Patent Publication Number: US-8988417-B2

Title: Rendering system and method based on weighted value of sub-pixel region

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims the priority benefit of Korean Patent Application No. 10-2010-0071841, filed on Jul. 26, 2010, in the Korean Intellectual Property Office, the disclosure of which is incorporated herein by reference. 
     BACKGROUND 
     1. Field 
     Example embodiments of the following description relate to a rendering system and method based on a weighted value of a sub-pixel region. 
     2. Description of the Related Art 
     To effectively implement a three-dimensional (3D) image, images having viewpoints different from each other may typically need to be respectively viewed by left/right eyes of human beings. To implement this 3D image without using a filter such as a glass, the 3D image may need to be spatially divided based on the viewpoints, which are referred to as an autostereoscopic display. In the autostereoscopic display, an image may be spatially divided using an optical device, and displayed. Here, as the optical device, optical lenses or an optical barrier may be representatively used. As an optical lens, a lenticular lens may be used by which respective pixel images are displayed only in a predetermined direction. In addition, using the optical barrier, only a predetermined pixel may be viewed from a predetermined direction due to a slit disposed in a front surface of a display. In a case of the autostereoscopic display using the lenses or the barrier, left/right viewpoint images, that is, two viewpoint images may be basically displayed, resulting in creation of a sweet spot having a significantly narrow width. The sweet spot may be expressed using a viewing distance and a viewing angle. Here, the viewing distance may be determined by a pitch of lenses or a slit, and the viewing angle may be determined by a number of expressible viewpoints. In this instance, a scheme of increasing the number of expressible viewpoints to widen the viewing angle may be referred to as an autostereoscopic multi-view display. 
     Accordingly, there is a desire for a rendering system and method that may more effectively provide a 3D image. 
     SUMMARY 
     The foregoing and/or other aspects are achieved by providing a rendering system including a pixel value providing unit to provide pixel values of sub-pixels, the sub-pixels representing a plurality of viewpoints as respective central viewpoints, and the plurality of viewpoints being represented by a single sub-pixel based on an inclined lens, a pixel value change unit to change a pixel value of the single sub-pixel using the provided pixel values, and a rendering unit to perform rendering using the changed pixel value. 
     The plurality of viewpoints represented by the single sub-pixel may be determined based on a pitch of the inclined lens and a slope of the inclined lens. 
     The rendering system may further include a ratio providing unit to provide a coverage ratio of each of the plurality of viewpoints with respect to the single sub-pixel. Here, the pixel value change unit may change the pixel value of the single sub-pixel by further using the provided coverage ratio. 
     The pixel value change unit may apply the provided coverage ratio, as a weighted value, to pixel values of sub-pixels corresponding to a corresponding viewpoint, and may change the pixel value of the single sub-pixel using the pixel values to which the provided coverage ratio is applied. 
     The pixel value change unit may change the pixel value of the single sub-pixel using pixel values of sub-pixels representing a same color as the single sub-pixel among the provided pixel values. 
     The rendering unit may perform the rendering by further using changed pixel values of sub-pixels representing, as central viewpoints, a same viewpoint as the single sub-pixel. 
     The foregoing and/or other aspects are achieved by providing a rendering method including providing pixel values of sub-pixels, the sub-pixels representing a plurality of viewpoints as respective central viewpoints, and the plurality of viewpoints being represented by a single sub-pixel based on an inclined lens, changing a pixel value of the single sub-pixel using the provided pixel values, and performing rendering using the changed pixel value. 
     Additional aspects, features, and/or advantages of example embodiments will be set forth in part in the description which follows and, in part, will be apparent from the description, or may be learned by practice of the disclosure. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       These and/or other aspects and advantages will become apparent and more readily appreciated from the following description of the example embodiments, taken in conjunction with the accompanying drawings of which: 
         FIG. 1  illustrates a diagram of a plurality of sub-pixels and inclined lenses according to example embodiments; 
         FIG. 2  illustrates a diagram of a single sub-pixel, and viewpoints associated with the single sub-pixel according to example embodiments; 
         FIG. 3  illustrates a diagram of a 4-view pixel rendering according to example embodiments; 
         FIG. 4  illustrates a diagram of a 12-view sub-pixel rendering according to example embodiments according to example embodiments; 
         FIG. 5  illustrates a block diagram of a rendering system according to example embodiments; 
         FIG. 6  illustrates a diagram of a 16-view pixel rendering according to example embodiments; 
         FIG. 7  illustrates a diagram of a 48-view sub-pixel rendering according to example embodiments; and 
         FIG. 8  illustrates a flowchart of a rendering method according to example embodiments. 
     
