Abstract:
A method of driving an auto-stereoscopic display apparatus includes detecting a position of a user to determine a target visible distance, determining at least one original pixel unit having a first unit width based on the target visible distance, wherein the pixel unit includes a plurality of pixel sets in a row, each pixel set including N pixels, comparing the target visible distance to a predetermined reference visible distance of the auto-stereoscopic display apparatus, and converting the original pixel unit to a compensated pixel unit having a second unit width different from the first unit width to project viewpoint sets through the N pixels to a viewing zone at the target visible distance.

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
       [0001]    This U.S. non-provisional patent application claims priority under 35 U.S.C. §119 from Korean Patent Application No. 10-2014-0059201, filed on May 16, 2014 in the Korean Intellectual Property Office, and all the benefits accruing therefrom, the contents of which are herein incorporated by reference in their entirety. 
       BACKGROUND 
       [0002]    1. Technical Field 
         [0003]    Embodiments of the present disclosure are directed to an auto-stereoscopic display apparatus having a wide viewing angle and a method of driving the auto-stereoscopic display apparatus. 
         [0004]    2. Discussion of the Related Art 
         [0005]    An auto-stereoscopic display technology applied to a three-dimensional image display apparatus displays a three-dimensional image without shutter glasses. Examples of auto-stereoscopic display technologies include a parallax barrier scheme and a lenticular lens scheme. 
         [0006]    A parallax barrier three-dimensional image display apparatus includes a parallax barrier, through which vertical lattice-shape openings are formed, disposed in front of a display panel that includes pixels arranged in rows by columns. The parallax barrier separates a right-eye image and a left-eye image with respect to right and left eyes of an observer to generate binocular disparity in different images. 
         [0007]    A lenticular lens three-dimensional image display apparatus includes a lenticular lens sheet that has a plurality of semi-cylindrical lenses arranged in a column direction that are disposed on the display panel, instead of the vertical lattice of the parallax barrier. 
       SUMMARY 
       [0008]    Embodiments of the present disclosure may provide an auto-stereoscopic display apparatus having a wide viewing angle. 
         [0009]    Embodiments of the present disclosure may provide a method of driving the auto-stereoscopic display apparatus. 
         [0010]    Embodiments of the inventive concept provide a method of driving an auto-stereoscopic display apparatus that includes detecting a position of a user to determine a target visible distance; determining at least one original pixel unit having a first unit width based on the target visible distance, where the pixel unit includes a plurality of pixel sets in a row, each pixel set including N pixels; comparing the target visible distance to a predetermined reference visible distance of the auto-stereoscopic display apparatus; converting the original pixel unit to a compensated pixel unit having a second unit width different from the first unit width; and projecting viewpoint sets through the N pixels to a viewing zone at the target visible distance. 
         [0011]    The target visible distance is less than the reference visible distance and the second unit width is greater than the first unit width. 
         [0012]    The compensated pixel unit may include a dummy pixel and the second unit width may be greater than the first unit width by a width of the dummy pixel. 
         [0013]    M is a number of the pixel sets included in the original pixel unit, L is a number of the original pixel units, and M and L are each a natural number satisfying 
         [0000]    
       
         
           
             
               
                 L 
                 + 
                 1 
               
               &gt; 
               
                 
                   M 
                   × 
                   
                     N 
                      
                     
                       ( 
                       
                         
                           W 
                           ref 
                         
                         - 
                         
                           W 
                           t 
                         
                       
                       ) 
                     
                   
                 
                 
                   W 
                   t 
                 
               
               &gt; 
               L 
             
             , 
           
         
       
     
         [0000]    where “N” denotes a number of the viewpoints, “Wref” denotes a width of the viewpoint image projected at the reference visible distance, and “Wt” denotes a width of the viewpoint image projected to the viewing zone at the target visible distance. 
         [0014]    The dummy pixel may be disposed at an end portion of the compensated pixel unit and may display a same image as an image displayed on the pixel disposed adjacent thereto. 
         [0015]    The target visible distance may be greater than the reference visible distance and the second unit width may be less than the first unit width. 
         [0016]    The method may further include defining one of the pixels of the original pixel unit as a dummy pixel, and excluding the dummy pixel from the compensated pixel unit such that the second unit width becomes narrower than the first unit width by a width of the dummy pixel. 
         [0017]    M is a number of the pixel sets included in the original pixel unit, L is a number of the original pixel units, and M and L are each a natural number satisfying 
         [0000]    
       
