Patent Publication Number: US-7724396-B2

Title: Method for dithering image data

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
   This application claims the priority benefit of Taiwan application serial no. 95134758, filed Sep. 20, 2006. All disclosure of the Taiwan application is incorporated herein by reference. 
   BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   The present invention relates to a method for dithering image data. More particularly, the present invention relates to a method for dithering image data capable of completely representing source signal grayscale values. 
   2. Description of Related Art 
   It is a common problem in the display of digital images that the grayscale resolution of a display device is less than the grayscale resolution of an output device. For example, the output device is a personal computer with an 8-bit resolution, while the display device is a thin film transistor liquid crystal display panel (TFT LCD panel) with a 6-bit resolution. At this time, the simplest method is to delete two least significant bits (LSB) of the signal grayscale value output from the personal computer, so as to turn the 8-bit grayscale value to a 6-bit grayscale value. However, the color levels of the displayed images are sacrificed if this method is adopted. 
   Accordingly, a method for increasing the color levels is developed, which performs dithering on the signal grayscale values of the output device. The method utilizes the feature that human eyes automatically average the grayscale values in a small region when viewing from distance to enable the average values to have more color levels. There are two common dithering methods: one of the methods includes the spatial dithering or also referred to as 2-dimensional dithering, and the other method includes the spatial dithering plus temporal dithering or also referred to as 3-dimensional dithering. 
   The 2-dimensional dithering process is performed in a unit of a pixel block of a fixed size. Table 1 is a table of correspondence between input blocks and output blocks according to the conventional 2-dimensional dithering method, in which the pixel block with a size of 4*2 is used. In the input block section, only two LSBs of the signal grayscale values, i.e., the bits deleted before being transmitted to the display device, are listed. In the output block section, 0 denotes that the signal grayscale value of this pixel needs a non-carry operation, and 1 denotes that the signal grayscale value of this pixel needs a carry operation. 
   
     
       
         
             
           
             
               TABLE 1 
             
           
          
             
                 
             
             
               Table of Correspondence of Conventional 2-Dimensional Dithering 
             
          
         
         
             
             
             
             
             
          
             
                 
               Input Blocks 
                 
               Output Blocks 
                 
             
             
                 
               (Two LSBs) 
                 
               (Carry) 
             
             
                 
                 
             
          
         
         
             
             
             
             
             
             
             
             
             
          
             
                 
               00 
               00 
               00 
               00 
               0 
               0 
               0 
               0 
             
             
                 
               00 
               00 
               00 
               00 
               0 
               0 
               0 
               0 
             
             
                 
               01 
               01 
               01 
               01 
               1 
               0 
               0 
               0 
             
             
                 
               01 
               01 
               01 
               01 
               0 
               0 
               1 
               0 
             
             
                 
               10 
               10 
               10 
               10 
               0 
               0 
               0 
               0 
             
             
                 
               10 
               10 
               10 
               10 
               1 
               1 
               1 
               1 
             
             
                 
               11 
               11 
               11 
               11 
               0 
               1 
               1 
               1 
             
             
                 
               11 
               11 
               11 
               11 
               1 
               1 
               0 
               1 
             
             
                 
                 
             
          
         
       
     
   
   The non-carry operation is performed to set the two LSBs of the signal grayscale value to 0, and the carry operation is performed to set the two LSBs of the signal grayscale value to 0 and then add 4 to the result. For example, Table 2 shows the output blocks of the signal grayscale values from 8 (1000 in binary) to 11 (1011 in binary) obtained in accordance with the rules of Table 1. As for the values from 8-11, the result of the carry operation is 12, and the result of the non-carry operation is 8. 
   
     
       
         
             
           
             
               TABLE 2 
             
           
          
             
                 
             
             
               Examples of Conventional 2-Dimensional Dithering 
             
          
         
         
             
             
             
             
             
          
             
                 
               Input Blocks 
                 
               Output Blocks 
                 
             
             
                 
               (Decimal) 
                 
               (Decimal) 
             
             
                 
                 
             
          
         
         
             
             
             
             
             
             
             
             
             
          
             
                 
               8 
               8 
               8 
               8 
               8 
               8 
               8 
               8 
             
             
                 
               8 
               8 
               8 
               8 
               8 
               8 
               8 
               8 
             
             
                 
               9 
               9 
               9 
               9 
               12 
               8 
               8 
               8 
             
             
                 
               9 
               9 
               9 
               9 
               8 
               8 
               12 
               8 
             
             
                 
               10 
               10 
               10 
               10 
               8 
               8 
               8 
               8 
             
             
                 
               10 
               10 
               10 
               10 
               12 
               12 
               12 
               12 
             
             
                 
               11 
               11 
               11 
               11 
               8 
               12 
               12 
               12 
             
             
                 
               11 
               11 
               11 
               11 
               12 
               12 
               8 
               12 
             
             
                 
                 
             
          
         
       
     
   
   It is known from Table 2 that the average values of four output blocks equal to the signal grayscale values of the respective corresponding input blocks, while Table 2 only uses two numerals 8 and 12 to represent 4 different color levels. The two LSBs of 8 and 12 are both 0, which is applicable to the 6-bit resolution. 
   In another aspect, the 3-dimensional dithering process is performed in a unit of the pixel block of a fixed size in several continuous frames. Table 3 is a table of correspondence between input blocks and output blocks according to the conventional 3-dimensional dithering method, in which the pixel block with the size of 4*2 in four continuous frames is used. Similarly, only two LSBs of the signal grayscale values are listed in the input block section in Table 3. After an input block is found, the fields under the input block are the corresponding output blocks in four continuous frames, wherein 0 denotes that the signal grayscale value of this pixel needs the non-carry operation, and 1 denotes that the signal grayscale value of this pixel needs the carry operation. According to the rules of Table 3, the overall average value of all pixels in the four continuous frames equals to the input signal grayscale value. 
   
     
       
         
             
           
             
               TABLE 3 
             
           
          
             
                 
             
             
               Table of Correspondence of Conventional 3-Dimensional Dithering 
             
          
         
         
             
             
          
             
                 
               Input Blocks (LSB) 
             
          
         
         
             
             
             
             
             
             
             
             
             
             
             
             
             
             
             
             
             
          
             
                 
               00 
               00 
               00 
               00 
               01 
               01 
               01 
               01 
               10 
               10 
               10 
               10 
               11 
               11 
               11 
               11 
             
             
                 
               00 
               00 
               00 
               00 
               01 
               01 
               01 
               01 
               10 
               10 
               10 
               10 
               11 
               11 
               11 
               11 
             
             
                 
                 
             
          
         
         
             
             
             
             
             
             
             
             
             
             
             
             
             
             
             
             
             
          
             
               1 st  Frame 
               0 
               0 
               0 
               0 
               1 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
               1 
               1 
               1 
             
             
               (Carry) 
               0 
               0 
               0 
               0 
               0 
               0 
               1 
               0 
               1 
               1 
               1 
               1 
               1 
               1 
               0 
               1 
             
             
               2 nd  Frame 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
               1 
               1 
               1 
               1 
               1 
               1 
               1 
               1 
               0 
             
             
               (Carry) 
               0 
               0 
               0 
               0 
               0 
               1 
               0 
               0 
               0 
               0 
               0 
               0 
               1 
               0 
               1 
               1 
             
             
               3 rd  Frame 
               0 
               0 
               0 
               0 
               0 
               0 
               1 
               0 
               0 
               0 
               0 
               0 
               1 
               1 
               0 
               1 
             
             
               (Carry) 
               0 
               0 
               0 
               0 
               1 
               0 
               0 
               0 
               1 
               1 
               1 
               1 
               0 
               1 
               1 
               1 
             
             
               4 th  Frame 
               0 
               0 
               0 
               0 
               0 
               1 
               0 
               0 
               1 
               1 
               1 
               1 
               1 
               0 
               1 
               1 
             
             
               (Carry) 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
               1 
               0 
               0 
               0 
               0 
               1 
               1 
               1 
               0 
             
             
                 
             
          
         
       
     
   
