Patent Publication Number: US-8525823-B2

Title: Liquid crystal display device

Description:
CROSS-REFERENCE TO RELATED APPLICATION(S) 
     This application is based upon and claims the benefit of priority from the prior Japanese Patent Application No. 2011-65273, filed on Mar. 24, 2011, the entire contents of which are incorporated herein by reference. 
     FIELD 
     Embodiments described herein relate generally to a liquid crystal display device. 
     BACKGROUND 
     A liquid crystal display (LCD) device which has a back light provided with light sources of a plurality of colors is known. In order to improve contrast of a video image to be displayed, to increase a color reproduction gamut and to reduce power consumption, a technique for controlling brightness and color of a light which is emitted from a backlight of an LCD device according to an input video signal is also known. 
     In the technique described above, the emission intensities of light sources of R (red), G (green) and B (blue) colors are set according to a maximum signal value among signal values of R, G and B color components of the input video signal. Further, the signal value to be transmitted to a liquid crystal panel is corrected considering that a light from a light source of each color is likely to leak from a liquid crystal cell of another color. 
     Since the technique is based on a precondition that the R, G and B color components of the input video signal correspond to the colors of the light sources in one-on-one manner respectively, the number of the colors of the light sources are limited to three of the R, G and B colors. 
     According to the above technique, when there is a pixel in which a certain color component has a maximum signal value, the intensity of the light source of the corresponding color is set to a maximum intensity. On the other hand, a lower limit of transmission rate of the liquid crystal panel is larger than zero. Thus, a pixel where the signal value of the color component is zero is difficult to be displayed. For example, when white (R=G=B=266) and red (R=255 and G=B=0) are simultaneously present within a screen, according to the above technique, all of the intensities of the R, G and B light sources are set to a maximum value, and all of the R, G and B signal values transmitted to the liquid crystal panel are set to a maximum value. As a result, the transmission rate becomes maximum, and “white” is accurately displayed. Since the light components of G and B are unnecessary to display red, the signal values to be transmitted to the liquid crystal panel are set to zero (G=B=0). However, since the lights of the G and B light sources leak actually, a desired red is not displayed and a color more whitish than assumed is displayed. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a block diagram of an LCD device according to a first embodiment. 
         FIG. 2A  is a schematic diagram of a backlight of the LCD device. 
         FIG. 2B  is a schematic diagram of a unit light source. 
         FIG. 3  is a flowchart illustrating an operation of the LCD device. 
         FIG. 4A  illustrates an example of an input image. 
         FIG. 4B  is a histogram of a relative gradation value of an input image. 
         FIG. 5A  is a schematic diagram for explaining a case where a white color is displayed in an LCD device according to a comparative example. 
         FIG. 5B  is a schematic diagram for explaining a case where a red color is displayed in an LCD device according to a comparative example. 
         FIG. 5C  is a schematic diagram for explaining a case where a white color is displayed in the LCD device according to the first embodiment. 
         FIG. 5D  is a schematic diagram for explaining a case where a red color is displayed in the LCD device according to the first embodiment. 
         FIG. 6A  is a schematic diagram of a backlight of an LCD device according to a second embodiment. 
         FIG. 6B  is a schematic diagram of another unit light source. 
         FIG. 7A  is a schematic diagram of a backlight of an LCD device according to a third embodiment. 
         FIG. 7B  is a schematic diagram of further another unit light source. 
         FIG. 8  is a block diagram of an LCD device according to a fourth embodiment. 
         FIG. 9  is a block diagram of an LCD device according to a fifth embodiment. 
         FIG. 10  is a conceptual diagram for explaining a convolution operation of the LCD device according to the fifth embodiment. 
         FIG. 11  is a block diagram of an LCD device according to a sixth embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     According to one embodiment, an image display device is provided. The image display device has a liquid crystal panel, a backlight, an intensity setting unit, a presumption unit, a signal correction unit, an error calculation unit and a control unit. 
     The backlight has a plurality of light sources which emit lights having different peak wavelengths. Emission intensities of the light sources are independently controllable, respectively. 
     The intensity setting unit sets intensities of the plurality of light sources, respectively. The presumption unit presumes color information of a transmitted light to be obtained when a mixture of lights emitted from the light sources at the intensities passes through the liquid crystal panel, based on intensity information representing the intensities set by the intensity setting unit. The signal correction unit corrects an input video signal according to the color information, and obtains a corrected video signal. The error calculation unit presumes a display image to be obtained when the liquid crystal panel receives the corrected video signal and the mixture light enters into the liquid crystal panel. The error calculation unit calculates display errors in brightness and color between the presumed display image and an input image corresponding to the input video signal. The control unit controls to set the intensities of the light sources as the emission intensities of the backlight so that the display errors obtained from the error calculation unit can be minimum. 
     Hereinafter, further embodiments will be described with reference to the drawings. In the drawings, the same reference numerals denote the same or similar portions respectively. 
     A first embodiment will be described with reference to  FIG. 1 . 
       FIG. 1  is a block diagram of an LCD device  100  according to the first embodiment. The LCD device  100  according to the embodiment is provided with a color conversion unit  102 , an intensity setting unit  104 , a color presumption unit  106 , a signal correction unit  108 , an error calculation unit  110 , a control unit  112 , a liquid crystal control unit  114 , a light source control unit  115 , and an image display unit  120 . 
     The image display unit  120  is provided with a backlight  119  and a liquid crystal panel  118 . The backlight  119  has light sources of a plurality of colors having different emission peak wavelengths. The backlight  119  can modulate an intensity of a light emitted through a whole surface of the backlight collectively. The liquid crystal panel  118  modulates transmittance i.e. transmission rate or reflectance i.e. reflection rate of the light from the backlight  119 . The following example shows a case where the backlight  119  includes light-emitting diode (LED) light sources of three primary colors of R, G and B whose intensities can be independently controlled. 
     The color conversion unit  102  performs gamma conversion and color conversion of an input video signal  101 , and obtains a converted video signal  103 . However, when the input video signal  101  is subjected to gamma conversion and color conversion outside the LCD device  100  in advance, the input video signal  101  may be used as the video signal  103  as it is. In this case, the LCD device  100  does not need necessarily to provided with the color conversion unit  102 . 
     The intensity setting unit  104  outputs a plurality of pieces of combination information sequentially. The pieces of combination information are obtained by changing gradation values of light source intensities of R, G, and B colors within a range from a minimum value to a maximum value. The pieces of combination information are previously stored in a lookup table, as light source intensity information  105 . The outputted light source intensity information  105  is provided to the color presumption unit  106  and the control unit  112 . The light source intensity information  105  is a set of information representing the intensity of the light source of each color. For example, in the case of three primary colors of R, G and B, the light source intensity information  105  represents a combination of information of an intensity of an R light source (a red light source), information of an intensity of a G light source (a green light source), and information of an intensity of a B light source (a blue light source). 
     The color presumption unit  106  presumes color information  107  of a transmitted light after a mixture of lights which is emitted from the light sources of the respective colors according to the light source intensity information  105  passes through the liquid crystal panel. The color presumption unit  106  provides the presumed color information  107  to the signal correction unit  108 . 
     The signal correction unit  108  calculates a corrected video signal  109  based on the color-converted video signal  103  and the color information  107  of the transmitted light. The signal correction unit  108  provides the calculated corrected video signal  109  to the error calculation unit  110  and the control unit  112 . The error calculation unit  110  calculates an error  111  to be caused at the time of video displaying, based on the corrected video signal  109  and the color-converted video signal  103 . The error  111  is calculated with respect to each of the pieces of light source intensity information  105  outputted sequentially as described above. 
     The control unit  112  sets a piece of light source intensity information which makes the error  111  minimum among the pieces of light source intensity information  105 , as emission intensity information  113  of the light sources. The control unit  112  provides the set emission intensity information  113  to the light source control unit  115 . 
     Further, the control unit  112  provides a corrected video signal  109   a  among the corrected video signals  109  which corresponds to the pieces of light source intensity information  105 , to the liquid crystal control unit  114 . The corrected video signal  109   a  is obtained when the light sources perform light emission according to the emission intensity information  113 . The liquid crystal control unit  114  generates a liquid crystal control signal  116  based on the corrected video signal  109   a , and displays the corrected video signal  109   a  on the liquid crystal panel  118 . The light source control unit  115  generates a light source control signal  117  based on the emission intensity information  113 , and causes the backlight  119  to emit light corresponding to the emission intensity information  113 . 
       FIG. 2A  is a schematic diagram of the backlight  119  according to the embodiment. The backlight  119  is provided with a plurality of light sources  121  arranged in a matrix form. Each light source  121  includes an R light source  122 , a G light source  123 , and a B light source  124  as a unit light source as illustrated in  FIG. 2B . Each of emission intensities of the R light source  122 , the G light source  123 , and the B light source  124  can be independently controlled. The same emission intensity is set to all of the R light sources  122  included in the light sources  121  of the backlight  119 . Similarly, the same emission intensity is set to all of the G light sources  123  included in the light sources  121  of the backlight  119 . Further, similarly, the same emission intensity is set to all of the B light sources  124  included in the light sources  121  of the backlight  119 . 
     The configuration of the backlight illustrated in  FIG. 2A  is exemplary, and the backlight may have a different configuration. For example, the light sources of the backlight  119  are not limited to the light sources of three colors of R, G, and B, and the backlight  119  may include light sources of four or more colors having different peak wavelengths, or light sources of two colors having different peak wavelengths. 
       FIG. 3  is a flowchart illustrating an operation of the LCD device  100  according to the embodiment. In step S 201 , the color conversion unit  102  performs color conversion of the input video signal  101 , and calculates the color-converted video signal  103 . Specifically, the color conversion unit  102  performs gamma conversion according to Formula 1 with respect to respective gradation values of R, G, and B sub pixels which are arranged in respective pixels of the input video signal  101 . 
     
       
         
           
             
               
                 
                   
                     
                       
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     In Formula 1, S in R(x, y), S in G(x, y) and S in B(x, y) represent gradation values of sub pixels of R, G, and B colors at coordinates (x, y) of the input video signal, and the gradation values are represented by 8 bits (a value 0 to a value 255). When gamma conversion is performed with respect to the gradation values S in R(x, y), S in G(x, y) and S in B(x, y) of the input video signal, gradation values L in R(x, y), L in G(x, y) and L in B(x, y) are obtained. The gradation values L in G(x, y), L in G(x, y) and L in B(x, y) are represented by relative values of zero (0) to one (1). γ represents a gamma coefficient. In the embodiment, gamma conversion is performed according to Formula 1, but processing of gamma conversion may be performed with reference to a previously prepared look-up table in which a gradation value of the input video signal is associated with a gradation value after gamma conversion. 
     The color conversion unit  102  performs the above described conversion of the values of the R, G, and B sub pixels of all pixels of the input video signal. The color conversion unit  102  obtains tristimulus values X in (x, y), Y in (x, y) and Z in (x, y) from the gradation values L in G(x, y), L in G(x, y) and L in B(x, y) of the input video signal based on Formula 2. 
     
       
         
           
             
               
                 
                   
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     “M” of Formula 2 represents a 3×3 color conversion matrix. The color conversion matrix is used for changing a color space. The color conversion matrix is appropriately selected according to characteristics of an output device. The tristimulus values X in (x, y), Y in (x, y) and Z in (x, y) may be calculated for each pixel based on the gradation values L in R(x, y), L in G(x, y) and L in B(x, y) of the input video signal using the color conversion matrix of Formula 2. Alternately, the tristimulus values X in (x, y), Y in (x, y) and Z in (x, y) may be calculated for each pixel with reference to a look-up table which stores a relation between the tristimulus values X in (x, y), Y in (x, y) and Z in (x, y) obtained by color conversion and the gradation values L in R(x, y), L in G(x, y) and L in B(x, y). The color-converted input video signal  103  is input to the signal correction unit  108  and the error calculation unit  110 . 
     On the other hand, in step S 202 , the intensity setting unit  104  sets the light source intensity information  105  of R, G, and B and provides the light source intensity information  105  to the color presumption unit  106 . As described above, the intensity setting unit  104  according to the embodiment provides a plurality of pieces of combination information obtained by changing light source intensities of R, G, and B colors within the range from the minimum value to the maximum value, to the presumption unit  106 . 
     For example, when the light source intensity of each color is represented in 8 bits, the number of steps of the intensity of each color is 256. Thus, intensities of three colors of R, G, and B have (2 8 ) 3  (=16,777,216) combinations. As will be described below as another embodiment, the intensity setting unit  104  may be configured to set the light source intensity information  105  of each of a plurality of colors which becomes a candidate of emission intensity  105 , based on the color-converted video signal  103 . In the case, the intensity setting unit  104  provides the light source intensity information  105  of the candidate to the color presumption unit  106 . 
     Specifically, the intensity setting unit  104  may provide some of the combinations of the steps of the intensity of each color rather than all of combinations to the color presumption unit  106 . For example, about 1000 steps (by 10 steps for each color of R, G and B) may be used. Further, as will be described below, the intensity setting unit  104  may be configured to update the light source intensity information  105  according to the error  111 . 
     In step S 203 , the color presumption unit  106  presumes color information of the transmitted light after the mixture of the lights from the light sources of respective colors passes through the liquid crystal panel. The color information presumed by the color presumption unit  106  includes first, second and third tristimulus value of the transmitted light. 
     The first tristimulus value is a value of the transmitted light obtained when the mixture light is irradiated to the R pixel (gradation value: R=255, G=B=0) of the liquid crystal panel. The second tristimulus value is a value of the transmitted light obtained when the mixture light is irradiated to the G pixel (gradation value: G=255, R=B=0). The third tristimulus value is a value of the transmitted light obtained when the mixture light is irradiated to the B pixel (gradation value: B=255, R=G=0). 
     Specifically, the tristimulus values to be obtained when the light sources of the respective colors emit monochromatic light are measured in advance. Then, the color presumption unit  106  adds the values obtained by multiplying the respective tristimulus values obtained at the time of monochromatic light emission by respective emission intensities of the light sources of the colors, so as to presume the tristimulus values of the mixture light. The color presumption unit  106  provides the presumed tristimulus values to the signal correction unit  108 . 
     The tristimulus values of the mixture light obtained when the light sources of R, G, and B colors emit light at intensities R BL , G BL  and B BL  are calculated by Formulae 3-1, 3-2 and 3-3. The formula 3-1 is a formula for obtaining tristimulus values X RW′ , Y RW′  and Z RW′  of the transmitted light obtained when the mixture light is irradiated to the R pixel (gradation value: R=255, G=B=0). The formula 3-2 is a formula for obtaining tristimulus values X GW′ , Y GW′  and Z GW′  of the transmitted light obtained when the mixture light is irradiated to the G pixel (gradation value: G=255, R=B=0). The formula 3-3 is a formula for obtaining tristimulus values X BW′ , Y BW′  and Z BW′  of the transmitted light obtained when the mixture light is irradiated to the B pixel (gradation value: B=255, R=G=0). Hereinafter, the value denoted by one or more English characters with “prime”, like X RW′ , represents an actually displayed value. 
     