    
    
     DETAILED DESCRIPTION 
     Reference will now be made in detail to example embodiments, examples of which are illustrated in the accompanying drawings, wherein like reference numerals refer to the like elements throughout. Example embodiments are described below to explain the present disclosure by referring to the figures. 
     A viewpoint image to be provided through a multi-view display may be displayed for each pixel unit, or for each sub-pixel unit. Here, the sub-pixel unit may be a minimal image display unit having a single piece of color information (for example, a unit to indicate each of red (R), green (G), and blue (B) in an RGB color space), and the pixel unit may be a minimal image display unit to express complete color information obtained by joining sub-pixels together (for example, R, G, and B sub-pixels being collectively considered together to be the single pixel). 
       FIG. 1  illustrates a plurality of sub-pixels and inclined lenses according to example embodiments. In  FIG. 1 , a plurality of rectangles may respectively indicate the plurality of sub-pixels, and the sub-pixels may be collected to form a single display. Additionally, “R”, “G”, and “B” in the rectangles may respectively indicate red, green, and blue in the RGB color space. 
     In  FIG. 1 , solid lines and dotted lines may schematically indicate lenses inclined on the display. For example, lenticular lenses may be used as the lenses. Here, a distance between the lines may indicate a pitch of the inclined lenses. 
     Additionally, two spaces formed between the solid lines and the dotted lines, and ten spaces formed among the dotted lines may respectively correspond to 12 viewpoints, for example a first viewpoint  101  through a twelfth viewpoint  112 , as illustrated in  FIG. 1 . 
     Each of the sub-pixels of  FIG. 1  may have influence on a plurality of viewpoints. For example, an R sub-pixel  121  representing a sixth viewpoint  106  as a central viewpoint may have influence on five viewpoints. Specifically, the R sub-pixel  121  may have influence on a fourth viewpoint  104 , a fifth viewpoint  105 , a seventh viewpoint  107 , and an eighth viewpoint  108 , as well as the sixth viewpoint  106 . 
       FIG. 2  illustrates a single sub-pixel, and viewpoints associated with the single sub-pixel according to example embodiments. Specifically,  FIG. 2  illustrates the R sub-pixel  121  representing the sixth viewpoint  106  as the center viewpoint, as described with reference to  FIG. 1 . As illustrated in  FIG. 2 , the R sub-pixel  121  may be divided into five regions, for example, a first region  201 , a second region  202 , a third region  203 , a fourth region  204 , and a fifth region  205  that respectively correspond to the eighth viewpoint  108 , the seventh viewpoint  107 , the sixth viewpoint  106 , the fifth viewpoint  105 , and the fourth viewpoint  104 . 
     Here, a rendering system according to example embodiments may calculate a coverage ratio of each of the fourth viewpoint  104  through the eighth viewpoint  108  with respect to the R sub-pixel  121 , based on areas of the first region  201  through the fifth region  205 . For example, when the total area of the R sub-pixel  121  is set to be “1”, each of the first region  201  and the fifth region  205  occupies “ 1/12” of the total area, each of the second region  202  and the fourth region  204  occupies “¼” of the total area, and the third  203  occupies “⅓” of the total area. Accordingly, coverage ratios of the fourth viewpoint  104  through the eighth viewpoint  108  with respect to the R sub-pixel  121  may be respectively calculated as “ 1/12”, “¼”, “⅓”, “¼”, and “ 1/12”. 
     Additionally, the rendering system may change a pixel value of the R sub-pixel  121  based on the calculated ratio, and based on pixel values of sub-pixels representing the fourth viewpoint  104  through the eighth viewpoint  108  as central viewpoints. The pixel value of the R sub-pixel  121  may be changed based on the below Equation 1, for example. 
     
