can be obtained by normalizing the equations (33). $\begin{array}{cc}{X}_{r,\mathrm{measured}}={X_{r,\max }\left(k_{r,\mathrm{gain}}·\frac{\mathrm{dr}}{2^N-1}+k_{r,\mathrm{offset}}\right)}^{{\gamma }_r}+X_{g,\min }+X_{b,\min }{Y}_{r,\mathrm{measured}}={Y_{r,\max }\left(k_{r,\mathrm{gain}}·\frac{\mathrm{dr}}{2^N-1}+k_{r,\mathrm{offset}}\right)}^{{\gamma }_r}+Y_{g,\min }+Y_{b,\min }{Z}_{r,\mathrm{measured}}={Z_{r,\max }\left(k_{r,\mathrm{gain}}·\frac{\mathrm{dr}}{2^N-1}+k_{r,\mathrm{offset}}\right)}^{{\gamma }_r}+Z_{g,\min }+Z_{b,\min }& \left(33\right)\\ r^{″}\left(X\right)=\frac{X_{r,\mathrm{measured}}}{X_{r,\max }}={\left(k_{r,\mathrm{gain}}·\frac{\mathrm{dr}}{2^N-1}+k_{r,\mathrm{offset}}\right)}^{{\gamma }_r}+\frac{X_{g,\max }}{X_{r,\max }}{k_{g,\mathrm{offset}}}^{{\gamma }_g}+\frac{X_{b,\max }}{X_{r,\max }}{k_{r,\mathrm{offset}}}^{{\gamma }_b}{r}^{″}\left(Y\right)=\frac{Y_{r,\mathrm{measured}}}{Y_{r,\max }}={\left(k_{r,\mathrm{gain}}·\frac{\mathrm{dr}}{2^N-1}+k_{r,\mathrm{offset}}\right)}^{{\gamma }_r}+\frac{Y_{g,\max }}{Y_{r,\max }}{k_{g,\mathrm{offset}}}^{{\gamma }_g}+\frac{Y_{b,\max }}{Y_{r,\max }}{k_{r,\mathrm{offset}}}^{{\gamma }_r}{r}^{″}\left(Z\right)=\frac{Z_{r,\mathrm{measured}}}{Z_{r,\max }}={\left(k_{r,\mathrm{gain}}·\frac{\mathrm{dr}}{2^N-1}+k_{r,\mathrm{offset}}\right)}^{{\gamma }_r}+\frac{Z_{g,\max }}{Z_{r,\max }}{k_{g,\mathrm{offset}}}^{{\gamma }_g}+\frac{Z_{b,\max }}{Z_{r,\max }}{k_{b,\mathrm{offset}}}^{{\gamma }_b}& \left(34\right)\end{array}$

[0190] In equations (34), the value of the offset terms (the rightest two terns of each of the equations (34)) differs for each of the channels of XYZ.

[0191] Now, equations (35) holds true.

[0192] X_r,max>X_g,max, X_b,max

[0193] Y_g,max>Y_r,max, Y_b,max

[0194] Z_b,max>Z_r,max, Z_g,max  (35)

[0195] Also, equations (36) holds true when the black level (0, 0, 0) is close to that of achromatic color.

[0196] (k_r,offset)^γ≈(k_g,offset)^γ≈(k_b,offset)^γ  (36)

[0197] Therefore, it will be seen that, in equations (34), the offset term of r″(X) (where the denominator X_r.maxhas a large value) is smaller than the offset terms of r″(Y) and r″(Z) (where the numerators Y_g.max, Z_b.maxhave a large value). This means that the TRC characteristics (tone characteristics) are different for each of the channels of XYZ so that three channels may be conceived for each of the RGB channels to produce a total of 9 TRCs. If such is the case, the XYZ3-stimulus values cannot be transformed by means of equation (37) of CIE122-1996 (same as equation (29) above) because no single TRC can be selected for each of r″, g″ and b″. $\begin{array}{cc}{\left[\begin{array}{c}X\\ Y\\ Z\end{array}\right]}_{\mathrm{measured}}=\left[\begin{array}{ccc}{X}_{r,\max }& X_{g,\max }& X_{b,\max }\\ Y_{r,\max }& Y_{g,\max }& Y_{b,\max }\\ Z_{r,\max }& Z_{g,\max }& Z_{b,\max }\end{array}\right]\left[\begin{array}{c}{r}^{″}\\ g^{″}\\ b^{″}\end{array}\right]& \left(37\right)\end{array}$