   However, the conventional dithering methods are disadvantageous in that not all signal grayscale values are represented. For example, in the above examples, the display device has a 6-bit resolution only, so the maximum value is 63, and after being multiplied by 4, only 252 signal grayscale values can be represented in maximum. However, the three primary colors red, green, and blue can be combined to represent 256 3 =16,777,216 color originally, while only 253 3 =16,194,277 is represented after the dithering, thus losing about 3.5% of the color levels. 
   SUMMARY OF THE INVENTION 
   The present invention is directed to a method for dithering image data, so as to represent all color levels of an output device with 2-dimensional dithering. 
   The present invention is also directed to a method for dithering image data, so as to represent all color levels of an output device with 3-dimensional dithering. 
   In order to achieve the aforementioned and other objectives, the present invention provides a method for dithering image data, which is suitable for representing A-bit grayscale levels with a B-bit resolution, where A and B are both positive integers and A&gt;B. The method includes the following steps. First, a signal grayscale value 0 is corresponded to a target grayscale value 0, and a grayscale value 2 A −1 is corresponded to a target grayscale value (2 B −1)*2 A−B . A target grayscale value corresponding to the signal grayscale value among the signal grayscale values from 1 to 2 A −2 is calculated through interpolation and rounding off. The 2 A  target grayscale values form a strictly increasing sequence. When represented in binary, each of the target grayscale values includes A integer digits and C decimal digits, where C is a positive integer. 
   Then, if the signal grayscale value to be represented is X, according to the correspondence between the 2 A  signal grayscales and the 2 A  target grayscale values, the target grayscale value Y corresponding to the signal grayscale value X is obtained. Then, D=A−B+C is calculated, and a value K of the D LSBs of Y is calculated. Finally, in one E*F pixel block, the grayscale values of N pixels are set to Y−K+2 A−B , and the other grayscale values of the rest E*F−N pixels are set to Y−K, wherein E*F is a multiple of 2 D , and N/(E*F)=K/2 A−B . 
   In order to achieve the aforementioned and other objectives, the present invention provides another method for dithering image data. The first few steps of this method are the same as the previous method, and the last step is changed as follows. Among altogether E*F*P pixels included an E*F pixel block in P continuous frames, the grayscale value of N pixels is set to Y−K+2 A−B , and the grayscale value of the rest E*F*P−N pixels is set to Y−K, wherein E*F*P is a multiple of 2 D , and N/(E*F*P)=K/2 A−B . 
   As described above, the present invention uses decimals. 2 A  target grayscale values within the interval from 0 to (2 B −1)*2 A−B  are calculated, and then the target grayscale values with decimals are represented by using finer 2-dimensional dithering or 3-dimensional dithering. Therefore, the present invention is superior compared to the prior art, and can represent all color levels of the output device. 
   In order to make the aforementioned and other objects, features and advantages of the present invention comprehensible, preferred embodiments accompanied with figures are described in detail below. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  is a flow chart of a method for dithering image data according to an embodiment of the present invention. 
   

   DESCRIPTION OF EMBODIMENTS 
   The present invention provides a 2-dimensional dithering method and a 3-dimensional dithering method. The present invention will be illustrated with a simple embodiment first, and then will be illustrated with more complicated general rules. 
   This embodiment uses a 6-bit resolution to represent 8-bit color levels. In consideration of the conventional dithering method dividing 252 signal grayscale values in maximum, the solution in this embodiment includes calculating 256 different target grayscale values within the interval from 0 to 252 to correspond to the original 256 signal grayscale values. Then, the target grayscale values are represented through 2-dimensional dithering or 3-dimensional dithering. Thus, the overall 256 grayscales are represented. 
   Table 4 is a table of correspondence of the signal grayscale values and the target grayscale values of this embodiment, in which the target grayscale values are obtained with interpolation first, and then are rounded off to multiples of 0.25. For example, if the signal grayscale value X=9, the target grayscale value Y=9. If X=60, then Y=59.25. If X=192, then Y=189.75. If X=255, then Y=252. 
   
     
       
         
             
           
             
               TABLE 4 
             
           
          
             
                 
             
             
               Table of Correspondence between Signal Grayscale Values and Target 
             
             
               Grayscale Values of an Embodiment of the Present Invention 
             
          
         
         
             
             
             
          
             
                 
               Signal Grayscale 
               Target Grayscale 
             
             
                 
               Value X 
               Value Y 
             
             
                 
                 
             
             
                 
               0 ≦ X ≦ 10 
               Y = X 
             
             
                 
               11 ≦ X ≦ 31 
               Y = X − 0.25 
             
             
                 
               32 ≦ X ≦ 53 
               Y = X − 0.5 
             
             
                 
               54 ≦ X ≦ 74 
               Y = X − 0.75 
             
             
                 
               75 ≦ X ≦ 95 
               Y = X − 1 
             
             
                 
               96 ≦ X ≦ 116 
               Y = X − 1.25 
             
             
                 
               117 ≦ X ≦ 138 
               Y = X − 1.5 
             
             
                 
               139 ≦ X ≦ 159 
               Y = X − 1.75 
             
             
                 
               160 ≦ X ≦ 180 
               Y = X − 2 
             
             
                 
               181 ≦ X ≦ 201 
               Y = X − 2.25 
             
             
                 
               202 ≦ X ≦ 223 
               Y = X − 2.5 
             
             
                 
               224 ≦ X ≦ 244 
               Y = X − 2.75 
             
             
                 
               245 ≦ X ≦ 255 
               Y = X − 3 
             
             
                 
                 
             
          
         
       
     
   
   By looking up Table 4, any signal grayscale value from 0 to 255 can be converted to the corresponding target grayscale value. The next step involves representing the target grayscale values with decimals by using 2-dimensional dithering or 3-dimensional dithering. If the 2-dimensional dithering is used, the average grayscale value in a pixel block must be made equal to the target grayscale value. If the 3-dimensional dithering is used, the average grayscale value in one pixel block in several continuous frames must be made to equal to the target grayscale value. 
   Table 5 is a table of correspondence between the input blocks and the output blocks of the 2-dimensional dithering method in this embodiment. The 2-dimensional dithering in this embodiment uses 4*8 pixel blocks. Only four LSBs of the target grayscale values are listed in the input block sections in Table 5. It should be noted that all the target grayscale values of this embodiment include two decimal digits if expressed in binary, and the aforementioned four LSBs include the decimals. For example, the target grayscale value 106.75 is 01101010.11 in binary, and the four LSBs are 1011. That is, the 8-bit signal grayscale value is converted to a 10-bit target grayscale value, and four LSBs of the target grayscale value are taken to find out the corresponding output block by looking up Table 5. 
   
     
       
         
             
           
             
               TABLE 5 
             
           
          
             
                 
             
             
               Table of Correspondence of 2-Dimensional Dithering according to an 
             
             
               Embodiment of the Present Invention 
             
          
         
         
             
             
             
             
          
             
                 
               Output 
                 
               Output 
             
             
               Input Blocks 
               Blocks 
               Input Blocks 
               Blocks 
             
             
               (4 LSBs) 
               (Carry) 
               (4 LSBs) 
               (Carry) 
             
             
                 
             
          
         
         
             
             
             
             
             
             
             
             
             
             
             
             
             
             
             
             
          
             
               0000 
               0000 
               0000 
               0000 
               0 
               0 
               0 
               0 
               1000 
               1000 
               1000 
               1000 
               0 
               0 
               0 
               0 
             
             
               0000 
               0000 
               0000 
               0000 
               0 
               0 
               0 
               0 
               1000 
               1000 
               1000 
               1000 
               1 
               1 
               1 
               1 
             
             
               0000 
               0000 
               0000 
               0000 
               0 
               0 
               0 
               0 
               1000 
               1000 
               1000 
               1000 
               0 
               0 
               0 
               0 
             
             
               0000 
               0000 
               0000 
               0000 
               0 
               0 
               0 
               0 
               1000 
               1000 
               1000 
               1000 
               1 
               1 
               1 
               1 
             