       
         
           
             
               
                 
                   
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     In Formulae 3-1, 3-2 and 3-3, X RG , Y RG  and Z RG  represent an X component, a Y component, and a Z component of the tristimulus values of a light of the G light source passing through the R pixel, respectively. X GB , Y GB , Z GB  represent an X component, a Y component, and a Z component of the tristimulus values of a light of the B light source passing through the G pixel, respectively. X BR , Y BR , Z BR  represent an X component, a Y component, and a Z component of the tristimulus values of a light of the R light source passing through the B pixel, respectively. The same notation is applied to components of the other tristimulus values. 
     In step S 204 , the signal correction unit  108  produces a corrected video signal  109  for displaying the color-converted video signal  103  obtained when the mixture light corresponding to the transmitted light is irradiated to the liquid crystal panel  118 , based on the presumed color information  107  of the transmitted light. Specifically, correction signal values R LC (x, y), G LC (x, y), B LC (x, y) of the liquid crystal panel are calculated based on the tristimulus values of the mixture light and the tristimulus values X in (x, y), Y in (x, y) and Z in (x, y) of the video signal  103  of each pixel as in Formula 4. 
     
       
         
           
             
               
                 
                   
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                                   , 
                                   y 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               
                                 Y 
                                 in 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   x 
                                   , 
                                   y 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               
                                 Z 
                                 in 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   x 
                                   , 
                                   y 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     In Formulae 3-1, 3-2, 3-3 and 4, light leakage from the light sources arising when black is displayed on the liquid crystal panel  118  is not considered. The following Formulae 5 to 7 may be used for taking the light leakage into account. 
     Specifically, tristimulus values X KW′ , Y KW′  and Z KW′  of a light which are given when black is displayed on the liquid crystal panel are shown according to Formula 5. Formula 6 represents the relation among the tristimulus values X KW′ , Y KW′  and Z KW′  which is obtained when black is displayed, the tristimulus values X in (x, y), Y in (x, y) and Z in (x, y) of the color-converted video signal, and the correction signal values R LC (x, y), G LC (x, y), B LC (x, y). The correction signal values R LC (x, y), G LC (x, y) and B LC (x, y) can be calculated by Formula 7. 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             X 
                             
                               KW 
                               ′ 
                             
                           
                         
                       
                       
                         
                           
                             Y 
                             
                               KW 
                               ′ 
                             
                           
                         
                       
                       
                         
                           
                             Z 
                             
                               KW 
                               ′ 
                             
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       [ 
                       
                         
                           
                             
                               X 
                               KR 
                             
                           
                           
                             
                               X 
                               KG 
                             
                           
                           
                             
                               X 
                               KB 
                             
                           
                         
                         
                           
                             
                               Y 
                               KR 
                             
                           
                           
                             
                               Y 
                               KG 
                             
                           
                           
                             
                               Y 
                               KB 
                             
                           
                         
                         
                           
                             
                               Z 
                               KR 
                             
                           
                           
                             
                               Z 
                               KG 
                             
                           
                           
                             
                               Z 
                               KB 
                             
                           
                         
                       
                       ] 
                     
                     ⁡ 
                     
                       [ 
                       
                         
                           
                             
                               R 
                               BL 
                             
                           
                         
                         
                           
                             
                               G 
                               BL 
                             
                           
                         
                         
                           
                             
                               B 
                               BL 
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             
                               X 
                               in 
                             
                             ⁡ 
                             
                               ( 
                               
                                 x 
                                 , 
                                 y 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             
                               Y 
                               in 
                             
                             ⁡ 
                             
                               ( 
                               
                                 x 
                                 , 
                                 y 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             
                               Z 
                               in 
                             
                             ⁡ 
                             
                               ( 
                               
                                 x 
                                 , 
                                 y 
                               
                               ) 
                             
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       [ 
                       
                         
                           
                             
                               ( 
                               
                                 
                                   X 
                                   
                                     RW 
                                     ′ 
                                   
                                 
                                 - 
                                 
                                   X 
                                   
                                     KW 
                                     ′ 
                                   
                                 
                               
                               ) 
                             
                           
                           
                             
                               ( 
                               
                                 
                                   X 
                                   
                                     GW 
                                     ′ 
                                   
                                 
                                 - 
                                 
                                   X 
                                   
                                     KW 
                                     ′ 
                                   
                                 
                               
                               ) 
                             
                           
                           
                             
                               ( 
                               
                                 
                                   X 
                                   
                                     BW 
                                     ′ 
                                   
                                 
                                 - 
                                 
                                   X 
                                   
                                     KW 
                                     ′ 
                                   
                                 
                               
                               ) 
                             
                           
                         
                         
                           
                             
                               ( 
                               
                                 
                                   Y 
                                   
                                     RW 
                                     ′ 
                                   
                                 
                                 - 
                                 
                                   Y 
                                   
                                     KW 
                                     ′ 
                                   
                                 
                               
                               ) 
                             
                           
                           
                             
                               ( 
                               
                                 
                                   Y 
                                   
                                     GW 
                                     ′ 
                                   
                                 
                                 - 
                                 
                                   Y 
                                   
                                     KW 
                                     ′ 
                                   
                                 
                               
                               ) 
                             
                           
                           
                             
                               ( 
                               
                                 
                                   Y 
                                   
                                     BW 
                                     ′ 
                                   
                                 
                                 - 
                                 
                                   Y 
                                   
                                     KW 
                                     ′ 
                                   
                                 
                               
                               ) 
                             
                           
                         
                         
                           
                             
                               ( 
                               
                                 
                                   Z 
                                   
                                     RW 
                                     ′ 
                                   
                                 
                                 - 
                                 
                                   Z 
                                   
                                     KW 
                                     ′ 
                                   
                                 
                               
                               ) 
                             
                           
                           
                             
                               ( 
                               
                                 
                                   Z 
                                   
                                     GW 
                                     ′ 
                                   
                                 
                                 - 
                                 
                                   Z 
                                   
                                     KW 
                                     ′ 
                                   
                                 
                               
                               ) 
                             
                           
                           
                             
                               ( 
                               
                                 
                                   Z 
                                   
                                     BW 
                                     ′ 
                                   
                                 
                                 - 
                                 
                                   Z 
                                   
                                     KW 
                                     ′ 
                                   
                                 
                               
                               ) 
                             
                           
                         
                       
                       ] 
                     
                     ⁢ 
                     
                         
                       
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     R 
                                     LC 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     
                                       x 
                                       , 
                                       y 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   
                                     G 
                                     LC 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     
                                       x 
                                       , 
                                       y 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   
                                     B 
                                     LC 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     
                                       x 
                                       , 
                                       y 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           ] 
                         
                         + 
                         
                           [ 
                           
                             
                               
                                 
                                   X 
                                   
                                     KW 
                                     ′ 
                                   
                                 
                               
                             
                             
                               
                                 
                                   Y 
                                   
                                     KW 
                                     ′ 
                                   
                                 
                               
                             
                             
                               
                                 
                                   Z 
                                   
                                     KW 
                                     ′ 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             
                               R 
                               LC 
                             
                             ⁡ 
                             
                               ( 
                               
                                 x 
                                 , 
                                 y 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             
                               G 
                               LC 
                             
                             ⁡ 
                             
                               ( 
                               
                                 x 
                                 , 
                                 y 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             
                               B 
                               LC 
                             
                             ⁡ 
                             
                               ( 
                               
                                 x 
                                 , 
                                 y 
                               
                               ) 
                             
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       
                         [ 
                         
                           
                             
                               
                                 ( 
                                 
                                   
                                     X 
                                     
                                       RW 
                                       ′ 
                                     
                                   
                                   - 
                                   
                                     X 
                                     
                                       KW 
                                       ′ 
                                     
                                   
                                 
                                 ) 
                               
                             
                             
                               
                                 ( 
                                 
                                   
                                     X 
                                     
                                       GW 
                                       ′ 
                                     
                                   
                                   - 
                                   
                                     X 
                                     
                                       KW 
                                       ′ 
                                     
                                   
                                 
                                 ) 
                               
                             
                             
                               
                                 ( 
                                 
                                   
                                     X 
                                     
                                       BW 
                                       ′ 
                                     
                                   
                                   - 
                                   
                                     X 
                                     
                                       KW 
                                       ′ 
                                     
                                   
                                 
                                 ) 
                               
                             
                           
                           
                             
                               
                                 ( 
                                 
                                   
                                     Y 
                                     
                                       RW 
                                       ′ 
                                     
                                   
                                   - 
                                   
                                     Y 
                                     
                                       KW 
                                       ′ 
                                     
                                   
                                 
                                 ) 
                               
                             
                             
                               
                                 ( 
                                 
                                   
                                     Y 
                                     
                                       GW 
                                       ′ 
                                     
                                   
                                   - 
                                   
                                     Y 
                                     
                                       KW 
                                       ′ 
                                     
                                   
                                 
                                 ) 
                               
                             
                             
                               
                                 ( 
                                 
                                   
                                     Y 
                                     
                                       BW 
                                       ′ 
                                     
                                   
                                   - 
                                   
                                     Y 
                                     
                                       KW 
                                       ′ 
                                     
                                   
                                 
                                 ) 
                               
                             
                           
                           
                             
                               
                                 ( 
                                 
                                   
                                     Z 
                                     
                                       RW 
                                       ′ 
                                     
                                   
                                   - 
                                   
                                     Z 
                                     
                                       KW 
                                       ′ 
                                     
                                   
                                 
                                 ) 
                               
                             
                             
                               
                                 ( 
                                 
                                   
                                     Z 
                                     
                                       GW 
                                       ′ 
                                     
                                   
                                   - 
                                   
                                     Z 
                                     
                                       KW 
                                       ′ 
                                     
                                   
                                 
                                 ) 
                               
                             
                             
                               
                                 ( 
                                 
                                   
                                     Z 
                                     
                                       BW 
                                       ′ 
                                     
                                   
                                   - 
                                   
                                     Z 
                                     
                                       KW 
                                       ′ 
                                     
                                   
                                 
                                 ) 
                               
                             
                           
                         
                         ] 
                       
                       
                         - 
                         1 
                       
                     
                     ⁢ 
                     
                         
                       
                         [ 
                         
                           
                             
                               
                                 
                                   
                                     X 
                                     in 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     
                                       x 
                                       , 
                                       y 
                                     
                                     ) 
                                   
                                 
                                 - 
                                 
                                   X 
                                   
                                     KW 
                                     ′ 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   
                                     Y 
                                     in 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     
                                       x 
                                       , 
                                       y 
                                     
                                     ) 
                                   
                                 
                                 - 
                                 
                                   Y 
                                   
                                     KW 
                                     ′ 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   
                                     Z 
                                     in 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     
                                       x 
                                       , 
                                       y 
                                     
                                     ) 
                                   
                                 
                                 - 
                                 
                                   Z 
                                   
                                     KW 
                                     ′ 
                                   
                                 
                               
                             
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
     When pixel values of the correction signal values R LC (x, y), G LC (x, y) and B LC (x, y) are not within the range of zero (0) to one (1), the pixel values of the correction signal values R LC (x, y), G LC (x, y) and B LC (x, y) are corrected according to Formula 8, so that correction signal values R′ LC (x, y), G LC (x, y) and B LC (x, y) are obtained. 
     
       
         
           
             
               
                 
                   
                     
                       R 
                       LC 
                       ′ 
                     
                     ⁡ 
                     
                       ( 
                       
                         x 
                         , 
                         y 
                       
                       ) 
                     
                   
                   = 
                   
                     { 
                     
                       
                         
                           
                             
                               
                                 0 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         R 
                                         LC 
                                       
                                       ⁡ 
                                       
                                         ( 
                                         
                                           x 
                                           , 
                                           y 
                                         
                                         ) 
                                       
                                     
                                     &lt; 
                                     0 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   
                                     R 
                                     LC 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     
                                       x 
                                       , 
                                       y 
                                     
                                     ) 
                                   
                                 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     0 
                                     ≤ 
                                     
                                       
                                         R 
                                         LC 
                                       
                                       ⁡ 
                                       
                                         ( 
                                         
                                           x 
                                           , 
                                           y 
                                         
                                         ) 
                                       
                                     
                                     ≤ 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               
                                 1 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         R 
                                         LC 
                                       
                                       ⁡ 
                                       
                                         ( 
                                         
                                           x 
                                           , 
                                           y 
                                         
                                         ) 
                                       
                                     
                                     &gt; 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         ⁢ 
                         
                           
 
                         
                         ⁢ 
                         
                           
                             G 
                             LC 
                             ′ 
                           
                           ⁡ 
                           
                             ( 
                             
                               x 
                               , 
                               y 
                             
                             ) 
                           
                         
                       
                       = 
                       
                         { 
                         
                           
                             
                               
                                 
                                   
                                     0 
                                     ⁢ 
                                     
                                       ( 
                                       
                                         
                                           
                                             G 
                                             LC 
                                           
                                           ⁡ 
                                           
                                             ( 
                                             
                                               x 
                                               , 
                                               y 
                                             
                                             ) 
                                           
                                         
                                         &lt; 
                                         0 
                                       
                                       ) 
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       
                                         G 
                                         LC 
                                       
                                       ⁡ 
                                       
                                         ( 
                                         
                                           x 
                                           , 
                                           y 
                                         
                                         ) 
                                       
                                     
                                     ⁢ 
                                     
                                       ( 
                                       
                                         0 
                                         ≤ 
                                         
                                           
                                             G 
                                             LC 
                                           
                                           ⁡ 
                                           
                                             ( 
                                             
                                               x 
                                               , 
                                               y 
                                             
                                             ) 
                                           
                                         
                                         ≤ 
                                         1 
                                       
                                       ) 
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     1 
                                     ⁢ 
                                     
                                       ( 
                                       
                                         
                                           
                                             G 
                                             LC 
                                           
                                           ⁡ 
                                           
                                             ( 
                                             
                                               x 
                                               , 
                                               y 
                                             
                                             ) 
                                           
                                         
                                         &gt; 
                                         1 
                                       
                                       ) 
                                     
                                   
                                 
                               
                             
                             ⁢ 
                             
                               
 
                             
                             ⁢ 
                             
                               
                                 B 
                                 LC 
                                 ′ 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   x 
                                   , 
                                   y 
                                 
                                 ) 
                               
                             
                           
                           = 
                           
                             { 
                             
                               
                                 
                                   
                                     0 
                                     ⁢ 
                                     
                                       ( 
                                       
                                         
                                           
                                             B 
                                             LC 
                                           
                                           ⁡ 
                                           
                                             ( 
                                             
                                               x 
                                               , 
                                               y 
                                             
                                             ) 
                                           
                                         
                                         &lt; 
                                         0 
                                       
                                       ) 
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       
                                         B 
                                         LC 
                                       
                                       ⁡ 
                                       
                                         ( 
                                         
                                           x 
                                           , 
                                           y 
                                         
                                         ) 
                                       
                                     
                                     ⁢ 
                                     
                                       ( 
                                       
                                         0 
                                         ≤ 
                                         
                                           
                                             B 
                                             LC 
                                           
                                           ⁡ 
                                           
                                             ( 
                                             
                                               x 
                                               , 
                                               y 
                                             
                                             ) 
                                           
                                         
                                         ≤ 
                                         1 
                                       
                                       ) 
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     1 
                                     ⁢ 
                                     
                                       ( 
                                       
                                         
                                           
                                             B 
                                             LC 
                                           
                                           ⁡ 
                                           
                                             ( 
                                             
                                               x 
                                               , 
                                               y 
                                             
                                             ) 
                                           
                                         
                                         &gt; 
                                         1 
                                       
                                       ) 
                                     