       
         
           
             
               
                 
                   
                     r 
                     6 
                     ′ 
                   
                   = 
                   
                     
                       
                         1 
                         3 
                       
                       ⁢ 
                       
                         r 
                         6 
                       
                     
                     + 
                     
                       
                         1 
                         4 
                       
                       ⁢ 
                       
                         r 
                         5 
                       
                     
                     + 
                     
                       
                         1 
                         12 
                       
                       ⁢ 
                       
                         r 
                         4 
                       
                     
                     + 
                     
                       
                         1 
                         4 
                       
                       ⁢ 
                       
                         r 
                         7 
                       
                     
                     + 
                     
                       
                         1 
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                       ⁢ 
                       
                         r 
                         8 
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   1 
                 
               
             
           
         
       
     
     First, “r n ” may denote a pixel value of a sub-pixel representing an “n”-th viewpoint as a central viewpoint. For example, “r 6 ” may denote the pixel value of the R sub-pixel  121  representing the sixth viewpoint  106  as the central viewpoint, and “r 5 ” may denote a pixel value of a sub-pixel representing the fifth viewpoint  105  as a central viewpoint. Additionally, “r 6 ′” may denote a changed pixel value of the R sub-pixel  121  representing the sixth viewpoint  106  as the central viewpoint. Furthermore, each of fractional numbers may indicate a coverage ratio of each of the viewpoints with respect to a single sub-pixel as described above. The coverage ratio may be calculated based on a ratio of an area of the sub-pixel on which a lens is superimposed to the total area of the sub-pixel. 
     Accordingly, a pixel value of a single sub-pixel may be changed based on pixel values of sub-pixels representing viewpoints as central viewpoints. Here, the viewpoints may be influenced by the single sub-pixel. Rendering may be performed using the changed pixel value, thereby reducing a color distortion caused by using inclined lenses. 
       FIG. 3  illustrates a 4-view pixel rendering according to example embodiments. Specifically,  FIG. 3  illustrates sub-pixels and lenses for the 4-view pixel rendering in a display with four viewpoints. A pixel rendering may include a scheme of performing rending to display a single viewpoint image using all three types of sub-pixels, for example an R sub-pixel, a G sub-pixel, and a B sub-pixel. In other words, a first viewpoint  301 , a second viewpoint  302 , a third viewpoint  303 , and a fourth viewpoint  304  of  FIG. 3  may be respectively represented as central viewpoints of R, G, and B sub-pixels. Here, a single sub-pixel may have influence on a plurality of viewpoints. For example, a G sub-pixel  320  among sub-pixels representing the third viewpoint  303  as central viewpoints may have influence on the second viewpoint  302  and the fourth viewpoint  304 , in addition to the third viewpoint  303 , as illustrated in  FIG. 3 . In other words, the G sub-pixel  320  may be used to represent the second viewpoint  302  through the fourth viewpoint  304 . 
     In the 4-view pixel rendering, a single viewpoint image may be displayed for each pixel unit. In other words, the R, G, and B sub-pixels of  FIG. 3  may be collected to form a single pixel, and a single viewpoint may be represented by the R, G, and B sub-pixels. Here, pixel values of the R, G, and B sub-pixels of  FIG. 3  may be changed using the below Equation 2, for example. 
     
       
         
           
             
               
                 
                   { 
                   
                     
                       
                         
                           
                             
                               
                                 
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                                 = 
                                 
                                   
                                     
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                             4 
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                             ⁢ 
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                             ⁢ 
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                   Equation 
                   ⁢ 
                   
                       
                   
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                   2 
                 
               
             
           
         
       
     