         
           
             
               
                 L 
                 + 
                 1 
               
               &gt; 
               
                 
                   M 
                   × 
                   
                     N 
                      
                     
                       ( 
                       
                         
                           W 
                           t 
                         
                         - 
                         
                           W 
                           ref 
                         
                       
                       ) 
                     
                   
                 
                 
                   W 
                   t 
                 
               
               &gt; 
               L 
             
             , 
           
         
       
     
         [0000]    where “N” denotes a number of the viewpoints, “Wref” denotes a width of the viewpoint image projected at the reference visible distance, and “Wt” denotes a width of the viewpoint image projected to the viewing zone at the target visible distance. 
         [0018]    The dummy pixel may be disposed at an end portion of the original pixel unit. 
         [0019]    The target visible distance may correspond to an average of distances between the display unit and a plurality of users. 
         [0020]    Embodiments of the inventive concept provide an auto-stereoscopic display apparatus that includes a display unit that includes a plurality of original pixel units, each original pixel unit including a plurality of pixel sets arranged in a row, each pixel set including N pixels, the pixel sets displaying viewpoint sets that include N viewpoint images through the N pixels; a multi-viewpoint forming unit that faces the display unit to project the viewing sets to a plurality of viewing zones; a timing controller that outputs image data that includes pixel data corresponding to the pixels; a tracking part for detecting a position of a user and outputting a user position information; and a mapping part that includes a calculating unit for determining a target visible distance based on the user position information and for comparing the target visible distance to a reference visible distance to output a comparison result, and a mapping unit for receiving the image data and the comparison result and for converting the original pixel unit to a compensated pixel unit having a width different from that of the original pixel unit. 
         [0021]    The target visible distance may be less than the reference visible distance. 
         [0022]    The mapping unit may insert a dummy pixel data into the image data on the basis of the comparison result to convert the original pixel unit to the compensated pixel unit, where the width of the compensated pixel unit may be greater than the width of the original pixel unit by a width of the dummy pixel. 
         [0023]    M is a number of the pixel sets included in the original pixel unit, L is a number of the original pixel units, and M and L are each a natural number satisfying 
         [0000]    
       
         
           
             
               
                 L 
                 + 
                 1 
               
               &gt; 
               
                 
                   M 
                   × 
                   
                     N 
                      
                     
                       ( 
                       
                         
                           W 
                           ref 
                         
                         - 
                         
                           W 
                           t 
                         
                       
                       ) 
                     
                   
                 
                 
                   W 
                   t 
                 
               
               &gt; 
               L 
             
             , 
           
         
       
     
         [0000]    where “Wref” denotes a width of the viewpoint image projected at the reference visible distance and “Wt” denotes a width of the viewpoint image projected at the target visible distance. 
         [0024]    The target visible distance may be greater than the reference visible distance. 
         [0025]    The mapping unit may define one of the pixels of the original pixel unit as a dummy pixel, and may exclude the dummy pixel from the compensated pixel unit such that the width of the compensated pixel unit becomes less than the width of the original pixel unit by a width of the dummy pixel. 
         [0026]    M is a number of the pixel sets included in the original pixel unit, L is a number of the original pixel units, and M and L are each a natural number satisfying 
         [0000]    
       
         
           
             
               L 
               + 
               1 
             
             &gt; 
             
               
                 M 
                 × 
                 
                   N 
                    
                   
                     ( 
                     
                       
                         W 
                         t 
                       
                       - 
                       
                         W 
                         ref 
                       
                     
                     ) 
                   
                 
               
               
                 W 
                 t 
               
             
             &gt; 
             L 
           
         
       