                                   
                                 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
     In step S 205 , the error calculation unit  110  calculates the error  111  based on the corrected video signal  109  and the color-converted video signal  103 . When the light sources emit lights at light source intensities R BL , G BL , B BL  respectively and the pixel values of the correction signals R LC (x, y), G LC (x, y) and B LC (x, y) are not within the range of zero (0) to one (1), tristimulus values X′(x, y), Y′(x, y) and Z′(x, y) of the lights displayed on the screen are calculated according to Formula 9. When the correction signal values R LC (x, y), G LC (x, y), B LC (x, y) are all within the range of zero (0) to one (1), the error calculation unit  110  sets the error  111  to zero without calculating the tristimulus values X′(x, y), Y′(x, y) and Z′(x, y). 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             
                               X 
                               ′ 
                             
                             ⁡ 
                             
                               ( 
                               
                                 x 
                                 , 
                                 y 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             
                               Y 
                               ′ 
                             
                             ⁡ 
                             
                               ( 
                               
                                 x 
                                 , 
                                 y 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             
                               Z 
                               ′ 
                             
                             ⁡ 
                             
                               ( 
                               
                                 x 
                                 , 
                                 y 
                               
                               ) 
                             
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       [ 
                       
                         
                           
                             
                               X 
                               
                                 RW 
                                 ′ 
                               
                             
                           
                           
                             
                               X 
                               
                                 GW 
                                 ′ 
                               
                             
                           
                           
                             
                               X 
                               
                                 BW 
                                 ′ 
                               
                             
                           
                         
                         
                           
                             
                               Y 
                               
                                 RW 
                                 ′ 
                               
                             
                           
                           
                             
                               Y 
                               
                                 GW 
                                 ′ 
                               
                             
                           
                           
                             
                               Y 
                               
                                 BW 
                                 ′ 
                               
                             
                           
                         
                         
                           
                             
                               Z 
                               
                                 RW 
                                 ′ 
                               
                             
                           
                           
                             
                               Z 
                               
                                 GW 
                                 ′ 
                               
                             
                           
                           
                             
                               Z 
                               
                                 BW 
                                 ′ 
                               
                             
                           
                         
                       
                       ] 
                     
                     ⁡ 
                     
                       [ 
                       
                         
                           
                             
                               
                                 R 
                                 LC 
                                 ′ 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   x 
                                   , 
                                   y 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               
                                 G 
                                 LC 
                                 ′ 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   x 
                                   , 
                                   y 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               
                                 B 
                                 LC 
                                 ′ 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   x 
                                   , 
                                   y 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
     Further, the error calculation unit  110  calculates errors respectively between the tristimulus values X in (x, y), Y in (x, y), Z in (x, y) of the input video signal  103  and the tristimulus values (X′(x, y), Y′(x, y), Z′(x, y) which are actually displayed in a CIELAB space. The tristimulus values of the color-converted video signal  103  are tristimulus values of an ideal image. On the other hand, the tristimulus values actually displayed are tristimulus values of a display image. Specifically, the tristimulus values X in (x, y), Y in (x, y) and Z in (x, y) and the tristimulus values (X′(x, y), Y′(x, y) and Z′(x, y)) are converted into values L in (x, y), a in (x, y), b in (x, y) and values L′(x, y), a′(x, y), b′(x, y) of the CIELAB space according to Formula 10, respectively. 
     
       
         
           
             
               
                 
                   
                     
                       
                         L 
                         in 
                       
                       ⁡ 
                       
                         ( 
                         
                           x 
                           , 
                           y 
                         
                         ) 
                       
                     
                     = 
                     
                       
                         116 
                         * 
                         
                           
                             ( 
                             
                               
                                 
                                   Y 
                                   in 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     x 
                                     , 
                                     y 
                                   
                                   ) 
                                 
                               
                               
                                 Y 
                                 n 
                               
                             
                             ) 
                           
                           
                             1 
                             3 
                           
                         
                       
                       - 
                       16 
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         a 
                         in 
                       
                       ⁡ 
                       
                         ( 
                         
                           x 
                           , 
                           y 
                         
                         ) 
                       
                     
                     = 
                     
                       500 
                       * 
                       
                         { 
                         
                           
                             
                               ( 
                               
                                 
                                   
                                     X 
                                     in 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     
                                       x 
                                       , 
                                       y 
                                     
                                     ) 
                                   
                                 
                                 
                                   X 
                                   n 
                                 
                               
                               ) 
                             
                             
                               1 
                               3 
                             
                           
                           - 
                           
                             
                               ( 
                               
                                 
                                   
                                     Y 
                                     in 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     
                                       x 
                                       , 
                                       y 
                                     
                                     ) 
                                   
                                 
                                 
                                   Y 
                                   n 
                                 
                               
                               ) 
                             
                             
                               1 
                               3 
                             
                           
                         
                         } 
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         b 
                         in 
                       
                       ⁡ 
                       
                         ( 
                         
                           x 
                           , 
                           y 
                         
                         ) 
                       
                     
                     = 
                     
                       200 
                       * 
                       
                         { 
                         
                           
                             
                               ( 
                               
                                 
                                   
                                     Y 
                                     in 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     
                                       x 
                                       , 
                                       y 
                                     
                                     ) 
                                   
                                 
                                 
                                   Y 
                                   n 
                                 
                               
                               ) 
                             
                             
                               1 
                               3 
                             
                           
                           - 
                           
                             
                               ( 
                               
                                 
                                   
                                     Z 
                                     in 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     
                                       x 
                                       , 
                                       y 
                                     
                                     ) 
                                   
                                 
                                 
                                   Z 
                                   n 
                                 
                               
                               ) 
                             
                             
                               1 
                               3 
                             
                           
                         
                         } 
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         L 
                         ′ 
                       
                       ⁡ 
                       
                         ( 
                         
                           x 
                           , 
                           y 
                         
                         ) 
                       
                     
                     = 
                     
                       
                         116 
                         * 
                         
                           
                             ( 
                             
                               
                                 
                                   Y 
                                   ′ 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     x 
                                     , 
                                     y 
                                   
                                   ) 
                                 
                               
                               
                                 Y 
                                 n 
                               
                             
                             ) 
                           
                           
                             1 
                             3 
                           
                         
                       
                       - 
                       16 
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         a 
                         ′ 
                       
                       ⁡ 
                       
                         ( 
                         
                           x 
                           , 
                           y 
                         
                         ) 
                       
                     
                     = 
                     
                       500 
                       * 
                       
                         { 
                         
                           
                             
                               ( 
                               
                                 
                                   
                                     X 
                                     ′ 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     
                                       x 
                                       , 
                                       y 
                                     
                                     ) 
                                   
                                 
                                 
                                   X 
                                   n 
                                 
                               
                               ) 
                             
                             
                               1 
                               3 
                             
                           
                           - 
                           
                             
                               ( 
                               
                                 
                                   
                                     Y 
                                     ′ 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     
                                       x 
                                       , 
                                       y 
                                     
                                     ) 
                                   
                                 
                                 
                                   Y 
                                   n 
                                 
                               
                               ) 
                             
                             
                               1 
                               3 
                             
                           
                         
                         } 
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         b 
                         ′ 
                       
                       ⁡ 
                       
                         ( 
                         
                           x 
                           , 
                           y 
                         
                         ) 
                       
                     
                     = 
                     
                       200 
                       * 
                       
                         { 
                         
                           
                             
                               ( 
                               
                                 
                                   
                                     Y 
                                     ′ 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     
                                       x 
                                       , 
                                       y 
                                     
                                     ) 
                                   
                                 
                                 
                                   Y 
                                   n 
                                 
                               
                               ) 
                             
                             
                               1 
                               3 
                             
                           
                           - 
                           
                             
                               ( 
                               
                                 
                                   
                                     Z 
                                     ′ 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     
                                       x 
                                       , 
                                       y 
                                     
                                     ) 
                                   
                                 
                                 
                                   Z 
                                   n 
                                 
                               
                               ) 
                             
                             
                               1 
                               3 
                             
                           
                         
                         } 
                       
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
     X n , Y n  and Z n  of Formula 10 represent tristimulus values obtained when the RGB light sources are turned on at a maximum output (when white light is emitted). Further, a display error ΔE(x, y) between the values L in (x, y), a in (x, y) and b in (x, y) and the values L′(x, y), a′(x, y) and b′(x, y) is calculated according to Formula 11. 
     
       
         
           
             
               
                 
                   
                     Δ 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       E 
                       ⁡ 
                       
                         ( 
                         
                           x 
                           , 
                           y 
                         
                         ) 
                       
                     
                   
                   = 
                   
                     
                       
                         
                           
                             
                               
                                 ( 
                                 
                                   
                                     
                                       L 
                                       in 
                                     
                                     ⁡ 
                                     
                                       ( 
                                       
                                         x 
                                         , 
                                         y 
                                       
                                       ) 
                                     
                                   
                                   = 
                                   
                                     
                                       L 
                                       ′ 
                                     
                                     ⁡ 
                                     
                                       ( 
                                       
                                         x 
                                         , 
                                         y 
                                       
                                       ) 
                                     
                                   
                                 
                                 ) 
                               
                               2 
                             
                             + 
                             
                               ( 
                               
                                 
                                   
                                     a 
                                     in 
                                   
                                   ⁢ 
                                   
                                     ( 
                                     
                                       x 
                                       , 
                                       y 
                                     
                                     ) 
                                   
                                 
                                 - 
                               
                             
                           
                         
                       
                       
                         
                           
                             
                               
                                 
                                   
                                     a 
                                     ′ 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     
                                       x 
                                       , 
                                       y 
                                     
                                     ) 
                                   
                                 
                                 ) 
                               
                               2 
                             
                             + 
                             
                               
                                 ( 
                                 
                                   
                                     
                                       b 
                                       in 
                                     
                                     ⁡ 
                                     
                                       ( 
                                       
                                         x 
                                         , 
                                         y 
                                       
                                       ) 
                                     
                                   
                                   - 
                                   
                                     
                                       b 
                                       ′ 
                                     
                                     ⁡ 
                                     
                                       ( 
                                       
                                         x 
                                         , 
                                         y 
                                       
                                       ) 
                                     
                                   
                                 
                                 ) 
                               
                               2 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
     The display error ΔE(x, y) at coordinates (x, y) obtained when the light sources emit light at the light source intensities R BL , G BL , B BL  is calculated as described above. The CIELAB space is an equivalent color space. The display error ΔE(x, y) represents a display error of brightness and a color. The error calculation unit  110  inputs a maximum value among the display errors ΔE(x, y) of all pixels within the screen, to the control unit  112 , as the error  111  corresponding to the light source intensity information  105 . 
     In the embodiment, as described above, the maximum value among the display errors ΔE(x, y) of all of the pixels within the screen is used as the error  111 , but the sum or an average value of the display errors ΔE(x, y) may be used as the error  111 . Further, in the embodiment, the error  111  is set based on the display errors ΔE(x, y) of all of the pixels within the screen, but the error  111  may be set based on the display errors ΔE(x, y) of some pixels extracted from all of the pixels within the screen. 
     The control unit  112  obtains a minimum value from among the errors relating to the plurality of pieces of light source intensity information  105  set by and sequentially outputted from the light source setting unit  104 . The control unit  112  sets the light source intensity information  105  corresponding to the minimum value as the emission intensity information  113 . The control unit  112  provides the obtained emission intensity information  113  to the light source control unit  115 . 
     In step S 206 , to the liquid crystal control unit  114 , the control unit  112  provides the corrected video signal  109   a  corresponding to the emission intensity information  113 , among the corrected video signals  109  corresponding to the pieces of light source intensity information  105 . 
     The corrected video signal  109   a  corresponding to the emission intensity information  113  is a corrected video signal the error of which is minimum. In step S 207 , the liquid crystal control unit  114  provides the liquid crystal control signal  116  to the liquid crystal panel, and displays the corrected video signal  109   a  on the display area of the liquid crystal panel  118 . Further, the light source control unit  115  provides the light source control signal  117  to the backlight  119 , and performs control such that light having intensity according to the emission intensity information  113  is irradiated from the backlight  119 . 
       FIG. 4A  illustrates an example of an input image which is referred to in the following explanation.  FIG. 4B  is a histogram of a relative gradation value of the input image.  FIGS. 5A and 5B  are schematic diagrams to explain displaying by an LCD device according to a comparative example.  FIGS. 5C and 5D  are schematic diagrams to explain displaying according to the embodiment. 
     In  FIG. 4A , the lower half of the input image  400  is a white color area  401 , and the remaining upper half is a red color area  402 . In  FIG. 4B , the relative gradation value is a gradation value represented by a value between 0 and 1.0. In the input image  400  of  FIG. 4A , the relative gradation value of the R component is 1.0 in all of the pixels. The relative gradation values of the G component and the B component are zero (0) in half of the pixels and 1.0 in the remaining half of the pixels. 
     In the comparative example, the light source intensities of R, G and B colors are set according to maximum values of the R, G, and B components of the input image, respectively. When the light source intensities are BL R , BL G  and BL B , BL R  is 1.0, BL G  is 1.0, and BL B  is 1.0. 
       FIG. 5A  is a schematic diagram to be obtained when a white color is displayed by the LCD device according to the comparative example.  FIG. 5B  is a schematic diagram to be obtained when a red color is displayed by the LCD device according to the comparative example. The Lights having intensities according to light source intensities BL R , BL G  and BL B  respectively are emitted from a light source unit  501 , and passes through a liquid crystal panel  502 . In  FIGS. 5A ,  5 B, a graph  503  schematically represents magnitudes of intensity of light to be displayed and a display error ΔE, by upward arrows, respectively. 
     In a pixel displaying a white, assuming that the signal values provided to the liquid crystal panel  502  are denoted as LC R (W), LC G (W) and LC B (W), LC R (W) is set to 1.0, LC G (W) is set to 1.0, and LC B (W) is set to 1.0. The lights from the light sources pass through the pixel, so that an assumed white can be displayed. 
     In  FIG. 5A , X in (W), Y in (W) and Z in (W) are tristimulus values of a white color which is desired to be displayed, and X out (W), Y out (W) and Z out (W) are tristimulus values of a white color which is displayed by the conventional technique. In  FIG. 5B , X in (R), Y in (R) and Z in (R) are tristimulus values of a red color which is desired to be displayed, and X out (R), Y out (R) and Z out (R) are tristimulus values of a red color which is displayed by the conventional technique. 
     In a pixel displaying a red, assuming that light source intensities of the respective colors are BL R =1.0, BL G =1.0, and BL B =1.0, signal values of the respective colors provided to the LC panel are set to LC R (R)=1.0, LC G (R)=0.0, and LC B (R)=0.0. The red is displayed such that light of the G light source and light of the B light source are blocked by a liquid crystal cell. Even though the signal values of G and B of the liquid crystal panel are set to zero, light leaks from the G and B light sources so that the display error ΔE illustrated in  FIG. 5B  occurs actually. For this reason, in the actually displayed light, light of the G component and light of the B component increase so that the red looks whitish. 
       FIG. 5C  is a schematic diagram to be obtained when a white color is displayed according to the embodiment.  FIG. 5D  is a schematic diagram to be obtained when a red color is displayed according to the embodiment. In the embodiment, the error calculation unit  110  presumes an error between the tristimulus values of the display image obtained when the light source intensity is set to a certain value and the tristimulus values of the ideal image, and sets the light source intensity so as to minimize the error. 
     Thus, when the input image  400  of  FIG. 4A  is inputted, as illustrated in  FIGS. 5C and 5D , the light source intensities of the R, G and B colors are set so that the display error ΔE for displaying the red and the display error ΔE for display the white can have the same magnitude and be minimized. 
     As illustrated in  FIGS. 5C and 5D , since the light intensities of G and B according to the embodiment are weaker than those of the conventional technique, as illustrated in  FIGS. 5A and 5B . According to the embodiment, the display error of the white slightly occurs, but an error occurring when the red is displayed can be suppressed to a small value. Thus, an image close to an assumed color can be displayed as a whole. In  FIGS. 5C and 5D , X′ out (W), Y′ out (W) and Z′ out (W) are tristimulus values of the white color displayed by the LCD device according to the embodiment, and X′ out (R), Y′ out (R) and Z′ out (R) are tristimulus values of the red color displayed by the LCD device according to the embodiment. 
     In the embodiment, the number of colors of light sources is not limited, and an image can be displayed with a minimum error between an image desired to be displayed and an actually displayed image. 
     A second embodiment will be described below. The basic configuration of an LCD device according to the second embodiment is same as that of the LCD device of  FIG. 1 . 
       FIG. 6A  is a schematic diagram of a backlight  119   a  according to the second embodiment. The backlight  119   a  according to the second embodiment is provided with a plurality of light sources  121   a . Each of the light sources  121   a  includes an R light source  122 , a G light source  123 , a B light source  124 , and a Cy light source  125  (cyan), as a fourth light source, as illustrated in  FIG. 6B . In the embodiment, a Cy light source  125  of a cyan color is employed as the fourth light source, but a light source of a color other than a cyan may be used as the fourth light source. Further, the number of colors of light sources may be five or more. 
     In the case of the second embodiment, in an LCD device  100  of  FIG. 1 , an intensity setting unit  104  sets light source intensity information  105  of R, G, B and Cy, and provides the light source intensity information  105  of R, G, B and Cy to an color presumption unit  106 . In the same manner as in the first embodiment, the color presumption unit  106  presumes tristimulus values of a light obtained after a mixture of lights from the light sources of the respective colors passes through a liquid crystal panel. Specifically, in the embodiment, the tristimulus values of the mixture light are calculated by Formulae 12-1, 12-2 and 12-3. 
     Formula 12-1 is a formula for calculating tristimulus values of the transmitted light obtained when the mixture light is irradiated to an R pixel. Formula 12-2 is a formula for calculating tristimulus values of transmitted light obtained when the mixture light is irradiated to a G pixel. Formula 12-3 is a formula for calculating tristimulus values of transmitted light obtained when the mixture light is irradiated to a B pixel. 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             X 
                             