     Here, “g n ”, “b n ”, and “r n ” may respectively denote pixel values of G, B, and R sub-pixels that represent an “n”-th viewpoint as central viewpoints. For example, “g 3 ” may denote a pixel value of a G sub-pixel used to express a green color component among G, B, and R sub-pixels that represent the third viewpoint  303  as central viewpoints. Additionally, “g n ′”, “b n ′”, and “r n ′” may respectively denote changed pixel values of the G, B, and R sub-pixels that represent the “n”-th viewpoint as central viewpoints. In other words, the pixel rendering may be performed using changed pixel values of sub-pixels that represent a single viewpoint as central viewpoints. Furthermore, each of fractional numbers may denote a coverage ratio of each of viewpoints with respect to a single sub-pixel. For example, “ 1/12” in front of “g n−1 ” may denote a coverage ratio of an “n−1”-th viewpoint with respect to a G sub-pixel corresponding to “g n ”. Here, the “n−1”-th viewpoint may be expressed by “g n ”. In this example, the coverage ratio may be calculated based on a ratio of an area of the sub-pixel on which a lens is superimposed to the total area of the sub-pixel. 
       FIG. 4  illustrates a 12-view sub-pixel rendering according to example embodiments. Specifically,  FIG. 4  illustrates sub-pixels and lenses for the 12-view sub-pixel rendering in a display with 12 viewpoints. A sub-pixel rendering may include a scheme of performing rendering to display a single viewpoint image using each of R, G, and B sub-pixels. In other words, the 12 viewpoints of  FIG. 4  may be respectively represented as central viewpoints of R, G, and B sub-pixels. For example, an eighth viewpoint may be represented as a central viewpoint of a G sub-pixel  410 , as illustrated in  FIG. 4 . In this example, the G sub-pixel  410  may have influence on some viewpoints other than eighth viewpoint. Specifically, the G sub-pixel  410  may have influence on five viewpoints, for example a sixth viewpoint through a tenth viewpoint. In other words, the G sub-pixel  410  may be used to represent the five viewpoints. 
     In the 12-view sub-pixel rendering, a single viewpoint image may be displayed for each sub-pixel unit. In other words, each of the R, G, and B sub-pixels of  FIG. 4  may be used to represent a single viewpoint. Here, pixel values of the R, G, and B sub-pixels of  FIG. 4  may be changed using the below Equation 3, for example. 
     
       
         
           
             
               
                 
                   
                     
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                   3 
                 
               
             
           
         
       
     
     Here, “x n ” may denote a pixel value of a sub-pixel that represents an “n”-th viewpoint as a central viewpoint. For example, “x 3 ” may denote a pixel value of a sub-pixel that represents a third viewpoint as a central viewpoint. Additionally, “x n ′” may denote a changed pixel value of the sub-pixel that represents the “n”-th viewpoint as the central viewpoint. In other words, the sub-pixel rendering may be performed using a changed pixel values of a sub-pixel that represents a corresponding viewpoint as a central viewpoint. Furthermore, each of fractional numbers may indicate a coverage ratio of each of viewpoints with respect to a single sub-pixel as described above. The coverage ratio may be calculated based on a ratio of an area of the sub-pixel on which a lens is superimposed to the total area of the sub-pixel. 
     As described above with reference to  FIGS. 3 and 4 , in the pixel rendering and the sub-pixel rendering, a pixel value of a single sub-pixel may be changed based on a number of viewpoints that may be represented by the single sub-pixel, and based on a coverage ratio of each of the viewpoints with respect to the single sub-pixel, and the rendering may be performed based on the changed pixel value. Here, the number of viewpoints and the coverage ratio may be determined based on a pitch of a lens and a slope of the lens. 
       FIGS. 1 through 4  merely illustrate examples, and the number of viewpoints and the coverage ratio may vary based on the pitch of the lens and the slope of the lens and thus, a scheme of changing a pixel value of a sub-pixel may be generalized and expressed by the below Equation 4.
 