[0198] Therefore, equations (33) will be developed to produce equations (38) $\begin{array}{cc}\begin{array}{c}{X}_{r,\mathrm{measured}}={X_{r,\max }\left(k_{r,\mathrm{gain}}·\frac{\mathrm{dr}}{2^N-1}+k_{r,\mathrm{offset}}\right)}^{{\gamma }_r}+X_{g,\min }+X_{b,\min }\\ ={X_{r,\max }\left(k_{r,\mathrm{gain}}·\frac{\mathrm{dr}}{2^N-1}+k_{r,\mathrm{offset}}\right)}^{{\gamma }_r}+\left(X_{r,\min }+X_{g,\min }+X_{b,\min }\right)-X_{r,\min }\\ =\left\{{X_{r,\max }\left(k_{r,\mathrm{gain}}·\frac{\mathrm{dr}}{2^N-1}+k_{r,\mathrm{offset}}\right)}^{{\gamma }_r}-X_{r,\min }\right\}+X_{k,\min }\\ Y_{r,\mathrm{measured}}={Y_{r,\max }\left(k_{r,\mathrm{gain}}·\frac{\mathrm{dr}}{2^N-1}+k_{r,\mathrm{offset}}\right)}^{{\gamma }_r}+Y_{g,\min }+Y_{b,\min }\\ ={Y_{r,\max }\left(k_{r,\mathrm{gain}}·\frac{\mathrm{dr}}{2^N-1}+k_{r,\mathrm{offset}}\right)}^{{\gamma }_r}+\left(Y_{r,\min }+Y_{g,\min }+Y_{b,\min }\right)-Y_{r,\min }\\ =\left\{{Y_{r,\max }\left(k_{r,\mathrm{gain}}·\frac{\mathrm{dr}}{2^N-1}+k_{r,\mathrm{offset}}\right)}^{{\gamma }_r}-Y_{r,\min }\right\}+Y_{k,\min }\\ Z_{r,\mathrm{measured}}={Z_{r,\max }\left(k_{r,\mathrm{gain}}·\frac{\mathrm{dr}}{2^N-1}+k_{r,\mathrm{offset}}\right)}^{{\gamma }_r}+Z_{g,\min }+Z_{b,\min }\\ ={Z_{r,\max }\left(k_{r,\mathrm{gain}}·\frac{\mathrm{dr}}{2^N-1}+k_{r,\mathrm{offset}}\right)}^{{\gamma }_r}+\left(Z_{r,\min }+Z_{g,\min }+Z_{b,\min }\right)-Z_{r,\min }\\ =\left\{{Z_{r,\max }\left(k_{r,\mathrm{gain}}·\frac{\mathrm{dr}}{2^N-1}+k_{r,\mathrm{offset}}\right)}^{{\gamma }_r}-Z_{r,\min }\right\}+Z_{k,\min }\end{array}& \left(38\right)\end{array}$

[0199] Equations (38) can be transformed respectively into equations (39). $\begin{array}{cc}{X}_{r,\mathrm{measured}}-X_{k,\min }={X_{r,\max }\left(k_{r,\mathrm{gain}}·\frac{\mathrm{dr}}{2^N-1}+k_{r,\mathrm{offset}}\right)}^{{\gamma }_r}-X_{r,\min }{Y}_{r,\mathrm{measured}}-Y_{k,\min }={Y_{r,\max }\left(k_{r,\mathrm{gain}}·\frac{\mathrm{dr}}{2^N-1}+k_{r,\mathrm{offset}}\right)}^{{\gamma }_r}-Y_{r,\min }{Z}_{r,\mathrm{measured}}-Z_{k,\min }={Z_{r,\max }\left(k_{r,\mathrm{gain}}·\frac{\mathrm{dr}}{2^N-1}+k_{r,\mathrm{offset}}\right)}^{{\gamma }_r}-Z_{r,\min }& \left(39\right)\end{array}$