                               RW 
                               ′ 
                             
                           
                         
                       
                       
                         
                           
                             Y 
                             
                               RW 
                               ′ 
                             
                           
                         
                       
                       
                         
                           
                             Z 
                             
                               RW 
                               ′ 
                             
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       [ 
                       
                         
                           
                             
                               X 
                               RR 
                             
                           
                           
                             
                               X 
                               RG 
                             
                           
                           
                             
                               X 
                               RB 
                             
                           
                           
                             
                               X 
                               RC 
                             
                           
                         
                         
                           
                             
                               Y 
                               RR 
                             
                           
                           
                             
                               Y 
                               RG 
                             
                           
                           
                             
                               Y 
                               RB 
                             
                           
                           
                             
                               Y 
                               RC 
                             
                           
                         
                         
                           
                             
                               Z 
                               RR 
                             
                           
                           
                             
                               Z 
                               RG 
                             
                           
                           
                             
                               Z 
                               RB 
                             
                           
                           
                             
                               Z 
                               RC 
                             
                           
                         
                       
                       ] 
                     
                     ⁡ 
                     
                       [ 
                       
                         
                           
                             
                               R 
                               BL 
                             
                           
                         
                         
                           
                             
                               G 
                               BL 
                             
                           
                         
                         
                           
                             
                               B 
                               BL 
                             
                           
                         
                         
                           
                             
                               C 
                               BL 
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   
                     12 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     1 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             X 
                             
                               GW 
                               ′ 
                             
                           
                         
                       
                       
                         
                           
                             Y 
                             
                               GW 
                               ′ 
                             
                           
                         
                       
                       
                         
                           
                             Z 
                             
                               GW 
                               ′ 
                             
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       [ 
                       
                         
                           
                             
                               X 
                               GR 
                             
                           
                           
                             
                               X 
                               GG 
                             
                           
                           
                             
                               X 
                               GB 
                             
                           
                           
                             
                               X 
                               GC 
                             
                           
                         
                         
                           
                             
                               Y 
                               GR 
                             
                           
                           
                             
                               Y 
                               GG 
                             
                           
                           
                             
                               Y 
                               GB 
                             
                           
                           
                             
                               Y 
                               GC 
                             
                           
                         
                         
                           
                             
                               Z 
                               GR 
                             
                           
                           
                             
                               Z 
                               GG 
                             
                           
                           
                             
                               Z 
                               GB 
                             
                           
                           
                             
                               Z 
                               GC 
                             
                           
                         
                       
                       ] 
                     
                     ⁡ 
                     
                       [ 
                       
                         
                           
                             
                               R 
                               BL 
                             
                           
                         
                         
                           
                             
                               G 
                               BL 
                             
                           
                         
                         
                           
                             
                               B 
                               BL 
                             
                           
                         
                         
                           
                             
                               C 
                               BL 
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   
                     12 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     2 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             X 
                             
                               BW 
                               ′ 
                             
                           
                         
                       
                       
                         
                           
                             Y 
                             
                               BW 
                               ′ 
                             
                           
                         
                       
                       
                         
                           
                             Z 
                             
                               BW 
                               ′ 
                             
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       [ 
                       
                         
                           
                             
                               X 
                               BR 
                             
                           
                           
                             
                               X 
                               BG 
                             
                           
                           
                             
                               X 
                               BB 
                             
                           
                           
                             
                               X 
                               BC 
                             
                           
                         
                         
                           
                             
                               Y 
                               BR 
                             
                           
                           
                             
                               Y 
                               BG 
                             
                           
                           
                             
                               Y 
                               BB 
                             
                           
                           
                             
                               Y 
                               BC 
                             
                           
                         
                         
                           
                             
                               Z 
                               BR 
                             
                           
                           
                             
                               Z 
                               BG 
                             
                           
                           
                             
                               Z 
                               BB 
                             
                           
                           
                             
                               Z 
                               BC 
                             
                           
                         
                       
                       ] 
                     
                     ⁡ 
                     
                       [ 
                       
                         
                           
                             
                               R 
                               BL 
                             
                           
                         
                         
                           
                             
                               G 
                               BL 
                             
                           
                         
                         
                           
                             
                               B 
                               BL 
                             
                           
                         
                         
                           
                             
                               C 
                               BL 
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   
                     12 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     3 
                   
                   ) 
                 
               
             
           
         
       
     
     In Formulae 12-1, 12-2 and 12-3, X RC  represents an X component of a light of the Cy light source passing through the R pixel, Y RC  represents a Y component of a light of the Cy light source passing through the R pixel, and Z RC  represents a Z component of a light of the Cy light source passing through the R pixel. The same notation is applied to the remaining components of the tristimulus values. 
     Then, a signal correction unit  108  of  FIG. 1  obtains a corrected video signal  109  for displaying a color-converted video signal  103  when the mixture light corresponding to the transmitted light is irradiated to a liquid crystal panel  118 , based on presumed color information  107  of the transmitted light. Specifically, correction signal values R LC (x, y), G LC (x, y), B LC (x, y) of the liquid crystal panel are calculated by Formula 13. 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             
                               R 
                               LC 
                             
                             ⁡ 
                             
                               ( 
                               
                                 x 
                                 , 
                                 y 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             
                               G 
                               LC 
                             
                             ⁡ 
                             
                               ( 
                               
                                 x 
                                 , 
                                 y 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             
                               B 
                               LC 
                             
                             ⁡ 
                             
                               ( 
                               
                                 x 
                                 , 
                                 y 
                               
                               ) 
                             
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       
                         [ 
                         
                           
                             
                               
                                 X 
                                 
                                   RW 
                                   ′ 
                                 
                               
                             
                             
                               
                                 X 
                                 
                                   GW 
                                   ′ 
                                 
                               
                             
                             
                               
                                 X 
                                 
                                   BW 
                                   ′ 
                                 
                               
                             
                           
                           
                             
                               
                                 Y 
                                 
                                   RW 
                                   ′ 
                                 
                               
                             
                             
                               
                                 Y 
                                 
                                   GW 
                                   ′ 
                                 
                               
                             
                             
                               
                                 Y 
                                 
                                   BW 
                                   ′ 
                                 
                               
                             
                           
                           
                             
                               
                                 Z 
                                 
                                   RW 
                                   ′ 
                                 
                               
                             
                             
                               
                                 Z 
                                 
                                   GW 
                                   ′ 
                                 
                               
                             
                             
                               
                                 Z 
                                 
                                   BW 
                                   ′ 
                                 
                               
                             
                           
                         
                         ] 
                       
                       
                         - 
                         1 
                       
                     
                     ⁡ 
                     
                       [ 
                       
                         
                           
                             
                               
                                 X 
                                 in 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   x 
                                   , 
                                   y 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               
                                 Y 
                                 in 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   x 
                                   , 
                                   y 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               
                                 Z 
                                 in 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   x 
                                   , 
                                   y 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
     In Formulae 12-1, 12-2, 12-3 and 13, leakage of light from the light sources arising when black is displayed on the liquid crystal panel is not considered. Formula 14 and Formulae 6, 7 used in the first embodiment may be used for taking the light leakage into account. Specifically, tristimulus values X KW′ , Y KW′ , Z KW′  of a light which are given when black is displayed on the liquid crystal panel are calculated according to Formula 14. Formula 6 represents a relation among the tristimulus values X KW′ , Y KW′  and Z KW′  which is obtained when black is displayed, tristimulus values X in (x, y), Y in (x, y) and Z in (x, y) of the input video, and correction signal values R LC (x, y), G LC (x, y) and B LC (x, y). The correction signal values R LC (x, y), G LC (x, y) and B LC (x, y) are calculated by Formula 7. 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             X 
                             
                               KW 
                               ′ 
                             
                           
                         
                       
                       
                         
                           
                             Y 
                             
                               KW 
                               ′ 
                             
                           
                         
                       
                       
                         
                           
                             Z 
                             
                               KW 
                               ′ 
                             
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       [ 
                       
                         
                           
                             
                               X 
                               KR 
                             
                           
                           
                             
                               X 
                               KG 
                             
                           
                           
                             
                               X 
                               KB 
                             
                           
                           
                             
                               X 
                               KC 
                             
                           
                         
                         
                           
                             
                               Y 
                               KR 
                             
                           
                           
                             
                               Y 
                               KG 
                             
                           
                           
                             
                               Y 
                               KB 
                             
                           
                           
                             
                               Y 
                               KC 
                             
                           
                         
                         
                           
                             
                               Z 
                               KR 
                             
                           
                           
                             
                               Z 
                               KG 
                             
                           
                           
                             
                               Z 
                               KB 
                             
                           
                           
                             
                               Z 
                               KC 
                             
                           
                         
                       
                       ] 
                     
                     ⁡ 
                     
                       [ 
                       
                         
                           
                             
                               R 
                               BL 
                             
                           
                         
                         
                           
                             
                               G 
                               BL 
                             
                           
                         
                         
                           
                             
                               B 
                               BL 
                             
                           
                         
                         
                           
                             
                               C 
                               BL 
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
           
         
       
     
     When the values of R LC (x, y), G LC (x, y) and B LC (x, y) are not within a range of zero (0) to one (1), the values R LC (x, y), G LC (x, y) and B LC (x, y) are corrected similarly to the first embodiment, so that values R′ LC (x, y), G′ LC (x, y) and B′ LC (x, y) are obtained. 
     Further, similarly to the first embodiment, an error calculation unit  110  calculates an error  111  based on the corrected video signal  109  and the color-converted video signal  103 . A control unit  112  sets the light source intensity information having a minimum error as emission intensity information  113 , with reference to the pieces of light source intensity information  105  and the errors  111  corresponding to the pieces of light source intensity information  105 . The pieces of light source intensity information  105  is obtained by combining pieces of light source intensity information of four colors and outputted from the light source setting unit  104  sequentially. 
     The control unit  112  provides the emission intensity information  113  to a light source control unit  115 . Further, the control unit  112  provides a corrected video signal  109   a  corresponding to the emission intensity information  113 , among the pieces of corrected video signals  109 , to a liquid crystal control unit  114 . The corrected video signal  109   a  corresponding to the emission intensity information  113  is a corrected video signal having the minimum error. The liquid crystal control unit  114  provides a liquid crystal control signal  116  to a liquid crystal panel  118 , and displays the corrected video signal  109   a  on the display area of the liquid crystal panel  118 . Further, the light source control unit  115  provides a light source control signal  117  to the backlight  119 , and performs control such that a light having intensity according to the emission intensity information  113  is irradiated from the backlight  119 . 
     According to the embodiment, since the light sources of four or more colors are used, the reproducible color reproduction gamut increases, and an image can be displayed with a minimum error between an image desired to be displayed and an actually displayed image. 
     A third embodiment will be described. The basic configuration of an LCD device according to the third embodiment is same as that of the LCD device of  FIG. 1 . 
       FIG. 7A  is a schematic diagram of a backlight of the LCD device according to the third embodiment. In the third embodiment, each light source  121   b  of a backlight  119   b  is provided with two kinds of light sources, which are a first and a second white light sources  126 ,  127  as illustrated in  FIG. 7B . The first and the second white light sources  126 ,  127  are two kinds of white LEDs having emission peaks at different wavelengths, respectively. The first and the second white light sources  126 ,  127  are not limited to the white LEDs so far as the light sources  126 ,  127  have emission peaks at different wavelengths. 
     Hereinafter, the first white light source  126  is defined as W 1 , and the second white light source  127  is defined as W 2 . In the third embodiment, an intensity setting unit  104  of  FIG. 1  determines light source intensity information  105  of the first and second white light source W 1 , W 2 , and provides the light source intensity information  105  to a color presumption unit  106 . The color presumption unit  106  presumes tristimulus values of a light obtained after a mixture of lights emitted from the two kinds of white light sources W 1 , W 2  at intensities W 1   BL , W 2   BL  passes through a liquid crystal panel. In the third embodiment, the tristimulus values of the mixture light are calculated by the following Formulae 15-1, 15-2 and 15-3. 
     Formula 15-1 is a formula for obtaining tristimulus values of a transmitted light obtained when the mixture light is irradiated to an R pixel. Formula 15-2 is a formula for obtaining tristimulus values of a transmitted light obtained when the mixture light is irradiated to a G pixel. Formula 15-3 is a formula for obtaining tristimulus values of a transmitted light obtained when the mixture light is irradiated to a B pixel. 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             X 
                             
                               RW 
                               ′ 
                             
                           
                         
                       
                       
                         
                           
                             Y 
                             
                               RW 
                               ′ 
                             
                           
                         
                       
                       
                         
                           
                             Z 
                             
                               RW 
                               ′ 
                             
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       [ 
                       
                         
                           
                             
                               X 
                               
                                 RW 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 1 
                               
                             
                           
                           
                             
                               X 
                               
                                 RW 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 2 
                               
                             
                           
                         
                         
                           
                             
                               Y 
                               
                                 RW 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 1 
                               
                             
                           
                           
                             
                               Y 
                               
                                 RW 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 2 
                               
                             
                           
                         
                         
                           
                             
                               Z 
                               
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                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
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                               Z 
                               
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                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 2 
                               
                             
                           
                         
                       
                       ] 
                     