 x   n ′= . . . α n   x   n +α n−1   x   n−1 +α n−2   x   n−2 +α n+1   x   n+1 +α n+2   x   n+2    Equation 4
 
     if n&lt;1 n=n+N 
     else if n&gt;N n=n % N 
     Here, in the case of the sub-pixel rendering, “x” may denote a component of a set including R, G, and B color components, that is, may denote a color of a sub-pixel representing a corresponding viewpoint as a central viewpoint. Additionally, in the case of the pixel rendering, “x” may denote a same color as a color of a sub-pixel having a pixel value to be changed among R, G, and B sub-pixels. Furthermore, “N” may denote a total number of viewpoints, and “α” may denote a weighted value based on a coverage ratio of a viewpoint with respect to a sub-pixel. 
       FIG. 5  illustrates a block diagram of a rendering system  500  according to example embodiments. The rendering system  500  may include a pixel value providing unit  510 , a pixel value change unit  530 , and a rendering unit  540 . 
     The pixel value providing unit  510  may provide pixel values of sub-pixels that represent a plurality of viewpoints as respective central viewpoints. Here, the plurality of viewpoints may be represented based on an inclined lens by a single sub-pixel. The plurality of viewpoints represented by the single sub-pixel may be determined based on a pitch of the inclined lens and a slope of the inclined lens. In other words, the pixel value providing unit  510  may provide the pixel values of the sub-pixels that represent, as central viewpoints, the viewpoints determined based on the pitch and the slope of the inclined lens. 
     The pixel value change unit  530  may change a pixel value of a single sub-pixel using the provided pixel values. For example, the pixel value change unit  530  may determine, as a pixel value to be changed, a result of an operation between the provided pixel values. 
     Here, during the operation, a weighted value may be applied to each of the pixel values. To apply the weighted value, the rendering system  500  may further include a ratio providing unit  520 , as illustrated in  FIG. 5 . 
     The ratio providing unit  520  may provide a coverage ratio of each of the plurality of viewpoints with respect to the single sub-pixel. Here, the pixel value change unit  530  may change the pixel value of the single sub-pixel by further using the provided coverage ratio. For example, the pixel value change unit  530  may apply the provided coverage ratio, as a weighted value, to pixel values of sub-pixels corresponding to a corresponding viewpoint, and may change the pixel value of the single sub-pixel using the pixel values to which the provided coverage ratio is applied, through Equation 4 as described above. Here, the coverage ratio may be calculated as a ratio of an area occupied by each of the viewpoints with respect to a single pixel value, and may be calculated based on a ratio of an area of the sub-pixel on which a lens is superimposed to the total area of the sub-pixel. 
     The coverage ratio is merely an example and accordingly, another element may be used as a weighted value. For example, a weighted value based on a distance from a central viewpoint among all weighted values to indicate a proportion of viewpoints with respect to a single pixel may be used to change a pixel value. 
     Additionally, in the case of pixel rendering, the pixel value change unit  530  may change the pixel value of the single sub-pixel using pixel values of sub-pixels representing the same color as the single sub-pixel among the provided pixel values. In other words, in the case of the sub-pixel rendering, a single sub-pixel may represent a single viewpoint as a central viewpoint, whereas in the case of the pixel rendering, a plurality of sub-pixels may represent a single viewpoint as central viewpoints. Accordingly, the pixel value change unit  530  may use only pixel values of sub-pixels representing the same color as a sub-pixel of which a pixel value is to be changed, among pixel values provided for pixel rendering. Here, the weighted value may equally be applied to the pixel values of the sub-pixels representing the same color as the sub-pixel, and the pixel value to be changed may be calculated through an operation between the pixel values to which the weighted value is applied. 
     The rendering unit  540  may perform rendering using the changed pixel value. Specifically, the rendering unit  540  may perform pixel rendering by using a pixel value of a single sub-pixel, and by further using changed pixel values of sub-pixels that represent, as central viewpoints, a same viewpoint as the single sub-pixel. In other words, to perform rendering with respect to a single viewpoint, pixel values of all sub-pixels representing the corresponding viewpoint as central viewpoints may be changed. The rendering unit  540  may perform pixel rendering using the changed pixel values. One of all known schemes of rendering pixels or sub-pixels may be used to perform rendering based on a provided pixel value. 
     Most of the operations have already been described and hence, repeated descriptions of  FIG. 5  are deemed redundant, and accordingly, will be omitted. 
       FIG. 6  illustrates a 16-view pixel rendering according to example embodiments. Specifically,  FIG. 6  illustrates sub-pixels and lenses for the 16-view pixel rendering in a display with 16 viewpoints. 
     In the 16-view pixel rendering, a single viewpoint image may be displayed for each pixel unit, as described above. In other words, the R, G, and B sub-pixels of  FIG. 6  may be collected to form a single pixel, and a single viewpoint may be represented by the R, G, and B sub-pixels. Here, pixel values of the R, G, and B sub-pixels of  FIG. 6  may be changed using the below Equation 5, for example. The generalized Equation 4 has been already provided, however, a changed pixel value of each of the R, G, and B sub-pixels to represent a single viewpoint may be expressed by Equation 5, in order to facilitate understanding of description. 
     