[0200] Then, equations (39) can be transformed respectively further into equations (40). $\begin{array}{cc}\frac{X_{r,\mathrm{measured}}-X_{k,\min }}{X_{r,\max }}={\left(k_{r,\mathrm{gain}}·\frac{\mathrm{dr}}{2^N-1}+k_{r,\mathrm{offset}}\right)}^{{\gamma }_r}-\frac{X_{r,\min }}{X_{r,\max }}\frac{Y_{r,\mathrm{measured}}-Y_{k,\min }}{Y_{r,\max }}={\left(k_{r,\mathrm{gain}}·\frac{\mathrm{dr}}{2^N-1}+k_{r,\mathrm{offset}}\right)}^{{\gamma }_r}-\frac{Y_{r,\min }}{Y_{r,\max }}\frac{Z_{r,\mathrm{measured}}-Z_{k,\min }}{Z_{r,\max }}={\left(k_{r,\mathrm{gain}}·\frac{\mathrm{dr}}{2^N-1}+k_{r,\mathrm{offset}}\right)}^{{\gamma }_r}-\frac{Z_{r,\min }}{Z_{r,\max }}& \left(40\right)\end{array}$

[0201] Thus, equation (41) holds true. $\begin{array}{cc}\frac{X_{r,\min }}{X_{r,\max }}=\frac{Y_{r,\min }}{Y_{r,\max }}=\frac{Z_{r,\min }}{Z_{r,\max }}={k_{r,\mathrm{offset}}}^{{\gamma }_r}& \left(41\right)\end{array}$

[0202] If the value of equation (41) is cr, equations (40) can be transcribed to equations (42). $\begin{array}{cc}\frac{X_{r,\mathrm{measured}}-X_{k,\min }}{X_{r,\max }}={\left(k_{r,\mathrm{gain}}·\frac{\mathrm{dr}}{2^N-1}+k_{r,\mathrm{offset}}\right)}^{{\gamma }_r}-C_r\frac{Y_{r,\mathrm{measured}}-Y_{k,\min }}{Y_{r,\max }}={\left(k_{r,\mathrm{gain}}·\frac{\mathrm{dr}}{2^N-1}+k_{r,\mathrm{offset}}\right)}^{{\gamma }_r}-C_r\frac{Z_{r,\mathrm{measured}}-Z_{k,\min }}{Z_{r,\max }}={\left(k_{r,\mathrm{gain}}·\frac{\mathrm{dr}}{2^N-1}+k_{r,\mathrm{offset}}\right)}^{{\gamma }_r}-C_r& \left(42\right)\end{array}$

[0203] When the two sides of the equations (43) are multiplied by formulas (43) respectively so as to normalized them and make them take a value that is equal to 1 at maximum, equations (44) below will be obtained. $\begin{array}{cc}\frac{X_{r,\max }}{X_{r,\max }-X_{r,\min }},\frac{Y_{r,\max }}{Y_{r,\max }-Y_{r,\min }},\frac{Z_{r,\max }}{Z_{r,\max }-Z_{r,\min }}& \left(43\right)\\ \begin{array}{c}{r}^{\mathrm{\prime \prime \prime }}\left(X\right)=\frac{X_{r,\mathrm{measured}}-X_{k,\min }}{X_{r,\max }-X_{r,\min }}\\ =\frac{X_{r,\max }}{X_{r,\max }-X_{r,\min }}\left\{{\left(k_{r,\mathrm{gain}}·\frac{\mathrm{dr}}{2^N-1}+k_{r,\mathrm{offset}}\right)}^{{\gamma }_r}-C_r\right\}\\ r^{\mathrm{\prime \prime \prime }}\left(Y\right)=\frac{Y_{r,\mathrm{measured}}-Y_{k,\min }}{Y_{r,\max }-Y_{r,\min }}\\ =\frac{Y_{r,\max }}{Y_{r,\max }-Y_{r,\min }}\left\{{\left(k_{r,\mathrm{gain}}·\frac{\mathrm{dr}}{2^N-1}+k_{r,\mathrm{offset}}\right)}^{{\gamma }_r}-C_r\right\}\\ r^{\mathrm{\prime \prime \prime }}\left(Z\right)=\frac{Z_{r,\mathrm{measured}}-Z_{k,\min }}{Z_{r,\max }-Z_{r,\min }}\\ =\frac{Z_{r,\max }}{Z_{r,\max }-Z_{r,\min }}\left\{{\left(k_{r,\mathrm{gain}}·\frac{\mathrm{dr}}{2^N-1}+k_{r,\mathrm{offset}}\right)}^{{\gamma }_r}-C_r\right\}\end{array}& \left(44\right)\end{array}$