             
               0000 
               0000 
               0000 
               0000 
               0 
               0 
               0 
               0 
               1000 
               1000 
               1000 
               1000 
               0 
               0 
               0 
               0 
             
             
               0000 
               0000 
               0000 
               0000 
               0 
               0 
               0 
               0 
               1000 
               1000 
               1000 
               1000 
               1 
               1 
               1 
               1 
             
             
               0000 
               0000 
               0000 
               0000 
               0 
               0 
               0 
               0 
               1000 
               1000 
               1000 
               1000 
               0 
               0 
               0 
               0 
             
             
               0000 
               0000 
               0000 
               0000 
               0 
               0 
               0 
               0 
               1000 
               1000 
               1000 
               1000 
               1 
               1 
               1 
               1 
             
             
               0001 
               0001 
               0001 
               0001 
               0 
               0 
               0 
               0 
               1001 
               1001 
               1001 
               1001 
               0 
               0 
               0 
               0 
             
             
               0001 
               0001 
               0001 
               0001 
               0 
               0 
               0 
               0 
               1001 
               1001 
               1001 
               1001 
               1 
               1 
               1 
               1 
             
             
               0001 
               0001 
               0001 
               0001 
               0 
               0 
               0 
               0 
               1001 
               1001 
               1001 
               1001 
               0 
               0 
               0 
               0 
             
             
               0001 
               0001 
               0001 
               0001 
               0 
               0 
               0 
               0 
               1001 
               1001 
               1001 
               1001 
               1 
               1 
               1 
               1 
             
             
               0001 
               0001 
               0001 
               0001 
               0 
               0 
               0 
               0 
               1001 
               1001 
               1001 
               1001 
               0 
               0 
               0 
               0 
             
             
               0001 
               0001 
               0001 
               0001 
               0 
               0 
               0 
               0 
               1001 
               1001 
               1001 
               1001 
               1 
               1 
               1 
               1 
             
             
               0001 
               0001 
               0001 
               0001 
               1 
               0 
               0 
               0 
               1001 
               1001 
               1001 
               1001 
               0 
               1 
               1 
               1 
             
             
               0001 
               0001 
               0001 
               0001 
               0 
               0 
               1 
               0 
               1001 
               1001 
               1001 
               1001 
               1 
               1 
               0 
               1 
             
             
               0010 
               0010 
               0010 
               0010 
               0 
               0 
               0 
               0 
               1010 
               1010 
               1010 
               1010 
               0 
               0 
               0 
               0 
             
             
               0010 
               0010 
               0010 
               0010 
               0 
               0 
               0 
               0 
               1010 
               1010 
               1010 
               1010 
               1 
               1 
               1 
               1 
             
             
               0010 
               0010 
               0010 
               0010 
               1 
               0 
               0 
               0 
               1010 
               1010 
               1010 
               1010 
               0 
               1 
               1 
               1 
             
             
               0010 
               0010 
               0010 
               0010 
               0 
               0 
               1 
               0 
               1010 
               1010 
               1010 
               1010 
               1 
               1 
               0 
               1 
             
             
               0010 
               0010 
               0010 
               0010 
               0 
               0 
               0 
               0 
               1010 
               1010 
               1010 
               1010 
               0 
               0 
               0 
               0 
             
             
               0010 
               0010 
               0010 
               0010 
               0 
               0 
               0 
               0 
               1010 
               1010 
               1010 
               1010 
               1 
               1 
               1 
               1 
             
             
               0010 
               0010 
               0010 
               0010 
               1 
               0 
               0 
               0 
               1010 
               1010 
               1010 
               1010 
               0 
               1 
               1 
               1 
             
             
               0010 
               0010 
               0010 
               0010 
               0 
               0 
               1 
               0 
               1010 
               1010 
               1010 
               1010 
               1 
               1 
               0 
               1 
             
             
               0011 
               0011 
               0011 
               0011 
               1 
               0 
               0 
               0 
               1011 
               1011 
               1011 
               1011 
               0 
               1 
               1 
               1 
             
             
               0011 
               0011 
               0011 
               0011 
               0 
               0 
               1 
               0 
               1011 
               1011 
               1011 
               1011 
               1 
               1 
               0 
               1 
             
             
               0011 
               0011 
               0011 
               0011 
               1 
               0 
               0 
               0 
               1011 
               1011 
               1011 
               1011 
               0 
               1 
               1 
               1 
             
             
               0011 
               0011 
               0011 
               0011 
               0 
               0 
               1 
               0 
               1011 
               1011 
               1011 
               1011 
               1 
               1 
               0 
               1 
             
             
               0011 
               0011 
               0011 
               0011 
               1 
               0 
               0 
               0 
               1011 
               1011 
               1011 
               1011 
               0 
               1 
               1 
               1 
             
             
               0011 
               0011 
               0011 
               0011 
               0 
               0 
               1 
               0 
               1011 
               1011 
               1011 
               1011 
               1 
               1 
               0 
               1 
             
             
               0011 
               0011 
               0011 
               0011 
               0 
               0 
               0 
               0 
               1011 
               1011 
               1011 
               1011 
               0 
               0 
               0 
               0 
             
             
               0011 
               0011 
               0011 
               0011 
               0 
               0 
               0 
               0 
               1011 
               1011 
               1011 
               1011 
               1 
               1 
               1 
               1 
             
             
               0100 
               0100 
               0100 
               0100 
               1 
               0 
               0 
               0 
               1100 
               1100 
               1100 
               1100 
               0 
               1 
               1 
               1 
             
             
               0100 
               0100 
               0100 
               0100 
               0 
               0 
               1 
               0 
               1100 
               1100 
               1100 
               1100 
               1 
               1 
               0 
               1 
             
             
               0100 
               0100 
               0100 
               0100 
               1 
               0 
               0 
               0 
               1100 
               1100 
               1100 
               1100 
               0 
               1 
               1 
               1 
             
             
               0100 
               0100 
               0100 
               0100 
               0 
               0 
               1 
               0 
               1100 
               1100 
               1100 
               1100 
               1 
               1 
               0 
               1 
             
             
               0100 
               0100 
               0100 
               0100 
               1 
               0 
               0 
               0 
               1100 
               1100 
               1100 
               1100 
               0 
               1 
               1 
               1 
             
             
               0100 
               0100 
               0100 
               0100 
               0 
               0 
               1 
               0 
               1100 
               1100 
               1100 
               1100 
               1 
               1 
               0 
               1 
             
             
               0100 
               0100 
               0100 
               0100 
               1 
               0 
               0 
               0 
               1100 
               1100 
               1100 
               1100 
               0 
               1 
               1 
               1 
             
             
               0100 
               0100 
               0100 
               0100 
               0 
               0 
               1 
               0 
               1100 
               1100 
               1100 
               1100 
               1 
               1 
               0 
               1 
             
             
               0101 
               0101 
               0101 
               0101 
               1 
               0 
               0 
               0 
               1101 
               1101 
               1101 
               1101 
               0 
               1 
               1 
               1 
             
             
               0101 
               0101 
               0101 
               0101 
               0 
               0 
               1 
               0 
               1101 
               1101 
               1101 
               1101 
               1 
               1 
               0 
               1 
             
             
               0101 
               0101 
               0101 
               0101 
               1 
               0 
               0 
               0 
               1101 
               1101 
               1101 
               1101 
               0 
               1 
               1 
               1 
             
             
               0101 
               0101 
               0101 
               0101 
               0 
               0 
               1 
               0 
               1101 
               1101 
               1101 
               1101 
               1 
               1 
               0 
               1 
             
             
               0101 
               0101 
               0101 
               0101 
               1 
               0 
               0 
               0 
               1101 
               1101 
               1101 
               1101 
               0 
               1 
               1 
               1 
             
             
               0101 
               0101 
               0101 
               0101 
               0 
               0 
               1 
               0 
               1101 
               1101 
               1101 
               1101 
               1 
               1 
               0 
               1 
             
             
               0101 
               0101 
               0101 
               0101 
               0 
               0 
               0 
               0 
               1101 
               1101 
               1101 
               1101 
               1 
               1 
               1 
               1 
             