                     ⁡ 
                     
                       [ 
                       
                         
                           
                             
                               W 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 1 
                                 BL 
                               
                             
                           
                         
                         
                           
                             
                               W 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 2 
                                 BL 
                               
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   
                     15 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     1 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     [ 
                     
                       
                         
                           
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                               ′ 
                             
                           
                         
                       
                       
                         
                           
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                               ′ 
                             
                           
                         
                       
                       
                         
                           
                             Z 
                             
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                               ′ 
                             
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       [ 
                       
                         
                           
                             
                               X 
                               
                                 GW 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 1 
                               
                             
                           
                           
                             
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                                 ⁢ 
                                 
                                     
                                 
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                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
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                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
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                               Z 
                               
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                                 ⁢ 
                                 
                                     
                                 
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                                 ⁢ 
                                 
                                     
                                 
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                       ] 
                     
                     ⁡ 
                     
                       [ 
                       
                         
                           
                             
                               W 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 1 
                                 BL 
                               
                             
                           
                         
                         
                           
                             
                               W 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 2 
                                 BL 
                               
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   
                     15 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     2 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             X 
                             
                               BW 
                               ′ 
                             
                           
                         
                       
                       
                         
                           
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                               ′ 
                             
                           
                         
                       
                       
                         
                           
                             Z 
                             
                               BW 
                               ′ 
                             
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       [ 
                       
                         
                           
                             
                               X 
                               
                                 BW 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 1 
                               
                             
                           
                           
                             
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                                 ⁢ 
                                 
                                     
                                 
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                                 ⁢ 
                                 
                                     
                                 
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                                 ⁢ 
                                 
                                     
                                 
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                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
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                       ] 
                     
                     ⁡ 
                     
                       [ 
                       
                         
                           
                             
                               W 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 1 
                                 BL 
                               
                             
                           
                         
                         
                           
                             
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                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 2 
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                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   
                     15 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     3 
                   
                   ) 
                 
               
             
           
         
       
     
     In Formulae 15-1, 15-2 and 15-3, X RW1  represents an X component of a light of the light source W 1  which passes through the R pixel. Y RW1  represents a Y component of a light of the light source W 1  which passes through the R pixel. Z RW1  represents a Z component of a light of the light source W 1  which passes through the R pixel. The same notation is applied to light components of the light source W 2 . 
     A signal correction unit  108  produces a corrected video signal  109  for displaying an input video signal  103  obtained when the mixture light corresponding to transmitted light is irradiated to a liquid crystal panel  118 , based on color information  107  of the transmitted light. Specifically, correction signal values R LC (x, y), G LC (x, y) and B LC (x, y) of the liquid crystal panel are calculated by Formula 16. 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             
                               R 
                               LC 
                             
                             ⁡ 
                             
                               ( 
                               
                                 x 
                                 , 
                                 y 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             
                               G 
                               LC 
                             
                             ⁡ 
                             
                               ( 
                               
                                 x 
                                 , 
                                 y 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             
                               B 
                               LC 
                             
                             ⁡ 
                             
                               ( 
                               
                                 x 
                                 , 
                                 y 
                               
                               ) 
                             
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       
                         [ 
                         
                           
                             
                               
                                 X 
                                 
                                   RW 
                                   ′ 
                                 
                               
                             
                             
                               
                                 X 
                                 
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                                   ′ 
                                 
                               
                             
                             
                               
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                         ] 
                       
                       
                         - 
                         1 
                       
                     
                     ⁡ 
                     
                       [ 
                       
                         
                           
                             
                               
                                 X 
                                 in 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   x 
                                   , 
                                   y 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               
                                 Y 
                                 in 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   x 
                                   , 
                                   y 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               
                                 Z 
                                 in 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   x 
                                   , 
                                   y 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
           
         
       
     
     In Formulae 15-1, 15-2, 15-3 and 16, leakage of light from the light sources arising when black is displayed on the liquid crystal panel is not considered. Formula 17 and Formulae 6, 7 used in the first embodiment may be used for taking the light leakage into account. Specifically, tristimulus values X KW′ , Y KW′  and Z KW′  of a light which are given when black is displayed on the liquid crystal panel is calculated according to Formula 17. The Formula 6 represents the relation among the tristimulus values X KW′ , Y KW′  and Z KW′  which is given when black is displayed, tristimulus values X in (x, y), Y in (x, y) and Z in (x, y) of the input video, and correction signal values R LC (x, y), G LC (x, y) and B LC (x, y). The correction signal values R LC (x, y), G LC (x, y) and B LC (x, y) are calculated by the Formula 7. 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             X 
                             
                               KW 
                               ′ 
                             
                           
                         
                       
                       
                         
                           
                             Y 
                             
                               KW 
                               ′ 
                             
                           
                         
                       
                       
                         
                           
                             Z 
                             
                               KW 
                               ′ 
                             
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       [ 
                       
                         
                           
                             
                               X 
                               
                                 KW 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 1 
                               
                             
                           
                           
                             
                               X 
                               
                                 KW 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 2 
                               
                             
                           
                         
                         
                           
                             
                               Y 
                               
                                 KW 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 1 
                               
                             
                           
                           
                             
                               Y 
                               
                                 KW 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 2 
                               
                             
                           
                         
                         
                           
                             
                               Z 
                               
                                 KW 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 1 
                               
                             
                           
                           
                             
                               Z 
                               
                                 KW 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 2 
                               
                             
                           
                         
                       
                       ] 
                     
                     ⁡ 
                     
                       [ 
                       
                         
                           
                             
                               W 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 1 
                                 BL 
                               
                             
                           
                         
                         
                           
                             
                               W 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 2 
                                 BL 
                               
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   17 
                   ) 
                 
               
             
           
         
       
     
     When the values R LC (x, y), G LC (x, y) and B LC (x, y) are not within a range of from zero (0) to one (1), the values R LC (x, y), G LC (x, y) and B LC (x, y) are corrected similarly to the first and second embodiments, so that values R′ LC (x, y), G′ LC (x, y) and B′ LC (x, y) are obtained. 
     Further, similarly to the first and second embodiments, an error calculation unit  110  calculates an error  111  based on the corrected video signal  109  and the color-converted video signal  103 . A control unit  112  sets light source intensity information having a minimum error as emission intensity information  113 , with reference to the pieces of light source intensity information  105  and the errors corresponding to the pieces of light source intensity information  105 . The pieces of light source intensity information  105  include intensity information of light sources for two colors, and are outputted sequentially from the light source setting unit  104 . 
     The control unit  112  provides the emission intensity information  113  to a light source control unit  115 . Further, the control unit  112  provides a corrected video signal  109   a  corresponding to the emission intensity information  113 , among the pieces of corrected video signals  109 , to a liquid crystal control unit  114 . The liquid crystal control unit  114  provides a liquid crystal control signal  116  to the liquid crystal panel  118 , and displays the corrected video signal  109   a  on the display area of the liquid crystal panel  118 . The light source control unit  115  provides a light source control signal  117  to the backlight  119 , and performs control such that the light having the intensity according to the emission intensity information  113  is irradiated from the backlight  119 . 
     According to the third embodiment, since the light sources of two colors are used, the reproducible color reproduction gamut increases, and an image can be displayed with a minimum error between an image desired to be displayed and an actually displayed image. 
     A fourth embodiment will be described below.  FIG. 8  is a block diagram of an LCD device  100   a  according to the fourth embodiment. 
     The basic configuration of an LCD device  100   a  according to the fourth embodiment is same as that of the first embodiment. The fourth embodiment is different from the first embodiment in the following point. In  FIG. 8 , an intensity setting unit  104  sets an initial value of light source intensity information  105  according to a color-converted video signal  103 . In addition, the intensity setting unit  104  updates the light source intensity information  105  according to error information  130  inputted from a control unit  112  to the intensity setting unit  104 . 
     The color-converted video signal  103  is inputted to a signal correction unit  108 , an error calculation unit  110 , and the intensity setting unit  104 . The intensity setting unit  104  obtains the initial value of the light source intensity information  105  according to the video signal  103 . In order to obtain light source intensities of respective colors based on the color-converted video signal, a plurality of kinds of methods may be used. 
     For example, when the number of light sources corresponds to three primary colors of R, G and B, a 3×3 color conversion matrix N as shown in Formula 18 may be prepared in advance. By Formula 18, maximum values X max , Y max  and Z max  of the tristimulus values of all pixels within the screen are converted into light source intensities R BL , G BL  and B BL . 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             R 
                             BL 
                           
                         
                       
                       
                         
                           
                             G 
                             BL 
                           
                         
                       
                       
                         
                           
                             B 
                             BL 
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     N 
                     ⁡ 
                     
                       [ 
                       
                         
                           
                             
                               X 
                               max 
                             
                           
                         
                         
                           
                             
                               Y 
                               max 
                             
                           
                         
                         
                           
                             
                               Z 
                               max 
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   18 
                   ) 
                 
               
             
           
         
       
     
     Initial values of the light source intensity information  105  are inputted to a color presumption unit  106 , similarly to the first embodiment. The color presumption unit  106  presumes the tristimulus values of a transmitted light. The signal correction unit  108  obtains a corrected video signal  109 . The error calculation unit  110  calculates an error  111 , and inputs the error  111  to the control unit  112 . Similarly to the first embodiment, the error calculation unit  110  calculates display errors ΔE(x, y) for all pixels, and obtains a maximum value ΔE max  among the display errors ΔE(x, y). The error calculation unit  110  calculates ΔL max , Δa max , and Δb max  which are errors of the L, a and b components of a CIELAB space between a display image and an ideal image, with respect to a pixel whose display error ΔE(x, y) has the maximum value ΔE max . 
     The error calculation unit  110  inputs the maximum values ΔE max , ΔL max , Δa max , and Δb max  to the control unit  112 , as the error  111 . The sum or average of the values of each of ΔE(x, y), ΔL(x, y), Δa(x, y) and Δb(x, y) with respect to all pixels provided within a screen may be used as the error  111 . In the fourth embodiment, the error  111  is set based on the display errors ΔE(x, y) of all of the pixels provided within the screen, but the error  111  may be set based on the display errors ΔE(x, y) of some pixels extracted from all of the pixels provided within the screen. 
     The control unit  112  compares the display error ΔE max  with a threshold value which is set advance. When the display error ΔE max  is smaller than the threshold value, the control unit  112  determines that the display error ΔE max  is significantly small. 
     When it is determined that the display error ΔE max  is significantly small, the control unit  112  inputs the light source intensity information  105  corresponding to the display error ΔE max  to a light source control unit  115 , as emission intensity information  113 , and inputs a corrected video signal  109   a  corresponding to the display error ΔE max  to a liquid crystal control unit  114 . 
     When it is determined that the display error ΔE max  is not significantly small, the control unit  112  inputs the display errors ΔE max , ΔL max , Δa max  and Δb max  to the intensity setting unit  104 , as the error information  130 . 
     The intensity setting unit  104  updates the light source intensity information  105  based on stored light source intensity information and the error information  130 , and then inputs the updated light source intensity information  105  to the color presumption unit  106 . 
     The update processing of the light source intensity information  105  will be described in detail below. In the fourth embodiment, as described above, the control unit  112  inputs the display errors ΔE max , ΔL max , Δa max  and Δb max  of the L, a and b components of the CIELAB space between the display image and the ideal image, to the intensity setting unit  104 , as the error information  130 . The intensity setting unit  104  determines change amounts of the light source intensity information  105  of respective colors according to values of the display errors ΔE max , ΔL max , Δa max  and Δb max . Specifically, when the colors of the light sources are three primary colors of R, G and B, the change amounts ΔR max , ΔG max  and ΔB max  of intensities of R, G and B colors are calculated based on the display errors ΔE max , ΔL max , Δa max  and Δb max . The light source intensities are updated according to Formula 19. In Formula 19, R BL   i , G BL   i  and B BL   i  are light source intensities respectively calculated by an i-th update, and the initial values are R BL   0 , G BL   0  and B BL   0 .
 
 R   BL   i+1   =R   BL   i   +ΔR   max  
 
 G   BL   i+1   =G   BL   i   +ΔG   max  
 
 B   BL   i+1   =B   BL   i   +ΔB   max   (19)
 
     ΔR, ΔG and ΔB which can reduce ΔE max  most efficiently can be obtained, and the obtained ΔR, ΔG, ΔB are set as the change amounts ΔR max , ΔG max  and ΔB max  respectively. 
     Alternately, ΔR max , ΔG max  and ΔB max  may be determined as follows. The largest value among |ΔL max |, |Δa max | and |Δb max | which are absolute values of ΔL max , Δa max  and Δb max  is obtained. When |ΔL max | among the absolute values is the largest value, ΔR, ΔG, ΔB capable of most efficiently reducing ΔL max  are determined as the change amounts ΔR max , ΔG max  and ΔB max . When |Δa max | is the largest value, ΔR, ΔG, ΔB capable of most efficiently reducing Δa max  are determined as the change amounts ΔR max , ΔG max  and ΔB max . When |Δb max | is the largest value, ΔR, ΔG, ΔB capable of most efficiently reducing Δb max  are determined as the change amounts ΔR max , ΔG max  and ΔB max . 
     The change amounts ΔR max , ΔG max  and ΔB max  may be obtained by calculation. A relation between ΔL max , Δa max , Δb max  and ΔR max , ΔG max , ΔB max  may be stored in a look-up table in advance, and ΔR max , ΔG max  and ΔB max  may be obtained with reference to the look-up table. 
     The values of the display errors ΔL max , Δa max  and Δb max  reflect excess or shortage of light source intensity of each color. For example, when the light source intensity of the R component is insufficient, the values of the display errors ΔL max , Δa max  and Δb max  are associated with a change amount ΔR of a positive value. On the other hand, when the light source intensity of the R component is excessive, the values of the display errors ΔL max , Δa max  and Δb max  are associated with a change amount ΔR of a negative value. This is similarly applied even when the number of light sources is not three that is necessary to produce three colors. 
     In the embodiment, a backlight capable of modulating intensity of the light which is emitted through the whole surface collectively is used as the backlight  119 . Further, ΔE max  is calculated for all pixels provided within the screen, and the light source intensity of the backlight is updated. Another backlight may be used. The backlight is capable of controlling light source intensity of each color, independently for each of a plurality of illumination areas obtained by dividing the screen. In this case, ΔE max  can be calculated for each illumination area, and the light source intensity can be updated for each illumination area. 
     The color presumption unit  106 , the signal correction unit  108 , the error calculation unit  110  and the control unit  112  respectively shown in  FIG. 8  perform the above described processing based on the updated light source intensity information  105 . The update processing is repeated until the control unit  112  determines that the display error ΔE max  is sufficiently small. When the number of update times previously set is reached, the control unit  112  may determines the lastly updated light source intensity information  105  as the emission intensity information  113 . 
     The liquid crystal control unit  114  provides a liquid crystal control signal  116  to the liquid crystal panel, and displays a corrected video signal  109   a  on the display area of a liquid crystal panel  118 . Further, the light source control unit  115  provides a light source control signal  117  to a backlight  119 , and performs control such that the light having intensity according to the emission intensity information  113  is irradiated from the backlight  119 . 
     As described above, according to the embodiment, an image can be displayed with a minimum error between an image desired to be displayed and an actually displayed image, at a small number of calculation times without calculating and evaluating the errors by an enormous number of intensity combinations. 
       FIG. 9  is a block diagram of an LCD device according to a fifth embodiment. In an LCD device  100   b  of the embodiment, in addition to the configuration of the first embodiment, a backlight  119  is provided with light sources of a plurality of colors which are capable of controlling light source intensities of respective colors, independently for each of a plurality of areas. The areas are obtained by dividing a screen and have different emission peak wavelengths. Further, in the LCD device  100   b , an intensity distribution presumption unit  131  is provided. The unit  131  presumes a spatial distribution of light source intensity, based on light source intensity information  105 . The following example shows a case where the light sources emit three colors of R, G and B, but the number of colors of the light sources is not limited to three. 
     The backlight  119  of the embodiment has a basic configuration same as that of the backlight of the first embodiment which is described above with reference to  FIGS. 2A and 2B . The backlight  119  of the embodiment can individually control intensities of an R light source  122 , a G light source  123 , and a B light source  124  for each light source  121  illustrated in  FIG. 2B . An illumination area of each of the light sources  121  is a portion of a display area of a liquid crystal panel  118  and corresponds to any one of areas obtained by virtually dividing the display area of the liquid crystal panel  118 . The illumination area of each of the light sources  121  is decided based on a spatial arrangement of the light sources  121  on the backlight  119 . 
     An illumination area of a video image to be displayed in the vicinity of an arrangement position of each light source  121  is decided for each light source  121  in advance. In  FIG. 9 , an intensity setting unit  104  sets the light source intensity information  105  of R, G and B for each illumination area, and provides the light source intensity information  105  to the intensity distribution presumption unit  131 . 
     The intensity distribution calculation unit  131  calculates an intensity distribution information  132  of a light irradiated to the liquid crystal panel  118  from the backlight  119 , according to the light source intensity information  105  for each of the colors of the light sources. Specifically, a convolution operation represented by Formula 20 is performed using the light source intensity information  105  of each illumination area and the previously obtained light source intensity distribution of each color of the light sources, so that the intensity distribution information  132  of the light source at a position (x, y) is obtained. 
     