       
         
           
             
               
                 
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                   ⁢ 
                   5 
                 
               
             
           
         
       
     
     Here, “g n ”, “b n ”, and “r n ” respectively denote pixel values of G, B, and R sub-pixels that represent an “n”-th viewpoint as central viewpoints. Additionally, “g n ′”, “b n ′”, and “r n ′” respectively denote changed pixel values of the G, B, and R sub-pixels that represent the “n”-th viewpoint as central viewpoints. In other words, the pixel rendering may be performed using changed pixel values of sub-pixels that represent a single viewpoint as central viewpoints. Furthermore, each of fractional numbers may denote a coverage ratio of each of viewpoints with respect to a single sub-pixel. For example, “⅙” in front of “g n−1 ” denote a coverage ratio of an “n−1”-th viewpoint with respect to a G sub-pixel corresponding to “g n ”. Here, the “n−1”-th viewpoint may be expressed by “g n ”. In this example, the coverage ratio may be calculated based on a ratio of an area of the sub-pixel on which a lens related to the “n−1”-th viewpoint is superimposed to the total area of the sub-pixel. 
       FIG. 7  illustrates a 48-view sub-pixel rendering according to example embodiments. Specifically,  FIG. 7  illustrates sub-pixels and lenses for the 48-view sub-pixel rendering in a display with 48 viewpoints. 
     In the 48-view sub-pixel rendering, a single viewpoint image may be displayed for each sub-pixel unit. In other words, each of the R, G, and B sub-pixels of  FIG. 7  may be used to represent a single viewpoint. Here, pixel values of the R, G, and B sub-pixels may be changed using the below Equation 6, for example. 
     
       
         
           
             
               
                 
                   
                     
                       x 
                       n 
                       ′ 
                     
                     = 
                     
                       
                         
                           1 
                           4 
                         
                         ⁢ 
                         
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                       + 
                       
                         
                           5 
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                         ⁢ 
                         
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                             - 
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                       + 
                       
                         
                           1 
                           8 
                         
                         ⁢ 
                         
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                       + 
                       
                         
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                       + 
                       
                         
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                     x 
                     ∈ 
                     
                       { 
                       
                         r 
                         , 
                         g 
                         , 
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                       } 
                     
                   
                   ⁢ 
                   
                     
 
                   
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                         if 
                         ⁢ 
                         
                             
                         
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                         n 
                       
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                       48 
                     
                   
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                         else 
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                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   6 
                 
               
             
           
         
       
     