             
               0101 
               0101 
               0101 
               0101 
               1 
               1 
               1 
               1 
               1101 
               1101 
               1101 
               1101 
               1 
               1 
               1 
               1 
             
             
               0110 
               0110 
               0110 
               0110 
               1 
               0 
               0 
               0 
               1110 
               1110 
               1110 
               1110 
               0 
               1 
               1 
               1 
             
             
               0110 
               0110 
               0110 
               0110 
               0 
               0 
               1 
               0 
               1110 
               1110 
               1110 
               1110 
               1 
               1 
               0 
               1 
             
             
               0110 
               0110 
               0110 
               0110 
               0 
               0 
               0 
               0 
               1110 
               1110 
               1110 
               1110 
               1 
               1 
               1 
               1 
             
             
               0110 
               0110 
               0110 
               0110 
               1 
               1 
               1 
               1 
               1110 
               1110 
               1110 
               1110 
               1 
               1 
               1 
               1 
             
             
               0110 
               0110 
               0110 
               0110 
               1 
               0 
               0 
               0 
               1110 
               1110 
               1110 
               1110 
               0 
               1 
               1 
               1 
             
             
               0110 
               0110 
               0110 
               0110 
               0 
               0 
               1 
               0 
               1110 
               1110 
               1110 
               1110 
               1 
               1 
               0 
               1 
             
             
               0110 
               0110 
               0110 
               0110 
               0 
               0 
               0 
               0 
               1110 
               1110 
               1110 
               1110 
               1 
               1 
               1 
               1 
             
             
               0110 
               0110 
               0110 
               0110 
               1 
               1 
               1 
               1 
               1110 
               1110 
               1110 
               1110 
               1 
               1 
               1 
               1 
             
             
               0111 
               0111 
               0111 
               0111 
               0 
               0 
               0 
               0 
               1111 
               1111 
               1111 
               1111 
               1 
               1 
               1 
               1 
             
             
               0111 
               0111 
               0111 
               0111 
               1 
               1 
               1 
               1 
               1111 
               1111 
               1111 
               1111 
               1 
               1 
               1 
               1 
             
             
               0111 
               0111 
               0111 
               0111 
               0 
               0 
               0 
               0 
               1111 
               1111 
               1111 
               1111 
               1 
               1 
               1 
               1 
             
             
               0111 
               0111 
               0111 
               0111 
               1 
               1 
               1 
               1 
               1111 
               1111 
               1111 
               1111 
               1 
               1 
               1 
               1 
             
             
               0111 
               0111 
               0111 
               0111 
               0 
               0 
               0 
               0 
               1111 
               1111 
               1111 
               1111 
               1 
               1 
               1 
               1 
             
             
               0111 
               0111 
               0111 
               0111 
               1 
               1 
               1 
               1 
               1111 
               1111 
               1111 
               1111 
               1 
               1 
               1 
               1 
             
             
               0111 
               0111 
               0111 
               0111 
               1 
               0 
               0 
               0 
               1111 
               1111 
               1111 
               1111 
               0 
               1 
               1 
               1 
             
             
               0111 
               0111 
               0111 
               0111 
               0 
               0 
               1 
               0 
               1111 
               1111 
               1111 
               1111 
               1 
               1 
               0 
               1 
             
             
                 
             
          
         
       
     
   
   In the output block sections of Table 5, 0 denotes that the corresponding pixel needs the non-carry operation, and 1 denotes that the corresponding pixel needs the carry operation. In this embodiment, the non-carry operation is performed to set four LSBs of the target grayscale value to 0, and the carry operation is performed to set the four LSBs of the target grayscale value to 0 and then add 4 to the result. After setting, the average grayscale values of the output blocks are made equal to the target grayscale values, and the four LSBs of the grayscale values in the output blocks equal to 0. After the four LSBs are deleted, 6-bit integers are obtained, which are applicable to the display device. 
   Tables 6-1 to 6-8 are tables of correspondence between the input blocks and the output blocks of the 3-dimensional dithering method in this embodiment. The 3-dimensional dithering method of this embodiment uses a 4*2 pixel block in 16 continuous frames as the unit for processing. Similar to the 2-dimensional dithering method, only four LSBs of the target grayscale values are listed in the input block sections in Tables 6-1 to 6-8. After an input block is found with the four LSBs, the fields under the input block are the output blocks in 16 continuous frames. Also, in the output block sections of Tables 6-1 to 6-8, 0 denotes the non-carry operation, and 1 denotes the carry operation. By setting the grayscales in accordance with the rules of Tables 6-1 to 6-8, the average grayscale values of the pixel blocks in 16 continuous frames are made equal to the target grayscale values. 
   
     
       
         
             
           
             
               TABLE 6-1 
             
           
          
             
                 
             
             
               Table of Correspondence of 3-Dimensional Dithering according to an 
             
             
               Embodiment of the Present Invention 
             
          
         
         
             
             
          
             
                 
               Input Blocks 
             
             
                 
               (4 LSBs) 
             
          
         
         
             
             
             
             
             
             
             
             
             
          
             
                 
               0000 
               0000 
               0000 
               0000 
               0001 
               0001 
               0001 
               0001 
             
             
                 
               0000 
               0000 
               0000 
               0000 
               0001 
               0001 
               0001 
               0001 
             
             
                 
                 
             
          
         
         
             
             
             
             
             
             
             
             
             
          
             
               1 st  Frame 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
             
             
               (Carry) 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
             
             
               2 nd  Frame 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
             
             
               (Carry) 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
             
             
               3 rd  Frame 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
             
             
               (Carry) 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
             
             
               4 th  Frame 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
             
             
               (Carry) 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
             
             
               5 th  Frame 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
             
             
               (Carry) 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
             
             
               6 th  Frame 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
             
             
               (Carry) 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
             
             
               7 th  Frame 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
             
             
               (Carry) 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
             
             
               8 th  Frame 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
             
             
               (Carry) 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
             
             
               9 th  Frame 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
             
             
               (Carry) 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
             
             
               10 th  Frame 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
             
             
               (Carry) 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
             
             
               11 th  Frame 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
             
             
               (Carry) 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
             
             
               12 th  Frame 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
             
             
               (Carry) 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
             
             
               13 th  Frame 
               0 
               0 
               0 
               0 
               1 
               0 
               0 
               0 
             
             
               (Carry) 
               0 
               0 
               0 
               0 
               0 
               0 
               1 
               0 
             
             
               14 th  Frame 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
               1 
             
             
               (Carry) 
               0 
               0 
               0 
               0 
               0 
               1 
               0 
               0 
             
             
               15 th  Frame 
               0 
               0 
               0 
               0 
               0 
               0 
               1 
               0 
             
             
               (Carry) 
               0 
               0 
               0 
               0 
               1 
               0 
               0 
               0 
             
             
               16 th  Frame 
               0 
               0 
               0 
               0 
               0 
               1 
               0 
               0 
             
             
               (Carry) 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
               1 
             
             
                 
             
          
         
       
     
   
   
     
       
         
             
           
             
               TABLE 6-2 
             
           
          
             
                 
             
             
               Table of Correspondence of 3-Dimensional Dithering according to an 
             
             
               Embodiment of the Present Invention 
             
          
         
         
             
             
          
             
                 
               Input Blocks 
             
             
                 
               (4 LSBs) 
             
          
         
         
             
             
             
             
             
             
             
             
             
          
             
                 
               0010 
               0010 
               0010 
               0010 
               0011 
               0011 
               0011 
               0011 
             
             
                 
               0010 
               0010 
               0010 
               0010 
               0011 
               0011 
               0011 
               0011 
             
             
                 
                 
             
          
         
         
             
             
             
             
             
             
             
             
             
          
             
               1 st  Frame 
               0 
               0 
               0 
               0 
               1 
               0 
               0 
               0 
             
             
               (Carry) 
               0 
               0 
               0 
               0 
               0 
               0 
               1 
               0 
             
             
               2 nd  Frame 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
               1 
             
             
               (Carry) 
               0 
               0 
               0 
               0 
               0 
               1 
               0 
               0 
             