       
         
           
             
               
                 
                   
                     
                       
                         R 
                         d 
                       
                       ⁡ 
                       
                         ( 
                         
                           x 
                           , 
                           y 
                         
                         ) 
                       
                     
                     = 
                     
                       
                         ∑ 
                         
                           j 
                           = 
                           0 
                         
                         
                           N 
                           - 
                           1 
                         
                       
                       ⁢ 
                       
                         
                           ∑ 
                           
                             i 
                             = 
                             0 
                           
                           
                             M 
                             - 
                             1 
                           
                         
                         ⁢ 
                         
                           
                             
                               P 
                               R 
                             
                             ⁡ 
                             
                               ( 
                               
                                 i 
                                 , 
                                 j 
                               
                               ) 
                             
                           
                           · 
                           
                             
                               R 
                               BL 
                             
                             ⁡ 
                             
                               ( 
                               
                                 
                                   x 
                                   - 
                                   
                                     
                                       ( 
                                       
                                         M 
                                         - 
                                         1 
                                       
                                       ) 
                                     
                                     2 
                                   
                                   + 
                                   i 
                                 
                                 , 
                                 
                                   y 
                                   - 
                                   
                                     
                                       ( 
                                       
                                         N 
                                         - 
                                         1 
                                       
                                       ) 
                                     
                                     2 
                                   
                                   + 
                                   j 
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         G 
                         d 
                       
                       ⁡ 
                       
                         ( 
                         
                           x 
                           , 
                           y 
                         
                         ) 
                       
                     
                     = 
                     
                       
                         ∑ 
                         
                           j 
                           = 
                           0 
                         
                         
                           N 
                           - 
                           1 
                         
                       
                       ⁢ 
                       
                         
                           ∑ 
                           
                             i 
                             = 
                             0 
                           
                           
                             M 
                             - 
                             1 
                           
                         
                         ⁢ 
                         
                           
                             
                               P 
                               G 
                             
                             ⁡ 
                             
                               ( 
                               
                                 i 
                                 , 
                                 j 
                               
                               ) 
                             
                           
                           · 
                           
                             
                               G 
                               BL 
                             
                             ⁡ 
                             
                               ( 
                               
                                 
                                   x 
                                   - 
                                   
                                     
                                       ( 
                                       
                                         M 
                                         - 
                                         1 
                                       
                                       ) 
                                     
                                     2 
                                   
                                   + 
                                   i 
                                 
                                 , 
                                 
                                   y 
                                   - 
                                   
                                     
                                       ( 
                                       
                                         N 
                                         - 
                                         1 
                                       
                                       ) 
                                     
                                     2 
                                   
                                   + 
                                   j 
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         B 
                         d 
                       
                       ⁡ 
                       
                         ( 
                         
                           x 
                           , 
                           y 
                         
                         ) 
                       
                     
                     = 
                     
                       
                         ∑ 
                         
                           j 
                           = 
                           0 
                         
                         
                           N 
                           - 
                           1 
                         
                       
                       ⁢ 
                       
                         
                           ∑ 
                           
                             i 
                             = 
                             0 
                           
                           
                             M 
                             - 
                             1 
                           
                         
                         ⁢ 
                         
                           
                             
                               P 
                               B 
                             
                             ⁡ 
                             
                               ( 
                               
                                 i 
                                 , 
                                 j 
                               
                               ) 
                             
                           
                           · 
                           
                             
                               B 
                               BL 
                             
                             ⁡ 
                             
                               ( 
                               
                                 
                                   x 
                                   - 
                                   
                                     
                                       ( 
                                       
                                         M 
                                         - 
                                         1 
                                       
                                       ) 
                                     
                                     2 
                                   
                                   + 
                                   i 
                                 
                                 , 
                                 
                                   y 
                                   - 
                                   
                                     
                                       ( 
                                       
                                         N 
                                         - 
                                         1 
                                       
                                       ) 
                                     
                                     2 
                                   
                                   + 
                                   j 
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   20 
                   ) 
                 
               
             
           
         
       
     
     In Formula 20, R d (x, y) represents an intensity distribution of a light of an R light source  122 . G d (x, y) represents an intensity distribution of a light of the G light source  123 . B d (x, y) represents an intensity distribution of a light of the B light source  124 . M and N represent an odd number representing the size of the emission intensity distribution in a horizontal direction and an odd number representing the size of the emission intensity distribution in a vertical direction, respectively. R BL (x, y), G BL (x, y) and B BL (x, y) represent light source intensities of the R light source  122 , the G light source  123  and the B light source  124  in the illumination area including coordinates (x, y), respectively. P R (i, j), P G (i, j) and P B (i, j) represent intensities of the emission intensity distribution of R, G and B at a position (i, j), respectively. 
     An example of the convolution operation will be described with reference to  FIG. 10 . A plurality of illumination areas  1000  is set on an image. A black circle  1001  is positioned at a pixel position of the coordinates (x, y), which is a position of a target pixel whose intensities distributions R d (x, y), G d (x, y) and B d (x, y) are to be calculated. An emission intensity distribution area  1002  is a rectangular area of M×N pixels. A white circle  1003  is positioned at the relative coordinates (i, j) within the emission intensity distribution area  1002 , and is positioned at (x−(M−1)/2+i, y−(N−1)/2+j), as coordinates of a pixel of an image. As for an area corresponding to a contour portion of the image, the convolution operation of Formula 20 is performed using the information of light source intensity obtained by specular-reflecting light corresponding to the light source intensity information  105 . As a result, R d (x, y), G d (x, y) and B d (x, y) which are the intensity distribution information  132  are obtained. 
     The intensity distribution information  132  calculated by the intensity distribution calculation unit  131  is inputted to a color presumption unit  106 . In the embodiment, the intensity distributions of all pixel positions are calculated. However, as a simplified configuration of the embodiment, the intensity distribution may be presumed by assuming that the lights having the same intensities as the emission intensities of the light sources for each illumination area is irradiated to the respective pixels provided within each illumination area. Specifically, the intensity distribution may be presumed by Formula 21. In Formula 21, for example, R BL (x, y) is the light source intensity of the R light source  122  for the illumination area including the coordinates (x, y).
 
 R   d ( x,y )= R   BL ( x,y )
 
 G   d ( x,y )= G   BL ( x,y )
 
 B   d ( x,y )= B   BL ( x,y )  (21)
 
     Then, the color presumption unit  106  presumes the tristimulus values of the light which is obtained after a mixture of lights from the light sources of the respective colors irradiated to each pixel position of a liquid crystal panel passes through the liquid crystal panel. In the embodiment, the tristimulus values of the mixture light at the coordinates (x, y) are calculated by Formulae 22-1, 22-2 and 22-3 based on the intensities R d (x, y), G d (x, y) and B d (x, y) at the coordinates (x, y). 
     Formula 22-1 is a formula for obtaining tristimulus values of the transmitted light when the mixture light is irradiated to the R pixel. Formula 22-2 is a formula for obtaining tristimulus values of the transmitted light when the mixture light is irradiated to the G pixel. Formula 22-3 is a formula for obtaining tristimulus values of the transmitted light when the mixture light is irradiated to the B pixel. 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             
                               X 
                               
                                 RW 
                                 ′ 
                               
                             
                             ⁡ 
                             
                               ( 
                               
                                 x 
                                 , 
                                 y 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             
                               Y 
                               
                                 RW 
                                 ′ 
                               
                             
                             ⁡ 
                             
                               ( 
                               
                                 x 
                                 , 
                                 y 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             
                               Z 
                               
                                 RW 
                                 ′ 
                               
                             
                             ⁡ 
                             
                               ( 
                               
                                 x 
                                 , 
                                 y 
                               
                               ) 
                             
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       [ 
                       
                         
                           
                             
                               X 
                               RR 
                             
                           
                           
                             
                               X 
                               RG 
                             
                           
                           
                             
                               X 
                               RB 
                             
                           
                         
                         
                           
                             
                               Y 
                               RR 
                             
                           
                           
                             
                               Y 
                               RG 
                             
                           
                           
                             
                               Y 
                               RB 
                             
                           
                         
                         
                           
                             
                               Z 
                               RR 
                             
                           
                           
                             
                               Z 
                               RG 
                             
                           
                           
                             
                               Z 
                               RB 
                             
                           
                         
                       
                       ] 
                     
                     ⁡ 
                     
                       [ 
                       
                         
                           
                             
                               
                                 R 
                                 d 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   x 
                                   , 
                                   y 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               
                                 G 
                                 d 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   x 
                                   , 
                                   y 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               
                                 B 
                                 d 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   x 
                                   , 
                                   y 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   
                     22 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     1 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             
                               X 
                               
                                 GW 
                                 ′ 
                               
                             
                             ⁡ 
                             
                               ( 
                               
                                 x 
                                 , 
                                 y 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             
                               Y 
                               
                                 GW 
                                 ′ 
                               
                             
                             ⁡ 
                             
                               ( 
                               
                                 x 
                                 , 
                                 y 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             
                               Z 
                               
                                 GW 
                                 ′ 
                               
                             
                             ⁡ 
                             
                               ( 
                               
                                 x 
                                 , 
                                 y 
                               
                               ) 
                             
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       [ 
                       
                         
                           
                             
                               X 
                               GR 
                             
                           
                           
                             
                               X 
                               GG 
                             
                           
                           
                             
                               X 
                               GB 
                             
                           
                         
                         
                           
                             
                               Y 
                               GR 
                             
                           
                           
                             
                               Y 
                               GG 
                             
                           
                           
                             
                               Y 
                               GB 
                             
                           
                         
                         
                           
                             
                               Z 
                               GR 
                             
                           
                           
                             
                               Z 
                               GG 
                             
                           
                           
                             
                               Z 
                               GB 
                             
                           
                         
                       
                       ] 
                     
                     ⁡ 
                     
                       [ 
                       
                         
                           
                             
                               
                                 R 
                                 d 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   x 
                                   , 
                                   y 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               
                                 G 
                                 d 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   x 
                                   , 
                                   y 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               
                                 B 
                                 d 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   x 
                                   , 
                                   y 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   
                     22 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     2 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             
                               X 
                               
                                 BW 
                                 ′ 
                               
                             
                             ⁡ 
                             
                               ( 
                               
                                 x 
                                 , 
                                 y 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             
                               Y 
                               
                                 BW 
                                 ′ 
                               
                             
                             ⁡ 
                             
                               ( 
                               
                                 x 
                                 , 
                                 y 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             
                               Z 
                               
                                 BW 
                                 ′ 
                               
                             
                             ⁡ 
                             
                               ( 
                               
                                 x 
                                 , 
                                 y 
                               
                               ) 
                             
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       [ 
                       
                         
                           
                             
                               X 
                               BR 
                             
                           
                           
                             
                               X 
                               BG 
                             
                           
                           
                             
                               X 
                               BB 
                             
                           
                         
                         
                           
                             
                               Y 
                               BR 
                             
                           
                           
                             
                               Y 
                               BG 
                             
                           
                           
                             
                               Y 
                               BB 
                             
                           
                         
                         
                           
                             
                               Z 
                               BR 
                             
                           
                           
                             
                               Z 
                               BG 
                             
                           
                           
                             
                               Z 
                               BB 
                             
                           
                         
                       
                       ] 
                     
                     ⁡ 
                     
                       [ 
                       
                         
                           
                             
                               
                                 R 
                                 d 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   x 
                                   , 
                                   y 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               
                                 G 
                                 d 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   x 
                                   , 
                                   y 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               
                                 B 
                                 d 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   x 
                                   , 
                                   y 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   
                     22 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     3 
                   
                   ) 
                 
               
             
           
         
       
     
     In the Formulae 22-1, 22-2 and 22-3, for example, X RG  represents an X component of light of the G light source passing through the R pixel. Y RG  represents a Y component of light of the G light source passing through the R pixel. Z RG  represents a Z component of light of the G light source passing through the R pixel. The same notation is applied to the remaining components of the tristimulus values. 
     A signal correction unit  108  obtains a corrected video signal  109  for displaying a video image to be formed by an input video signal  103  under irradiation of the mixture light, and inputs the obtained corrected video signal  109  to an error calculation unit  110 . Specifically, the correction signal values R LC (x, y), G LC (x, y) and B LC (x, y) of the liquid crystal panel are calculated by Formula 23. 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             
                               R 
                               LC 
                             
                             ⁡ 
                             
                               ( 
                               
                                 x 
                                 , 
                                 y 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             
                               G 
                               LC 
                             
                             ⁡ 
                             
                               ( 
                               
                                 x 
                                 , 
                                 y 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             
                               B 
                               LC 
                             
                             ⁡ 
                             
                               ( 
                               
                                 x 
                                 , 
                                 y 
                               
                               ) 
                             
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       
                         [ 
                         
                           
                             
                               
                                 
                                   X 
                                   
                                     RW 
                                     ′ 
                                   
                                 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     x 
                                     , 
                                     y 
                                   
                                   ) 
                                 
                               
                             
                             
                               
                                 
                                   X 
                                   
                                     GW 
                                     ′ 
                                   
                                 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     x 
                                     , 
                                     y 
                                   
                                   ) 
                                 
                               
                             
                             
                               
                                 
                                   X 
                                   
                                     BW 
                                     ′ 
                                   
                                 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     x 
                                     , 
                                     y 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   Y 
                                   
                                     RW 
                                     ′ 
                                   
                                 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     x 
                                     , 
                                     y 
                                   
                                   ) 
                                 
                               
                             
                             
                               
                                 
                                   Y 
                                   
                                     GW 
                                     ′ 
                                   
                                 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     x 
                                     , 
                                     y 
                                   
                                   ) 
                                 
                               
                             