     Symbols in Equation 6 have already been described in detail and accordingly, further descriptions thereof will be omitted. 
       FIG. 8  illustrates a flowchart of a rendering method according to example embodiments. The rendering method according to example embodiments may be performed by the rendering system  500  of  FIG. 5 . Hereinafter, operations of the rendering method performed by the rendering system  500  will be described with reference to  FIG. 8 . 
     In operation  810 , the rendering system  500  may provide pixel values of sub-pixels that represent a plurality of viewpoints as respective central viewpoints. Here, the plurality of viewpoints may be represented based on an inclined lens by a single sub-pixel. The plurality of viewpoints represented by the single sub-pixel may be determined based on a pitch of the inclined lens and a slope of the inclined lens. In other words, the rendering system  500  may provide the pixel values of the sub-pixels that represent, as central viewpoints, the viewpoints determined based on the pitch and the slope of the inclined lens. 
     In operation  820 , the rendering system  500  may provide a coverage ratio of each of the plurality of viewpoints with respect to the single sub-pixel. Here, the coverage ratio may be calculated as a ratio of an area occupied by each of the viewpoints with respect to a single pixel value, and may be calculated based on a ratio of an area of the sub-pixel on which a lens is superimposed to the total area of the sub-pixel. 
     In operation  830 , the rendering system  500  may change a pixel value of a single sub-pixel based on the provided pixel values and the provided coverage ratio. For example, the rendering system  500  may apply the provided coverage ratio, as a weighted value, to pixel values of sub-pixels corresponding to a corresponding viewpoint, and may change the pixel value of the single sub-pixel using the pixel values to which the provided coverage ratio is applied, through Equation 4 as described above. 
     Additionally, in the case of pixel rendering, the rendering system  500  may change the pixel value of the single sub-pixel using pixel values of sub-pixels representing the same color as the single sub-pixel among the provided pixel values. In other words, in the case of the sub-pixel rendering, a single sub-pixel may represent a single viewpoint as a central viewpoint, whereas in the case of the pixel rendering, a plurality of sub-pixels may represent a single viewpoint as central viewpoints. Accordingly, the rendering system  500  may use only pixel values of sub-pixels representing the same color as a sub-pixel of which a pixel value is to be changed, among pixel values provided for pixel rendering. Here, the weighted value may equally be applied to the pixel values of the sub-pixels representing the same color as the sub-pixel, and the pixel value to be changed may be calculated through an operation between the pixel values to which the weighted value is applied. 
     Here, operation  820  may be omitted. In other words, another weighted value, instead of the coverage ratio, may be used for an operation of changing a pixel value. For example, a weighted value based on a distance from a central viewpoint among all weighted values to indicate a proportion of viewpoints with respect to a single pixel may be used to change a pixel value 
     In operation  840 , the rendering system  500  may perform rendering using the changed pixel value. Specifically, the rendering system  500  may perform pixel rendering by using a pixel value of a single sub-pixel, and by further using changed pixel values of sub-pixels that represent, as central viewpoints, the same viewpoint as the single sub-pixel. In other words, to perform rendering with respect to a single viewpoint, pixel values of all sub-pixels representing the single viewpoint as central viewpoints may be changed. The rendering system  500  may perform pixel rendering using the changed pixel values. One of all known schemes of rendering pixels or sub-pixels may be used to perform rendering based on a provided pixel value. 
     Most of the operations have already been described and hence, repeated descriptions of  FIG. 8  are deemed redundant, and accordingly, will be omitted. 
     As described above, according to example embodiments, a pixel value of a single sub-pixel that represents multiple viewpoints may be changed using pixel values of sub-pixels corresponding to neighboring viewpoints that are influenced by the single sub-pixel, thereby preventing a color from being distorted during rendering. 
     Additionally, according to example embodiments, a weighted value based on a coverage ratio of an inclined lens with respect to a single sub-pixel that represents multiple viewpoints may be applied to pixel values of sub-pixels corresponding to neighboring viewpoints that are influenced by the single sub-pixel. A pixel value of the single sub-pixel may be changed using the pixel values to which the weighted value is applied. Thus, it is possible to prevent a color from being distorted during rendering. 
     The methods according to the above-described example embodiments may be recorded in non-transitory computer-readable media including program instructions to implement various operations embodied by a computer. The media may also include, alone or in combination with the program instructions, data files, data structures, and the like. The program instructions recorded on the media may be those specially designed and constructed for the purposes of the example embodiments, or they may be of the kind well-known and available to those having skill in the computer software arts. Examples of non-transitory computer-readable media include magnetic media such as hard disks, floppy disks, and magnetic tape; optical media such as CD ROM disks and DVDs; magneto-optical media such as optical disks; and hardware devices that are specially configured to store and perform program instructions, such as read-only memory (ROM), random access memory (RAM), flash memory, and the like. Examples of program instructions include both machine code, such as produced by a compiler, and files containing higher level code that may be executed by the computer using an interpreter. The described hardware devices may be configured to act as one or more software modules in order to perform the operations of the above-described example embodiments, or vice versa. 
     Although example embodiments have been shown and described, it would be appreciated by those skilled in the art that changes may be made in these example embodiments without departing from the principles and spirit of the disclosure, the scope of which is defined in the claims and their equivalents.