             
               3 rd  Frame 
               0 
               0 
               0 
               0 
               0 
               0 
               1 
               0 
             
             
               (Carry) 
               0 
               0 
               0 
               0 
               1 
               0 
               0 
               0 
             
             
               4 th  Frame 
               0 
               0 
               0 
               0 
               0 
               1 
               0 
               0 
             
             
               (Carry) 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
               1 
             
             
               5 th  Frame 
               1 
               0 
               0 
               0 
               1 
               0 
               0 
               0 
             
             
               (Carry) 
               0 
               0 
               1 
               0 
               0 
               0 
               1 
               0 
             
             
               6 th  Frame 
               0 
               0 
               0 
               1 
               0 
               0 
               0 
               1 
             
             
               (Carry) 
               0 
               1 
               0 
               0 
               0 
               1 
               0 
               0 
             
             
               7 th  Frame 
               0 
               0 
               1 
               0 
               0 
               0 
               1 
               0 
             
             
               (Carry) 
               1 
               0 
               0 
               0 
               1 
               0 
               0 
               0 
             
             
               8 th  Frame 
               0 
               1 
               0 
               0 
               0 
               1 
               0 
               0 
             
             
               (Carry) 
               0 
               0 
               0 
               1 
               0 
               0 
               0 
               1 
             
             
               9 th  Frame 
               0 
               0 
               0 
               0 
               1 
               0 
               0 
               0 
             
             
               (Carry) 
               0 
               0 
               0 
               0 
               0 
               0 
               1 
               0 
             
             
               10 th  Frame 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
               1 
             
             
               (Carry) 
               0 
               0 
               0 
               0 
               0 
               1 
               0 
               0 
             
             
               11 th  Frame 
               0 
               0 
               0 
               0 
               0 
               0 
               1 
               0 
             
             
               (Carry) 
               0 
               0 
               0 
               0 
               1 
               0 
               0 
               0 
             
             
               12 th  Frame 
               0 
               0 
               0 
               0 
               0 
               1 
               0 
               0 
             
             
               (Carry) 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
               1 
             
             
               13 th  Frame 
               1 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
             
             
               (Carry) 
               0 
               0 
               1 
               0 
               0 
               0 
               0 
               0 
             
             
               14 th  Frame 
               0 
               0 
               0 
               1 
               0 
               0 
               0 
               0 
             
             
               (Carry) 
               0 
               1 
               0 
               0 
               0 
               0 
               0 
               0 
             
             
               15 th  Frame 
               0 
               0 
               1 
               0 
               0 
               0 
               0 
               0 
             
             
               (Carry) 
               1 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
             
             
               16 th  Frame 
               0 
               1 
               0 
               0 
               0 
               0 
               0 
               0 
             
             
               (Carry) 
               0 
               0 
               0 
               1 
               0 
               0 
               0 
               0 
             
             
                 
             
          
         
       
     
   
   
     
       
         
             
           
             
               TABLE 6-3 
             
           
          
             
                 
             
             
               Table of Correspondence of 3-Dimensional Dithering according to an 
             
             
               Embodiment of the Present Invention 
             
          
         
         
             
             
          
             
                 
               Input Blocks 
             
             
                 
               (4 LSBs) 
             
          
         
         
             
             
             
             
             
             
             
             
             
          
             
                 
               0100 
               0100 
               0100 
               0100 
               0101 
               0101 
               0101 
               0101 
             
             
                 
               0100 
               0100 
               0100 
               0100 
               0101 
               0101 
               0101 
               0101 
             
             
                 
                 
             
          
         
         
             
             
             
             
             
             
             
             
             
          
             
               1 st  Frame 
               1 
               0 
               0 
               0 
               1 
               0 
               0 
               0 
             
             
               (Carry) 
               0 
               0 
               1 
               0 
               0 
               0 
               1 
               0 
             
             
               2 nd  Frame 
               0 
               0 
               0 
               1 
               0 
               0 
               0 
               1 
             
             
               (Carry) 
               0 
               1 
               0 
               0 
               0 
               1 
               0 
               0 
             
             
               3 rd  Frame 
               0 
               0 
               1 
               0 
               0 
               0 
               1 
               0 
             
             
               (Carry) 
               1 
               0 
               0 
               0 
               1 
               0 
               0 
               0 
             
             
               4 th  Frame 
               0 
               1 
               0 
               0 
               0 
               1 
               0 
               0 
             
             
               (Carry) 
               0 
               0 
               0 
               1 
               0 
               0 
               0 
               1 
             
             
               5 th  Frame 
               1 
               0 
               0 
               0 
               1 
               0 
               0 
               0 
             
             
               (Carry) 
               0 
               0 
               1 
               0 
               0 
               0 
               1 
               0 
             
             
               6 th  Frame 
               0 
               0 
               0 
               1 
               0 
               0 
               0 
               1 
             
             
               (Carry) 
               0 
               1 
               0 
               0 
               0 
               1 
               0 
               0 
             
             
               7 th  Frame 
               0 
               0 
               1 
               0 
               0 
               0 
               1 
               0 
             
             
               (Carry) 
               1 
               0 
               0 
               0 
               1 
               0 
               0 
               0 
             
             
               8 th  Frame 
               0 
               1 
               0 
               0 
               0 
               1 
               0 
               0 
             
             
               (Carry) 
               0 
               0 
               0 
               1 
               0 
               0 
               0 
               1 
             
             
               9 th  Frame 
               1 
               0 
               0 
               0 
               1 
               0 
               0 
               0 
             
             
               (Carry) 
               0 
               0 
               1 
               0 
               0 
               0 
               1 
               0 
             
             
               10 th  Frame 
               0 
               0 
               0 
               1 
               0 
               0 
               0 
               1 
             
             
               (Carry) 
               0 
               1 
               0 
               0 
               0 
               1 
               0 
               0 
             
             
               11 th  Frame 
               0 
               0 
               1 
               0 
               0 
               0 
               1 
               0 
             
             
               (Carry) 
               1 
               0 
               0 
               0 
               1 
               0 
               0 
               0 
             
             
               12 th  Frame 
               0 
               1 
               0 
               0 
               0 
               1 
               0 
               0 
             
             
               (Carry) 
               0 
               0 
               0 
               1 
               0 
               0 
               0 
               1 
             
             
               13 th  Frame 
               1 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
             
             
               (Carry) 
               0 
               0 
               1 
               0 
               1 
               1 
               1 
               1 
             
             
               14 th  Frame 
               0 
               0 
               0 
               1 
               1 
               1 
               1 
               1 
             
             
               (Carry) 
               0 
               1 
               0 
               0 
               0 
               0 
               0 
               0 
             
             
               15 th  Frame 
               0 
               0 
               1 
               0 
               0 
               0 
               0 
               0 
             
             
               (Carry) 
               1 
               0 
               0 
               0 
               1 
               1 
               1 
               1 
             
             
               16 th  Frame 
               0 
               1 
               0 
               0 
               1 
               1 
               1 
               1 
             
             
               (Carry) 
               0 
               0 
               0 
               1 
               0 
               0 
               0 
               0 
             
             
                 
             
          
         
       
     
   
   
     
       
         
             
           
             
               TABLE 6-4 
             
           
          
             
                 
             
             
               Table of Correspondence of 3-Dimensional Dithering according to an 
             
             
               Embodiment of the Present Invention 
             
          
         
         
             
             
          
             
                 
               Input Blocks 
             
             
                 
               (4 LSBs) 
             
          
         
         
             
             
             
             
             
             
             
             
             
          
             
                 
               0110 
               0110 
               0110 
               0110 
               0111 
               0111 
               0111 
               0111 
             
             
                 
               0110 
               0110 
               0110 
               0110 
               0111 
               0111 
               0111 
               0111 
             
             
                 
                 
             
          
         
         
             
             
             
             
             
             
             
             
             
          
             
               1 st  Frame 
               1 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
             
             
               (Carry) 
               0 
               0 
               1 
               0 
               1 
               1 
               1 
               1 
             