                             
                               
                                 
                                   Y 
                                   
                                     BW 
                                     ′ 
                                   
                                 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     x 
                                     , 
                                     y 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   Z 
                                   
                                     RW 
                                     ′ 
                                   
                                 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     x 
                                     , 
                                     y 
                                   
                                   ) 
                                 
                               
                             
                             
                               
                                 
                                   Z 
                                   
                                     GW 
                                     ′ 
                                   
                                 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     x 
                                     , 
                                     y 
                                   
                                   ) 
                                 
                               
                             
                             
                               
                                 
                                   Z 
                                   
                                     BW 
                                     ′ 
                                   
                                 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     x 
                                     , 
                                     y 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         ] 
                       
                       
                         - 
                         1 
                       
                     
                     ⁡ 
                     
                       [ 
                       
                         
                           
                             
                               
                                 X 
                                 in 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   x 
                                   , 
                                   y 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               
                                 Y 
                                 in 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   x 
                                   , 
                                   y 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               
                                 Z 
                                 in 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   x 
                                   , 
                                   y 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   23 
                   ) 
                 
               
             
           
         
       
     
     In the Formulae 22-1, 22-2, 22-3 and 23, leakage of light from the light sources arising when black is displayed on the liquid crystal panel is not considered. Formula 24 and the Formulae 6, 7 used in the first embodiment may be used for taking the light leakage into account. Tristimulus values X KW′ , Y KW′  and Z KW′  of a light to be given when black is displayed on the liquid crystal panel are obtained according to Formula 24. Formula 6 represents a relation among the tristimulus values X KW′ , Y KW′  and Z KW′ , to be given when black is displayed, tristimulus values X in (x, y), Y in (x, y) and Z in (x, y) of the input video, and the correction signal values R LC (x, y), G LC (x, y), B LC (x, y). The correction signal values R LC (x, y), G LC (x, y), B LC (x, y) are calculated by the Formula 7. 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             
                               X 
                               
                                 KW 
                                 ′ 
                               
                             
                             ⁡ 
                             
                               ( 
                               
                                 x 
                                 , 
                                 y 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             
                               Y 
                               
                                 KW 
                                 ′ 
                               
                             
                             ⁡ 
                             
                               ( 
                               
                                 x 
                                 , 
                                 y 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             
                               Z 
                               
                                 KW 
                                 ′ 
                               
                             
                             ⁡ 
                             
                               ( 
                               
                                 x 
                                 , 
                                 y 
                               
                               ) 
                             
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       [ 
                       
                         
                           
                             
                               X 
                               KR 
                             
                           
                           
                             
                               X 
                               KG 
                             
                           
                           
                             
                               X 
                               KB 
                             
                           
                         
                         
                           
                             
                               Y 
                               KR 
                             
                           
                           
                             
                               Y 
                               KG 
                             
                           
                           
                             
                               Y 
                               KB 
                             
                           
                         
                         
                           
                             
                               Z 
                               KR 
                             
                           
                           
                             
                               Z 
                               KG 
                             
                           
                           
                             
                               Z 
                               KB 
                             
                           
                         
                       
                       ] 
                     
                     ⁡ 
                     
                       [ 
                       
                         
                           
                             
                               
                                 R 
                                 d 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   x 
                                   , 
                                   y 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               
                                 G 
                                 d 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   x 
                                   , 
                                   y 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               
                                 B 
                                 d 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   x 
                                   , 
                                   y 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   24 
                   ) 
                 
               
             
           
         
       
     
     When the values of R LC (x, y), G LC (x, y) and B LC (x, y) are not within a range from zero (0) to one (1), the values of R LC (x, y), G LC (x, y) and B LC (x, y) are corrected similarly to the first and second embodiments, so that R′ LC (x, y), G′ LC (x, y) and B′ LC (x, y) are obtained. 
     Then, the error calculation unit  110  calculates an error  111  based on the corrected video signal  109  and the color-converted video signal  103 . When the correction signal values R LC (x, y), G LC (x, y), B LC (x, y) at the coordinates (x, y) are not within in the range from zero (0) to one (1), tristimulus values X′(x, y), Y′(x, y) and Z′(x, y) of a light displayed on the screen are calculated by Formula 25. When all of the correction signal values R LC (x, y), G LC (x, y) and B LC (x, y) are within the range from zero (0) to one (1), X′(x, y), Y′(x, y) and Z′(x, y) are not calculated, and the error  111  is set to zero. 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             
                               X 
                               ′ 
                             
                             ⁡ 
                             
                               ( 
                               
                                 x 
                                 , 
                                 y 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             
                               Y 
                               ′ 
                             
                             ⁡ 
                             
                               ( 
                               
                                 x 
                                 , 
                                 y 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             
                               Z 
                               ′ 
                             
                             ⁡ 
                             
                               ( 
                               
                                 x 
                                 , 
                                 y 
                               
                               ) 
                             
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       [ 
                       
                         
                           
                             
                               
                                 X 
                                 
                                   RW 
                                   ′ 
                                 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   x 
                                   , 
                                   y 
                                 
                                 ) 
                               
                             
                           
                           
                             
                               
                                 X 
                                 
                                   GW 
                                   ′ 
                                 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   x 
                                   , 
                                   y 
                                 
                                 ) 
                               
                             
                           
                           
                             
                               
                                 X 
                                 
                                   BW 
                                   ′ 
                                 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   x 
                                   , 
                                   y 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               
                                 Y 
                                 
                                   RW 
                                   ′ 
                                 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   x 
                                   , 
                                   y 
                                 
                                 ) 
                               
                             
                           
                           
                             
                               
                                 Y 
                                 
                                   GW 
                                   ′ 
                                 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   x 
                                   , 
                                   y 
                                 
                                 ) 
                               
                             
                           
                           
                             
                               
                                 Y 
                                 
                                   BW 
                                   ′ 
                                 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   x 
                                   , 
                                   y 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               
                                 Z 
                                 
                                   RW 
                                   ′ 
                                 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   x 
                                   , 
                                   y 
                                 
                                 ) 
                               
                             
                           
                           
                             
                               
                                 Z 
                                 
                                   GW 
                                   ′ 
                                 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   x 
                                   , 
                                   y 
                                 
                                 ) 
                               
                             
                           
                           
                             
                               
                                 Z 
                                 
                                   BW 
                                   ′ 
                                 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   x 
                                   , 
                                   y 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ] 
                     
                     ⁡ 
                     
                       [ 
                       
                         
                           
                             
                               
                                 R 
                                 LC 
                                 ′ 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   x 
                                   , 
                                   y 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               
                                 G 
                                 LC 
                                 ′ 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   x 
                                   , 
                                   y 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               
                                 B 
                                 LC 
                                 ′ 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   x 
                                   , 
                                   y 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   25 
                   ) 
                 
               
             
           
         
       
     
     The error between the ideal image and the display image is obtained as follows. An error between the tristimulus values X in (x, y), Y in (x, y) and Z in (x, y) of the color-converted video signal  103  at the coordinates (x, y) and the actually displayed tristimulus values X′(x, y), Y′(x, y) and Z′(x, y) is calculated in the CIELAB space. Specifically, X in (x, y), Y in (x, y), Z in (x, y) and X′(x, y), Y′(x, y), Z′(x, y) are converted into L in (x, y), a in (x, y), b in (x, y) and L′(x, y), a′(x, y), b′(x, y) of the CIELAB space, respectively, by Formula 26. 
     
       
         
           
             
               
                 
                   
                     
                       
                         L 
                         in 
                       
                       ⁡ 
                       
                         ( 
                         
                           x 
                           , 
                           y 
                         
                         ) 
                       
                     
                     = 
                     
                       
                         116 
                         * 
                         
                           
                             ( 
                             
                               
                                 
                                   Y 
                                   in 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     x 
                                     , 
                                     y 
                                   
                                   ) 
                                 
                               
                               
                                 Y 
                                 n 
                               
                             
                             ) 
                           
                           
                             1 
                             3 
                           
                         
                       
                       - 
                       16 
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         a 
                         in 
                       
                       ⁡ 
                       
                         ( 
                         
                           x 
                           , 
                           y 
                         
                         ) 
                       
                     
                     = 
                     
                       500 
                       * 
                       
                         { 
                         
                           
                             
                               ( 
                               
                                 
                                   
                                     X 
                                     in 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     
                                       x 
                                       , 
                                       y 
                                     
                                     ) 
                                   
                                 
                                 
                                   X 
                                   n 
                                 
                               
                               ) 
                             
                             
                               1 
                               3 
                             
                           
                           - 
                           
                             
                               ( 
                               
                                 
                                   
                                     Y 
                                     in 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     
                                       x 
                                       , 
                                       y 
                                     
                                     ) 
                                   
                                 
                                 
                                   Y 
                                   n 
                                 
                               
                               ) 
                             
                             
                               1 
                               3 
                             
                           
                         
                         } 
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         b 
                         in 
                       
                       ⁡ 
                       
                         ( 
                         
                           x 
                           , 
                           y 
                         
                         ) 
                       
                     
                     = 
                     
                       200 
                       * 
                       
                         { 
                         
                           
                             
                               ( 
                               
                                 
                                   
                                     Y 
                                     in 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     
                                       x 
                                       , 
                                       y 
                                     
                                     ) 
                                   
                                 
                                 
                                   Y 
                                   n 
                                 
                               
                               ) 
                             
                             
                               1 
                               3 
                             
                           
                           - 
                           
                             
                               ( 
                               
                                 
                                   
                                     Z 
                                     in 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     
                                       x 
                                       , 
                                       y 
                                     
                                     ) 
                                   
                                 
                                 
                                   Z 
                                   n 
                                 
                               
                               ) 
                             
                             
                               1 
                               3 
                             
                           
                         
                         } 
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         L 
                         ′ 
                       
                       ⁡ 
                       
                         ( 
                         
                           x 
                           , 
                           y 
                         
                         ) 
                       
                     
                     = 
                     
                       
                         116 
                         * 
                         
                           
                             ( 
                             
                               
                                 
                                   Y 
                                   ′ 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     x 
                                     , 
                                     y 
                                   
                                   ) 
                                 
                               
                               
                                 Y 
                                 n 
                               
                             
                             ) 
                           
                           
                             1 
                             3 
                           
                         
                       
                       - 
                       16 
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         a 
                         ′ 
                       
                       ⁡ 
                       
                         ( 
                         
                           x 
                           , 
                           y 
                         
                         ) 
                       
                     
                     = 
                     
                       500 
                       * 
                       
                         { 
                         
                           
                             
                               ( 
                               
                                 
                                   
                                     X 
                                     ′ 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     
                                       x 
                                       , 
                                       y 
                                     
                                     ) 
                                   
                                 
                                 
                                   X 
                                   n 
                                 
                               
                               ) 
                             
                             
                               1 
                               3 
                             
                           
                           - 
                           
                             
                               ( 
                               
                                 
                                   
                                     Y 
                                     ′ 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     
                                       x 
                                       , 
                                       y 
                                     
                                     ) 
                                   
                                 
                                 
                                   Y 
                                   n 
                                 
                               
                               ) 
                             
                             
                               1 
                               3 
                             
                           
                         
                         } 
                       
                     
                   
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     
                       
                         b 
                         ′ 
                       
                       ⁡ 
                       
                         ( 
                         
                           x 
                           , 
                           y 
                         
                         ) 
                       
                     
                     = 
                     
                       200 
                       * 
                       
                         { 
                         
                           
                             
                               ( 
                               
                                 
                                   
                                     Y 
                                     ′ 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     
                                       x 
                                       , 
                                       y 
                                     
                                     ) 
                                   
                                 
                                 
                                   Y 
                                   n 
                                 
                               
                               ) 
                             
                             
                               1 
                               3 
                             
                           
                           - 
                           
                             
                               ( 
                               
                                 
                                   
                                     Z 
                                     ′ 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     
                                       x 
                                       , 
                                       y 
                                     
                                     ) 
                                   
                                 
                                 
                                   Z 
                                   n 
                                 
                               
                               ) 
                             
                             
                               1 
                               3 
                             
                           
                         
                         } 
                       
                     
                   
                 
               
               
                 
                   ( 
                   26 
                   ) 
                 
               
             
           
         
       
     
     In Formula 26, X n , Y n  and Z n  represent the tristimulus values to be given when the R, G and B light sources emit light at a maximum output (in a case where a white light is emitted). Further, the display error ΔE(x, y) between the values L in (x, y), a in (x, y) and b in (x, y) and the values L′(x, y), a′(x, y) and b′(x, y) is calculated by Formula 27. 
     
       
         
           
             
               
                 
                   
                     Δ 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       E 
                       ⁡ 
                       
                         ( 
                         
                           x 
                           , 
                           y 
                         
                         ) 
                       
                     
                   
                   = 
                   
                     
                       
                         
                           
                             
                               
                                 ( 
                                 
                                   
                                     
                                       L 
                                       in 
                                     
                                     ⁡ 
                                     
                                       ( 
                                       
                                         x 
                                         , 
                                         y 
                                       
                                       ) 
                                     
                                   
                                   - 
                                   
                                     
                                       L 
                                       ′ 
                                     
                                     ⁡ 
                                     
                                       ( 
                                       
                                         x 
                                         , 
                                         y 
                                       
                                       ) 
                                     
                                   
                                 
                                 ) 
                               
                               2 
                             
                             + 
                           
                         
                       
                       
                         
                           
                             
                               
                                 ( 
                                 
                                   
                                     
                                       a 
                                       in 
                                     
                                     ⁡ 
                                     
                                       ( 
                                       
                                         x 
                                         , 
                                         y 
                                       
                                       ) 
                                     
                                   
                                   - 
                                   
                                     
                                       a 
                                       ′ 
                                     
                                     ⁡ 
                                     
                                       ( 
                                       
                                         x 
                                         , 
                                         y 
                                       
                                       ) 
                                     
                                   
                                 
                                 ) 
                               
                               2 
                             
                             + 
                           
                         
                       
                       
                         
                           
                             
                               ( 
                               
                                 
                                   
                                     b 
                                     in 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     
                                       x 
                                       , 
                                       y 
                                     
                                     ) 
                                   
                                 
                                 - 
                                 
                                   
                                     b 
                                     ′ 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     
                                       x 
                                       , 
                                       y 
                                     
                                     ) 
                                   
                                 
                               
                               ) 
                             
                             2 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   27 
                   ) 
                 
               
             
           
         
       
     
     The display errors ΔL(x, y), Δa(x, y) and Δb(x, y) of L, a and b components are calculated by Formula 28, respectively.
 