[0204] Thus, it will be seen that equation (45) below holds true. $\begin{array}{cc}\frac{X_{r,\max }}{X_{r,\max }-X_{r,\min }}=\frac{Y_{r,\max }}{Y_{r,\max }-Y_{r,\min }}=\frac{Z_{r,\max }}{Z_{r,\max }-Z_{r,\min }}& \left(45\right)\end{array}$

[0205] Therefore, equations (44) can be transcribed to produce equations (46) below. $\begin{array}{cc}{r}^{\mathrm{\prime \prime \prime }}\left(X\right)=\frac{X_{r,\mathrm{measured}}-X_{k,\min }}{X_{r,\max }-X_{r,\min }}=\left\{{\left(k_{r,\mathrm{gain}}^{\prime }·\frac{\mathrm{dr}}{2^N-1}+k_{r,\mathrm{offset}}^{\prime }\right)}^{{\gamma }_r}-C_r^{\prime }\right\}{r}^{\mathrm{\prime \prime \prime }}\left(Y\right)=\frac{Y_{r,\mathrm{measured}}-Y_{k,\min }}{Y_{r,\max }-Y_{r,\min }}=\left\{{\left(k_{r,\mathrm{gain}}^{\prime }·\frac{\mathrm{dr}}{2^N-1}+k_{r,\mathrm{offset}}^{\prime }\right)}^{{\gamma }_r}-C_r^{\prime }\right\}{r}^{\mathrm{\prime \prime \prime }}\left(Z\right)=\frac{Z_{r,\mathrm{measured}}-Z_{k,\min }}{Z_{r,\max }-Z_{r,\min }}=\left\{{\left(k_{r,\mathrm{gain}}^{\prime }·\frac{\mathrm{dr}}{2^N-1}+k_{r,\mathrm{offset}}^{\prime }\right)}^{{\gamma }_r}-C_r^{\prime }\right\}& \left(46\right)\end{array}$

[0206] As will be seen from the above equations, the TRCs of the channels of XYZ for red are expressed by an identical equation so that the TRC (tone) characteristics of the red channels can be expressed unequivocally by means of a GOGO model (which will be described hereinafter).

[0207] Thus, the TRCs for the channels of RGB are expressed by equations (47) below. $\begin{array}{cc}{r}^{\mathrm{\prime \prime \prime }}=\frac{X_{r,\mathrm{measured}}-X_{k,\min }}{X_{r,\max }-X_{g,\min }}=\left\{{\left(k_{r,\mathrm{gain}}^{\prime }·\frac{\mathrm{dr}}{2^N-1}+k_{r,\mathrm{offset}}^{\prime }\right)}^{{\gamma }_r}-C_r^{\prime }\right\}{g}^{\mathrm{\prime \prime \prime }}=\frac{Y_{g,\mathrm{measured}}-Y_{k,\min }}{Y_{g,\max }-Y_{g,\min }}=\left\{{\left(k_{g,\mathrm{gain}}^{\prime }·\frac{\mathrm{dr}}{2^N-1}+k_{g,\mathrm{offset}}^{\prime }\right)}^{{\gamma }_g}-C_g^{\prime }\right\}{b}^{\mathrm{\prime \prime \prime }}=\frac{Z_{b,\mathrm{measured}}-Z_{k,\min }}{Z_{b,\max }-Z_{b,\min }}=\left\{{\left(k_{b,\mathrm{gain}}^{\prime }·\frac{\mathrm{dr}}{2^N-1}+k_{b,\mathrm{offset}}^{\prime }\right)}^{{\gamma }_b}-C_b^{\prime }\right\}& \left(47\right)\end{array}$