             
               2 nd  Frame 
               0 
               0 
               0 
               1 
               1 
               1 
               1 
               1 
             
             
               (Carry) 
               0 
               1 
               0 
               0 
               0 
               0 
               0 
               0 
             
             
               3 rd  Frame 
               0 
               0 
               1 
               0 
               0 
               0 
               0 
               0 
             
             
               (Carry) 
               1 
               0 
               0 
               0 
               1 
               1 
               1 
               1 
             
             
               4 th  Frame 
               0 
               1 
               0 
               0 
               1 
               1 
               1 
               1 
             
             
               (Carry) 
               0 
               0 
               0 
               1 
               0 
               0 
               0 
               0 
             
             
               5 th  Frame 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
             
             
               (Carry) 
               1 
               1 
               1 
               1 
               1 
               1 
               1 
               1 
             
             
               6 th  Frame 
               1 
               1 
               1 
               1 
               1 
               1 
               1 
               1 
             
             
               (Carry) 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
             
             
               7 th  Frame 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
             
             
               (Carry) 
               1 
               1 
               1 
               1 
               1 
               1 
               1 
               1 
             
             
               8 th  Frame 
               1 
               1 
               1 
               1 
               1 
               1 
               1 
               1 
             
             
               (Carry) 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
             
             
               9 th  Frame 
               1 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
             
             
               (Carry) 
               0 
               0 
               1 
               0 
               1 
               1 
               1 
               1 
             
             
               10 th  Frame 
               0 
               0 
               0 
               1 
               1 
               1 
               1 
               1 
             
             
               (Carry) 
               0 
               1 
               0 
               0 
               0 
               0 
               0 
               0 
             
             
               11 th  Frame 
               0 
               0 
               1 
               0 
               0 
               0 
               0 
               0 
             
             
               (Carry) 
               1 
               0 
               0 
               0 
               1 
               1 
               1 
               1 
             
             
               12 th  Frame 
               0 
               1 
               0 
               0 
               1 
               1 
               1 
               1 
             
             
               (Carry) 
               0 
               0 
               0 
               1 
               0 
               0 
               0 
               0 
             
             
               13 th  Frame 
               0 
               0 
               0 
               0 
               1 
               0 
               0 
               0 
             
             
               (Carry) 
               1 
               1 
               1 
               1 
               0 
               0 
               1 
               0 
             
             
               14 th  Frame 
               1 
               1 
               1 
               1 
               0 
               0 
               0 
               1 
             
             
               (Carry) 
               0 
               0 
               0 
               0 
               0 
               1 
               0 
               0 
             
             
               15 th  Frame 
               0 
               0 
               0 
               0 
               0 
               0 
               1 
               0 
             
             
               (Carry) 
               1 
               1 
               1 
               1 
               1 
               0 
               0 
               0 
             
             
               16 th  Frame 
               1 
               1 
               1 
               1 
               0 
               1 
               0 
               0 
             
             
               (Carry) 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
               1 
             
             
                 
             
          
         
       
     
   
   
     
       
         
             
           
             
               TABLE 6-5 
             
           
          
             
                 
             
             
               Table of Correspondence of 3-Dimensional Dithering according to an 
             
             
               Embodiment of the Present Invention 
             
          
         
         
             
             
          
             
                 
               Input Blocks 
             
             
                 
               (4 LSBs) 
             
          
         
         
             
             
             
             
             
             
             
             
             
          
             
                 
               1000 
               1000 
               1000 
               1000 
               1001 
               1001 
               1001 
               1001 
             
             
                 
               1000 
               1000 
               1000 
               1000 
               1001 
               1001 
               1001 
               1001 
             
             
                 
                 
             
          
         
         
             
             
             
             
             
             
             
             
             
          
             
               1 st  Frame 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
             
             
               (Carry) 
               1 
               1 
               1 
               1 
               1 
               1 
               1 
               1 
             
             
               2 nd  Frame 
               1 
               1 
               1 
               1 
               1 
               1 
               1 
               1 
             
             
               (Carry) 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
             
             
               3 rd  Frame 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
             
             
               (Carry) 
               1 
               1 
               1 
               1 
               1 
               1 
               1 
               1 
             
             
               4 th  Frame 
               1 
               1 
               1 
               1 
               1 
               1 
               1 
               1 
             
             
               (Carry) 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
             
             
               5 th  Frame 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
             
             
               (Carry) 
               1 
               1 
               1 
               1 
               1 
               1 
               1 
               1 
             
             
               6 th  Frame 
               1 
               1 
               1 
               1 
               1 
               1 
               1 
               1 
             
             
               (Carry) 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
             
             
               7 th  Frame 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
             
             
               (Carry) 
               1 
               1 
               1 
               1 
               1 
               1 
               1 
               1 
             
             
               8 th  Frame 
               1 
               1 
               1 
               1 
               1 
               1 
               1 
               1 
             
             
               (Carry) 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
             
             
               9 th  Frame 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
             
             
               (Carry) 
               1 
               1 
               1 
               1 
               1 
               1 
               1 
               1 
             
             
               10 th  Frame 
               1 
               1 
               1 
               1 
               1 
               1 
               1 
               1 
             
             
               (Carry) 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
             
             
               11 th  Frame 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
             
             
               (Carry) 
               1 
               1 
               1 
               1 
               1 
               1 
               1 
               1 
             
             
               12 th  Frame 
               1 
               1 
               1 
               1 
               1 
               1 
               1 
               1 
             
             
               (Carry) 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
               0 
             
             
               13 th  Frame 
               0 
               0 
               0 
               0 
               0 
               1 
               1 
               1 
             
             
               (Carry) 
               1 
               1 
               1 
               1 
               1 
               1 
               0 
               1 
             
             
               14 th  Frame 
               1 
               1 
               1 
               1 
               1 
               1 
               1 
               0 
             
             
               (Carry) 
               0 
               0 
               0 
               0 
               1 
               0 
               1 
               1 
             
             
               15 th  Frame 
               0 
               0 
               0 
               0 
               1 
               1 
               0 
               1 
             
             
               (Carry) 
               1 
               1 
               1 
               1 
               0 
               1 
               1 
               1 
             
             
               16 th  Frame 
               1 
               1 
               1 
               1 
               1 
               0 
               1 
               1 
             
             
               (Carry) 
               0 
               0 
               0 
               0 
               1 
               1 
               1 
               0 
             
             
                 
             
          
         
       
     
   
   
     
       
         
             
           
             
               TABLE 6-6 
             
           
          
             
                 
             
             
               Table of Correspondence of 3-Dimensional Dithering according to an 
             
             
               Embodiment of the Present Invention 
             
          
         
         
             
             
          
             
                 
               Input Blocks 
             
             
                 
               (4 LSBs) 
             
          
         
         
             
             
             
             
             
             
             
             
             
          
             
                 
               1010 
               1010 
               1010 
               1010 
               1011 
               1011 
               1011 
               1011 
             
             
                 
               1010 
               1010 
               1010 
               1010 
               1011 
               1011 
               1011 
               1011 
             
             
                 
                 
             
          
         
         
             
             
             
             
             
             
             
             
             
          
             
               1 st  Frame 
               0 
               0 
               0 
               0 
               0 
               1 
               1 
               1 
             
             
               (Carry) 
               1 
               1 
               1 
               1 
               1 
               1 
               0 
               1 
             
             
               2 nd  Frame 
               1 
               1 
               1 
               1 
               1 
               1 
               1 
               0 
             
             
               (Carry) 
               0 
               0 
               0 
               0 
               1 
               0 
               1 
               1 
             
             
               3 rd  Frame 
               0 
               0 
               0 
               0 
               1 
               1 
               0 
               1 
             
             
               (Carry) 
               1 
               1 
               1 
               1 
               0 
               1 
               1 
               1 
             
             
               4 th  Frame 
               1 
               1 
               1 
               1 
               1 
               0 
               1 
               1 
             
             
               (Carry) 
               0 
               0 
               0 
               0 
               1 
               1 
               1 
               0 
             