Δ L ( x,y )= L   in ( x,y )− L ′( x,y )
 
Δ a ( x,y )= a   in ( x,y )− a ′( x,y )
 
Δ b ( x,y )= b   in ( x,y )− b ′( x,y )  (28)
 
     The error calculation unit  110  obtains the largest value ΔE max  among the display errors ΔE(x, y) of all pixels provided within the screen. The error calculation unit  110  obtains ΔL max , Δa max  and Δb max  which are the errors of the “L” component, the “a” component, and the “b” component of the pixel whose display error ΔE is the largest value ΔE max . The error calculation unit  110  inputs ΔE max , ΔL max , Δa max  and Δb max  to a control unit  112 , as the error  111  corresponding to the light source intensity information  105 . 
     In the embodiment, ΔE(x, y), ΔL(x, y), Δa(x, y) and Δb(x, y) of the pixel whose display error ΔE(x, y) is the largest value are used as the error  111 . Alternately, the total sum or the average of the respective values ΔE(x, y), ΔL(x, y), Δa(x, y) and Δb(x, y) of the pixels may be used as the error  111 . Further, in the embodiment, the error  111  is set based on the display errors ΔE(x, y) of all pixels within the screen. Alternately, the error  111  may be set based on the display errors ΔE(x, y) of some pixels extracted from all of the pixels within the screen. 
     The control unit  112  compares the display error ΔE max  with a previously set threshold value. When the display error ΔE max  is smaller than the threshold value, the control unit  112  determines that the display error ΔE max  is sufficiently small. 
     When it is determined that the display error ΔE max  is sufficiently small, the control unit  112  inputs the light source intensity information  105  corresponding to the display error ΔE max  to a light source control unit  115  as emission intensity information  113 , and inputs a corrected video signal  109   a  corresponding to the display error ΔE max , to a liquid crystal control unit  114 . 
     When it is determined that the display error ΔE max  is not sufficiently small, the control unit  112  inputs the display errors ΔL max , Δa max , Δb max  and ΔE max  to the intensity setting unit  104  as error information  130 . The intensity setting unit  104  updates the light source intensity information  105  based on the light source intensity information  105  and the error information  130 , and inputs the updated light source intensity information  105  to the color presumption unit  106 . 
     The update processing of the light source intensity information  105  according to the fifth embodiment will be described in detail. In the embodiment, the control unit  112  inputs the display errors ΔL max , Δa max  and Δb max  between the display image and the ideal image with respect to the L, a and b components of the CIELAB space, to the intensity setting unit  104 , as the error information  130 . The intensity setting unit  104  sets a change amount of the light source intensity information  105  of the colors of each illumination area according to the values of ΔL max , Δa max  and Δb max . 
     When the number of the colors of the light sources is three in accordance with three primary colors of R, G and B, ΔR(k), ΔG(k) and ΔB(k) which are intensity change amounts ΔR max , ΔG max  and ΔB max  of the R, G and B colors of each illumination area are obtained based on ΔL max , Δa max  and Δb max , and, using the intensity change amounts, the light source intensity information  105  is updated. 
     In order to obtain the intensity change amounts ΔR max , ΔG max  and ΔB max , for example, values ΔR, ΔG, ΔB which are capable of reducing ΔE max  most efficiently are set as the values ΔR max , ΔG max , ΔB max . 
     Alternately, ΔR max , ΔG max  and ΔB max  may be set by the following method. The largest value among |ΔL max |, |Δa max | and |Δb max | which are absolute values of ΔL max , Δa max  and Δb max  is obtained. Further, when |ΔL max | is the largest value, the values ΔR, ΔG, ΔB which are capable of reducing ΔL max  most efficiently are set as the change amounts ΔR max , ΔG max  and ΔB max . When |Δa max | is the largest value, the values ΔR, ΔG and ΔB which are capable of reducing Δa max  most efficiently are set as the change amounts ΔR max , ΔG max  and ΔB max . In addition, when |Δb max | is the largest value, the values ΔR, ΔG and ΔB which are capable of reducing Δb max  most efficiently are set as the change amounts ΔR max , ΔG max  and ΔB max . 
     The values ΔR max , ΔG max  and ΔB max  may be obtained by calculation. A relation between ΔL max , Δa max  and Δb max  and the values ΔR max , ΔG max  and ΔB max  may be stored in a look-up table in advance, and the values ΔR max , ΔG max , ΔB max  may be calculated with reference to the look-up table. 
     The values of the display errors ΔL max , Δa max  and Δb max  reflect excess or shortage of light source intensities of the respective colors. For example, when the light source intensity of the R component is insufficient, the values of the display errors ΔL max , Δa max  and Δb max  are associated with a change amount ΔR max  of a positive value. On the contrary, when the light source intensity of the R component is excessive, the values of the display errors ΔL max , Δa max  and Δb max  are associated with a change amount ΔR max  of a negative value. This is similarly applied even when the number of light sources is not three that is necessary to produce three colors. 
     The intensity setting unit  104  sets the intensity change amounts of the respective color light sources of each illumination area, according to the intensity change amounts ΔR max , ΔG max , ΔB max  corresponding to the display errors ΔL max , Δa max , Δb max , light source intensity distributions P R (i, j), P G (i, j), P B (i, j) of the respective color light sources, and the position of an area in which ΔL max , Δa max , Δb max  are generated. For example, the intensity change amounts of an illumination area k is set by Formula 29.
 
Δ R ( k )=Δ R   max   ×P   R ( m−x   max   ,n−y   max )
 
Δ G ( k )=Δ G   max   ×P   G ( m−x   max   ,n−y   max )
 
Δ B ( k )=Δ B   max   ×P   B ( m−x   max   ,n−y   max )  (29)
 
     In Formula 29, ΔR(k), ΔG(k) and ΔB(k) represent intensity change amounts of the illumination area k respectively. m and n represent an x coordinate and a y coordinate of the center position of the illumination area k, respectively. x max  and y max  represent an x coordinate and a y coordinate of a pixel position where the display errors ΔL max , Δa max  and Δb max  are generated, respectively. P R (i, j) represents the intensity of the light source intensity distribution of R light at a position (i, j). The same notation is applied to the light source intensity distributions of G light and B light. 
     Further, light source intensity values R BL (k) i , G BL (k) i , B BL (k) i  are updated based on ΔR(k), ΔG(k), ΔB(k) according to Formula 30. R BL (k) i , G BL (k) i , B BL (k) i  represent the light source intensities of the illumination area k calculated by an i-th update. The initial values of the light source intensity values are R BL (k) 0 , G BL (k) 0 , B BL (k) 0 .
 
 R   BL ( k ) i+1   =R   BL ( k ) i   +ΔR ( k )
 
 G   BL ( k ) i+1   =G   BL ( k ) i   +ΔG ( k )
 
 B   BL ( k ) i+1   =B   BL ( k ) i   +ΔB ( k )  (30)
 
     Then, the intensity distribution presumption unit  131 , the color presumption unit  106 , the signal correction unit  108 , the error calculation unit  110 , and the control unit  112  perform the above described processing based on the updated light source intensity information  105 . 
     The update processing is repeated until the control unit  112  determines that the display error ΔE max  is sufficiently small. When the number of update times previously set is reached, the control unit  112  may set the lastly updated light source intensity information  105  as the emission intensity information  113 . 
     The liquid crystal control unit  114  provides a liquid crystal control signal  116  to the liquid crystal panel, and displays an image of the corrected video signal  109   a  on a display area of the liquid crystal panel  118 . Further, the light source control unit  115  provides a light source control signal  117  to the backlight  119 , and performs control such that light having intensity according to the emission intensity information  113  is irradiated from the backlight  119 . 
     As described above, according to the fifth embodiment, the screen is divided into a plurality of areas, and the light source intensity and the video signal can be controlled more precisely. Thus, an image can be displayed with a minimum error between an image desired to be displayed and an actually displayed image. 
     A sixth embodiment will be described below.  FIG. 11  is a block diagram of an LCD device according to the sixth embodiment. The basic configuration of an LCD device  100   c  of the sixth embodiment is same as that of the first embodiment. The sixth embodiment is different from the first embodiment in that an intensity setting unit  104  sets light source intensity information  105  according to a color-converted video signal  103 . The following example shows a case where the colors of light sources are four colors of R, G, B and Cy, but the number of the colors of the light sources is not limited to four. 
     The intensity setting unit  104  of the embodiment sets the light source intensity information  105  according to the color-converted video signal  103 . In order to calculate light source intensities of respective colors from the color-converted video signal, a plurality of methods are applicable. The following example uses a method of converting maximum values X max , Y max , Z max  of tristimulus values of all pixels provided within a screen, into light source intensities R BL , G BL , B BL , C BL . A relation between the maximum values X max , Y max . Z max  and the values R BL , G BL , B BL , C BL  may be represented by Formula 31 using a 3×4 tristimulus value matrix. 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             X 
                             max 
                           
                         
                       
                       
                         
                           
                             Y 
                             max 
                           
                         
                       
                       
                         
                           
                             Z 
                             max 
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       [ 
                       
                         
                           
                             
                               X 
                               R 
                             
                           
                           
                             
                               X 
                               G 
                             
                           
                           
                             
                               X 
                               B 
                             
                           
                           
                             
                               X 
                               C 
                             
                           
                         
                         
                           
                             
                               Y 
                               R 
                             
                           
                           
                             
                               Y 
                               G 
                             
                           
                           
                             
                               Y 
                               B 
                             
                           
                           
                             
                               Y 
                               C 
                             
                           
                         
                         
                           
                             
                               Z 
                               R 
                             
                           
                           
                             
                               Z 
                               G 
                             
                           
                           
                             
                               Z 
                               B 
                             
                           
                           
                             
                               Z 
                               C 
                             
                           
                         
                       
                       ] 
                     
                     ⁡ 
                     
                       [ 
                       
                         
                           
                             
                               R 
                               BL 
                             
                           
                         
                         
                           
                             
                               G 
                               BL 
                             
                           
                         
                         
                           
                             
                               B 
                               BL 
                             
                           
                         
                         
                           
                             
                               C 
                               BL 
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   31 
                   ) 
                 
               
             
           
         
       
     
     In the Formula 31, X R , Y R , and Z R  represent tristimulus values which are given when an R light source emits light at maximum intensity. X G , Y G  and Z G  represent tristimulus values which are given when a G light source emits light at maximum intensity. X B , Y B , Z B  represent tristimulus values which are given when a B light source emits light at maximum intensity. X C , Y C , Z C  represent tristimulus values which are given when a Cy light source emits light at maximum intensity. 
     The maximum values X max , Y max  and Z max  are three elements, but the values R BL , G BL , B BL , C BL  are four elements. Thus, Formula 31 has a higher degree of freedom, and R BL , G BL , B BL , C BL  which satisfy Formula 31 are not determined uniquely. Accordingly, the light source intensity information  105  may be obtained by the following processing. A plurality of values is set for the intensity of a light source of a certain color. Further, the intensities of light sources of the remaining colors which satisfy Formula 31 are calculated with respect to each of the values. A combination of a plurality of light source intensities which satisfies the Formula 31 can be calculated, and the combination is set as the light source intensity information  105 . 
     The intensity setting unit  104  provides the light source intensity information  105  to a color presumption unit  106 . The color presumption unit  106  presumes tristimulus values of a light to be obtained after a mixture of lights which are emitted from light sources of respective colors passes through a liquid crystal panel, similarly to the first embodiment. A signal correction unit  108  calculates a corrected video signal  109  based on color information  107  of the transmitted light and the color-converted video signal  103 , and provides the calculated corrected video signal  109  to an error calculation unit  110 . 
     The error calculation unit  110  calculates an error  111  from the corrected video signal  109  and the input video signal  103 . A control unit  112  determines the light source intensity information having a minimum error as emission intensity information  113 , with reference to pieces of light source intensity information  105  set by the light source setting unit  104  and the errors corresponding to the pieces of light source intensity information  105 . 
     The control unit  112  provides the emission intensity information  113  to a light source control unit  115 . The control unit  112  provides a corrected video signal  109   a  corresponding to the emission intensity information  113 , to a liquid crystal control unit  114 . The liquid crystal control unit  114  provides a liquid crystal control signal  116  to a liquid crystal panel  118 , and displays the corrected video signal  109   a  on a display area of the liquid crystal panel  118 . Further, the light source control unit  115  provides a light source control signal  117  to a backlight  119 , and performs control such that a light having intensity according to the emission intensity information  113  is irradiated from the backlight  119 . 
     As described above, according to the sixth embodiment, an image can be displayed with a minimum error between an image desired to be displayed and an actually displayed image. The image can be displayed through a small number of calculations, without calculating and evaluating errors to be caused according to the pieces of light source intensity information of an enormous number of combinations of light source intensities. 
     A seventh embodiment will be described below. In an LCD device of the seventh embodiment, in addition to the configuration of the LCD device of the first embodiment, a backlight  119  is provided with light sources of a plurality of colors which are capable of controlling light source intensities of respective colors independently for each of a plurality of display areas. The display areas are obtained by dividing a screen. The light sources have different emission peak wavelengths. The following example shows a case where the light sources emit three colors of R, G and B, but the number of colors of the light sources is not limited to three. 
     A backlight of the embodiment has the same basic configuration as the backlight  119  of the first embodiment illustrated in  FIGS. 2A and 2B . The backlight can control intensities of an R light source  122 , a G light source  123  and a B light source  124  for each light source  121  illustrated in  FIG. 2A , individually. The illumination area of each of the light sources  121  is a portion of a display area of the liquid crystal panel  120  which corresponds to one of areas obtained by dividing the display area virtually. The illumination area of each of the light sources  121  is defined based on a spatial arrangement of the light sources  121  on the backlight  119 . 
     An illumination area of a video image which corresponds to the input video signal  103  and is displayed in the vicinity of the position of each light source  121  is defined for each light source  121 , in advance. 
     An intensity setting unit  104  sets light source intensity information  105  of R, G and B for each illumination area, and provides the light source intensity information  105  to a color presumption unit  106 . 
     The color presumption unit  106  presumes tristimulus values of a light to be obtained after a mixture of lights which are irradiated from light sources of respective colors to each pixel position of a liquid crystal panel for each illumination area passes through the liquid crystal panel. In the embodiment, the tristimulus values of the transmitted light are presumed under the assumption that a pixel within each illumination area is irradiated with a light having the same intensity as emission intensity of a light source of the illumination area but not irradiated with lights of the light sources of the other illumination areas. A signal correction unit  108  calculates a corrected video signal  109  based on color information  107  of the transmitted light and a video signal  103 , and provides the calculated corrected video signal  109  to an error calculation unit  110 . 
     Further, similarly to the first embodiment, the error calculation unit  110  calculates an error  111  based on the corrected video signal  109  and the color-converted video signal  103 . In the embodiment, a display error ΔE(x, y) of a pixel is provided to a control unit  112 , as the error  111  for each illumination area. The display error ΔE(x, y) is largest among the display errors of pixels provided within the illumination area 
     The control unit  112  determines a light source intensity information having a minimum error for each illumination area as emission intensity information  113 , with reference to the pieces of light source intensity information  105  which are set by the light source setting unit  104  for each illumination area, and the errors  111  corresponding to the pieces of light source intensity information  105 .
 
The control unit  112  provides the emission intensity information  113  to a light source control unit  115 . The control unit  112  provides a corrected video signal  109   a  corresponding to the emission intensity information  113  to a liquid crystal control unit  114 . The liquid crystal control unit  114  provides a liquid crystal control signal  116  to a liquid crystal panel  118 , and displays the corrected video signal  109   a  on a display area of the liquid crystal panel  118 . Further, the light source control unit  115  provides a light source control signal  117  to a backlight  119 , and performs control such that a light having intensity according to the emission intensity information  113  is irradiated from the backlight  119 .
 
     As described above, according to the seventh embodiment, the screen is divided into a plurality of areas, and the light source intensity and the video signal are controlled more precisely. Thus, an image can be displayed with a minimum error between an image desired to be displayed and an actually displayed image. 
     While certain embodiments have been described, these embodiments have been presented by way of example only, and are not intended to limit the scope of the inventions. Indeed, the novel embodiments described herein may be embodied in a variety of other forms; furthermore, various omissions, substitutions and changes in the form of the embodiments described herein may be made without departing from the spirit of the inventions. The accompanying claims and their equivalents are intended to cover such forms or modifications as would fall within the scope and spirit of the inventions.