             
               5 th  Frame 
               0 
               1 
               1 
               1 
               0 
               1 
               1 
               1 
             
             
               (Carry) 
               1 
               1 
               0 
               1 
               1 
               1 
               0 
               1 
             
             
               6 th  Frame 
               1 
               1 
               1 
               0 
               1 
               1 
               1 
               0 
             
             
               (Carry) 
               1 
               0 
               1 
               1 
               1 
               0 
               1 
               1 
             
             
               7 th  Frame 
               1 
               1 
               0 
               1 
               1 
               1 
               0 
               1 
             
             
               (Carry) 
               0 
               1 
               1 
               1 
               0 
               1 
               1 
               1 
             
             
               8 th  Frame 
               1 
               0 
               1 
               1 
               1 
               0 
               1 
               1 
             
             
               (Carry) 
               1 
               1 
               1 
               0 
               1 
               1 
               1 
               0 
             
             
               9 th  Frame 
               0 
               0 
               0 
               0 
               0 
               1 
               1 
               1 
             
             
               (Carry) 
               1 
               1 
               1 
               1 
               1 
               1 
               0 
               1 
             
             
               10 th  Frame 
               1 
               1 
               1 
               1 
               1 
               1 
               1 
               0 
             
             
               (Carry) 
               0 
               0 
               0 
               0 
               1 
               0 
               1 
               1 
             
             
               11 th  Frame 
               0 
               0 
               0 
               0 
               1 
               1 
               0 
               1 
             
             
               (Carry) 
               1 
               1 
               1 
               1 
               0 
               1 
               1 
               1 
             
             
               12 th  Frame 
               1 
               1 
               1 
               1 
               1 
               0 
               1 
               1 
             
             
               (Carry) 
               0 
               0 
               0 
               0 
               1 
               1 
               1 
               0 
             
             
               13 th  Frame 
               0 
               1 
               1 
               1 
               0 
               0 
               0 
               0 
             
             
               (Carry) 
               1 
               1 
               0 
               1 
               1 
               1 
               1 
               1 
             
             
               14 th  Frame 
               1 
               1 
               1 
               0 
               1 
               1 
               1 
               1 
             
             
               (Carry) 
               1 
               0 
               1 
               1 
               0 
               0 
               0 
               0 
             
             
               15 th  Frame 
               1 
               1 
               0 
               1 
               0 
               0 
               0 
               0 
             
             
               (Carry) 
               0 
               1 
               1 
               1 
               1 
               1 
               1 
               1 
             
             
               16 th  Frame 
               1 
               0 
               1 
               1 
               1 
               1 
               1 
               1 
             
             
               (Carry) 
               1 
               1 
               1 
               0 
               0 
               0 
               0 
               0 
             
             
                 
             
          
         
       
     
   
   
     
       
         
             
           
             
               TABLE 6-7 
             
           
          
             
                 
             
             
               Table of Correspondence of 3-Dimensional Dithering according to an 
             
             
               Embodiment of the Present Invention 
             
          
         
         
             
             
          
             
                 
               Input Blocks 
             
             
                 
               (4 LSBs) 
             
          
         
         
             
             
             
             
             
             
             
             
             
          
             
                 
               1100 
               1100 
               1100 
               1100 
               1101 
               1101 
               1101 
               1101 
             
             
                 
               1100 
               1100 
               1100 
               1100 
               1101 
               1101 
               1101 
               1101 
             
             
                 
                 
             
          
         
         
             
             
             
             
             
             
             
             
             
          
             
               1 st  Frame 
               0 
               1 
               1 
               1 
               0 
               1 
               1 
               1 
             
             
               (Carry) 
               1 
               1 
               0 
               1 
               1 
               1 
               0 
               1 
             
             
               2 nd  Frame 
               1 
               1 
               1 
               0 
               1 
               1 
               1 
               0 
             
             
               (Carry) 
               1 
               0 
               1 
               1 
               1 
               0 
               1 
               1 
             
             
               3 rd  Frame 
               1 
               1 
               0 
               1 
               1 
               1 
               0 
               1 
             
             
               (Carry) 
               0 
               1 
               1 
               1 
               0 
               1 
               1 
               1 
             
             
               4 th  Frame 
               1 
               0 
               1 
               1 
               1 
               0 
               1 
               1 
             
             
               (Carry) 
               1 
               1 
               1 
               0 
               1 
               1 
               1 
               0 
             
             
               5 th  Frame 
               0 
               1 
               1 
               1 
               0 
               1 
               1 
               1 
             
             
               (Carry) 
               1 
               1 
               0 
               1 
               1 
               1 
               0 
               1 
             
             
               6 th  Frame 
               1 
               1 
               1 
               0 
               1 
               1 
               1 
               0 
             
             
               (Carry) 
               1 
               0 
               1 
               1 
               1 
               0 
               1 
               1 
             
             
               7 th  Frame 
               1 
               1 
               0 
               1 
               1 
               1 
               0 
               1 
             
             
               (Carry) 
               0 
               1 
               1 
               1 
               0 
               1 
               1 
               1 
             
             
               8 th  Frame 
               1 
               0 
               1 
               1 
               1 
               0 
               1 
               1 
             
             
               (Carry) 
               1 
               1 
               1 
               0 
               1 
               1 
               1 
               0 
             
             
               9 th  Frame 
               0 
               1 
               1 
               1 
               0 
               1 
               1 
               1 
             
             
               (Carry) 
               1 
               1 
               0 
               1 
               1 
               1 
               0 
               1 
             
             
               10 th  Frame 
               1 
               1 
               1 
               0 
               1 
               1 
               1 
               0 
             
             
               (Carry) 
               1 
               0 
               1 
               1 
               1 
               0 
               1 
               1 
             
             
               11 th  Frame 
               1 
               1 
               0 
               1 
               1 
               1 
               0 
               1 
             
             
               (Carry) 
               0 
               1 
               1 
               1 
               0 
               1 
               1 
               1 
             
             
               12 th  Frame 
               1 
               0 
               1 
               1 
               1 
               0 
               1 
               1 
             
             
               (Carry) 
               1 
               1 
               1 
               0 
               1 
               1 
               1 
               0 
             
             
               13 th  Frame 
               0 
               1 
               1 
               1 
               1 
               1 
               1 
               1 
             
             
               (Carry) 
               1 
               1 
               0 
               1 
               1 
               1 
               1 
               1 
             
             
               14 th  Frame 
               1 
               1 
               1 
               0 
               1 
               1 
               1 
               1 
             
             
               (Carry) 
               1 
               0 
               1 
               1 
               1 
               1 
               1 
               1 
             
             
               15 th  Frame 
               1 
               1 
               0 
               1 
               1 
               1 
               1 
               1 
             
             
               (Carry) 
               0 
               1 
               1 
               1 
               1 
               1 
               1 
               1 
             
             
               16 th  Frame 
               1 
               0 
               1 
               1 
               1 
               1 
               1 
               1 
             
             
               (Carry) 
               1 
               1 
               1 
               0 
               1 
               1 
               1 
               1 
             
             
                 
             
          
         
       
     
   
   
     
       
         
             
           
             
               TABLE 6-8 
             
           
          
             
                 
             
             
               Table of Correspondence of 3-Dimensional Dithering according to an 
             
             
               Embodiment of the Present Invention 
             
          
         
         
             
             
          
             
                 
               Input Blocks 
             
             
                 
               (4 LSBs) 
             
          
         
         
             
             
             
             
             
             
             
             
             
          
             
                 
               1110 
               1110 
               1110 
               1110 
               1111 
               1111 
               1111 
               1111 
             
             
                 
               1110 
               1110 
               1110 
               1110 
               1111 
               1111 
               1111 
               1111 
             
             
                 
                 
             
          
         
         
             
             
             
             
             
             
             
             
             
          
             
               1 st  Frame 
               0 
               1 
               1 
               1 
               1 
               1 
               1 
               1 
             
             
               (Carry) 
               1 
               1 
               0 
               1 
               1 
               1 
               1 
               1 
             
             
               2 nd  Frame 
               1 
               1 
               1 
               0 
               1 
               1 
               1 
               1 
             
             
               (Carry) 
               1 
               0 
               1 
               1 
               1 
               1 
               1 
               1 
             
             
               3 rd  Frame 
               1 
               1 
               0 
               1 
               1 
               1 
               1 
               1 
             
             
               (Carry) 
               0 
               1 
               1 
               1 
               1 
               1 
               1 
               1 
             
             
               4 th  Frame 
               1 
               0 
               1 
               1 
               1 
               1 
               1 
               1 
             
             
               (Carry) 
               1 
               1 
               1 
               0 
               1 
               1 
               1 
               1 
             
             
               5 th  Frame 
               1 
               1 
               1 
               1 
               1 
               1 
               1 
               1 
             
             
               (Carry) 
               1 
               1 
               1 
               1 
               1 
               1 
               1 
               1 
             
             
               6 th  Frame 
               1 
               1 
               1 
               1 
               1 
               1 
               1 
               1 
             
             
               (Carry) 
               1 
               1 
               1 
               1 
               1 
               1 
               1 
               1 
             
             
               7 th  Frame 
               1 
               1 
               1 
               1 
               1 
               1 
               1 
               1 
             
             
               (Carry) 
               1 
               1 
               1 
               1 
               1 
               1 
               1 
               1 
             
             
               8 th  Frame 
               1 
               1 
               1 
               1 
               1 
               1 
               1 
               1 
             
             
               (Carry) 
               1 
               1 
               1 
               1 
               1 
               1 
               1 
               1 
             
             
               9 th  Frame 
               0 
               1 
               1 
               1 
               1 
               1 
               1 
               1 
             
             
               (Carry) 
               1 
               1 
               0 
               1 
               1 
               1 
               1 
               1 
             
             
               10 th  Frame 
               1 
               1 
               1 
               0 
               1 
               1 
               1 
               1 
             
             
               (Carry) 
               1 
               0 
               1 
               1 
               1 
               1 
               1 
               1 
             
             
               11 th  Frame 
               1 
               1 
               0 
               1 
               1 
               1 
               1 
               1 
             
             
               (Carry) 
               0 
               1 
               1 
               1 
               1 
               1 
               1 
               1 
             
             
               12 th  Frame 
               1 
               0 
               1 
               1 
               1 
               1 
               1 
               1 
             
             
               (Carry) 
               1 
               1 
               1 
               0 
               1 
               1 
               1 
               1 
             
             
               13 th  Frame 
               1 
               1 
               1 
               1 
               0 
               1 
               1 
               1 
             
             
               (Carry) 
               1 
               1 
               1 
               1 
               1 
               1 
               0 
               1 
             
             
               14 th  Frame 
               1 
               1 
               1 
               1 
               1 
               1 
               1 
               0 
             
             
               (Carry) 
               1 
               1 
               1 
               1 
               1 
               0 
               1 
               1 
             
             
               15 th  Frame 
               1 
               1 
               1 
               1 
               1 
               1 
               0 
               1 
             
             
               (Carry) 
               1 
               1 
               1 
               1 
               0 
               1 
               1 
               1 
             
             
               16 th  Frame 
               1 
               1 
               1 
               1 
               1 
               0 
               1 
               1 
             
             
               (Carry) 
               1 
               1 
               1 
               1 
               1 
               1 
               1 
               0 
             
             
                 
             
          
         
       
     
   
   The present invention is not limited to the above embodiments. More general rules will be illustrated below with reference to  FIG. 1 . 
     FIG. 1  is a flow chart of the 2-dimensional dithering method and the 3-dimensional dithering method according to another embodiment of the present invention. The first four steps of the two dithering methods are the same. The two dithering methods of this embodiment both represent A-bit grayscale levels with a B-bit resolution, where A and B are positive integers and A&gt;B. The 2-dimensional dithering method is illustrated first below. 
   Firstly, the table of correspondence between the signal grayscale values and the target grayscale values is established in Step  102 , i.e., the correspondence between the values is determined. The process involves designating a corresponding target grayscale value within the interval from 0 to (2 B −1)*2 A−B  for each signal grayscale value from 0 to 2 A −1. The 2 A  target grayscale values must form a strictly increasing sequence, i.e., to any two different signal grayscale values X1 and X2, if the corresponding target grayscale value of X1 is Y1, the corresponding target grayscale value of X2 is Y2, and if X1&gt;X2, then Y1&gt;Y2. In addition, if the target grayscale values are expressed in binary, each of the target grayscale values has A integer digits and C decimal digits, where C is a positive integer. 
   In this embodiment, the signal grayscale value 0 is corresponding to the target grayscale value 0, and the signal grayscale value 2 A −1 is corresponding to the target grayscale value (2 B −1)*2 A−B . 
   If the input signal grayscale value is X, in Step  104 , according to the correspondence between the 2 A  signal grayscales and the 2 A  target grayscale values, the target grayscale value Y corresponding to the signal grayscale value X is obtained. 
   If an E*F pixel block is used in this method, the target grayscale value Y must be represented by using the 2-dimensional dithering, i.e., the grayscale value of each pixel in the pixel block is set, such that the average grayscale value of the pixel block equals to Y. Before the above setting, two figures must be first calculated. First, the mantissa length D is calculated in Step  106 , i.e., the mantissa length D=A−B+C. Then, the mantissa K is calculated in Step  108 . The mantissa K is the values of the D LSBs of Y, and includes integer and decimal parts. It is known from the above description that the mantissa length D is the bit length of the mantissa K. 
   Then, the flow enters Step  110  to perform the carry and non-carry operations of the 2-dimensional dithering. In this method, among the E*F pixels in the pixel block, the grayscale values of N pixels are set to Y−K+2 A−B  (carry), and the grayscale values of the rest E*F−N pixels are set to Y−K (non-carry), wherein E*F is a multiple of 2 D , and N/(E*F)=K/2 A−B . 
   Finally, the D LSBs of the grayscale values of the E*F pixels are deleted, and the remainder are the B-bit grayscale values which are applicable to B-bit display devices. 
   By comparing this embodiment with the previous embodiment, it is found that as long as A is set to 8, B is set to 6, C is set to 2, D is set to 4, E is set to 4, and F is set to 8, the 2-dimensional dithering method of this embodiment will be equal to the 2-dimensional dithering method of the previous embodiment. 
   Then, the 3-dimensional dithering method of this embodiment is illustrated. Steps  102 - 108  of this method are the same as those of the 2-dimensional dithering method. Subsequently, the flow enters Step  114  to perform the carry and non-carry operations of the 3-dimensional dithering. 
   If this method uses an E*F pixel block in P continuous frames as the unit for processing, Step  114  is directed to enable the average grayscale value of the E*F*P pixels to equal to Y. The process of this embodiment involves setting the grayscale values of N pixels among the E*F*P pixels to Y−K+2 A−B  (carry), and setting the grayscale values of the rest E*F*P−N pixels to Y−K (non-carry), wherein E*F*P is a multiple of 2 D , and N/(E*F*P)=K/2 A−B . 
   Finally, the D LSBs of the grayscale values of the E*F*P pixels are deleted, and the remaining are the B-bit grayscale values which are applicable to B-bit display devices. 
   By comparing this embodiment with the previous embodiment, it is found that as long as A is set to 8, B is set to 6, C is set to 2, D is set to 4, E is set to 4, F is set to 2, and P is set to 16, the 3-dimensional dithering method of this embodiment will be equal to the 3-dimensional dithering method of the previous embodiment. 
   To sum up, the present invention uses decimals. 2 A  target grayscale values within the interval from 0 to (2 B −1)*2 A−B  are calculated, and then the target grayscale values with decimals are represented by using finer 2-dimensional dithering or 3-dimensional dithering. Therefore, the present invention is superior compared to the prior art, and can represent all color levels of the output device. 
   It will be apparent to those skilled in the art that various modifications and variations can be made to the structure of the present invention without departing from the scope or spirit of the invention. In view of the foregoing, it is intended that the present invention cover modifications and variations of this invention provided they fall within the scope of the following claims and their equivalents.