     
         [0000]    where “Wref” denotes a width of the viewpoint image projected at the reference visible distance and “Wt” denotes a width of the viewpoint image projected at the target visible distance. 
         [0027]    Embodiments of the inventive concept provide auto-stereoscopic display apparatus that includes a display unit with a plurality of original pixel units, each original pixel unit including a plurality of pixel sets arranged in a row, each pixel set including N pixels, wherein the pixel sets display viewpoint sets that include N viewpoint images through the N pixels; a tracking part for detecting a position of a user and for outputting a user position information; and a mapping part that includes a calculating unit for determining a target visible distance of the user based on the user position information and for comparing the target visible distance to a reference visible distance and outputting a comparison result, and a mapping unit for receiving the image data and the comparison result and for converting the original pixel unit to a compensated pixel unit having a width different from that of the original pixel unit. M is a number of the pixel sets included in the original pixel unit, L is a number of the original pixel units, and M and L are each a natural number that satisfies 
         [0000]    
       
         
           
             
               
                 L 
                 + 
                 1 
               
               &gt; 
               
                 
                   M 
                   × 
                   N 
                    
                   
                      
                     
                       
                         W 
                         ref 
                       
                       - 
                       
                         W 
                         t 
                       
                     
                      
                   
                 
                 
                   W 
                   t 
                 
               
               &gt; 
               L 
             
             , 
           
         
       
     
         [0000]    wherein “Wref” denotes a width of the viewpoint image projected to the reference visible distance and “Wt” denotes a width of the viewpoint image projected to a plurality of viewing zones at the target visible distance. 
         [0028]    The target visible distance may be less than the reference visible distance, the compensated pixel unit may include a dummy pixel, and a width of the compensated pixel unit may be greater than a width of the original pixel unit by a width of the dummy pixel. 
         [0029]    The target visible distance may be greater than the reference visible distance, one pixel of the original pixel unit may be defined as a dummy pixel, wherein the dummy pixel is excluded from the compensated pixel unit such that a width of the compensated pixel unit may be narrower than a width of the original pixel unit by a width of the dummy pixel. 
         [0030]    According to the above, a target visible distance may be determined based on the positions of the users, the target visible distance is compared to the reference visible distance, and the width of the pixel unit is changed depending on the positions of the users. Thus, the viewing range of the auto-stereoscopic display apparatus may be broadened. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0031]      FIG. 1  is a block diagram of an auto-stereoscopic display apparatus according to an exemplary embodiment of the present disclosure. 
           [0032]      FIG. 2  illustrates a method of displaying a three-dimensional image using an auto-stereoscopic display apparatus according to an exemplary embodiment of the present disclosure. 
           [0033]      FIG. 3  is a cross-sectional view of an auto-stereoscopic display apparatus shown in  FIG. 2 . 
           [0034]      FIG. 4  is a cross-sectional view of an auto-stereoscopic display apparatus that projects a three-dimensional image to viewing zones at a reference visible distance according to an exemplary embodiment of the present disclosure. 
           [0035]      FIGS. 5A and 5B  are cross-sectional views that illustrate a method of projecting a three-dimensional view to viewing zones at a target visible distance according to an exemplary embodiment of the present disclosure. 
           [0036]      FIG. 6  is a cross-sectional view of a display unit that projects a three-dimensional image to viewing zones at a reference visible distance according to an exemplary embodiment of the present disclosure. 
           [0037]      FIG. 7  is a cross-sectional view of a display unit that projects a three-dimensional image to viewing zones at a target visible distance according to an exemplary embodiment of the present disclosure. 
           [0038]      FIG. 8  illustrates a process of generating mapping image data shown in  FIG. 7 . 
           [0039]      FIGS. 9A and 9B  are cross-sectional views that illustrate a method of projecting a three-dimensional image to viewing zones at a target visible distance according to an exemplary embodiment of the present disclosure. 
           [0040]      FIG. 10  is a cross-sectional view of a display unit that projects a three-dimensional image to viewing zones at a reference visible distance according to an exemplary embodiment of the present disclosure. 
           [0041]      FIG. 11  is a cross-sectional view of a display unit that projects a three-dimensional image to viewing zones at a target visible distance according to an exemplary embodiment of the present disclosure. 
           [0042]      FIG. 12  illustrates a process of generating mapping image data shown in  FIG. 11 . 
       
    
    
     DETAILED DESCRIPTION 
       [0043]    It will be understood that when an element or layer is referred to as being “on”, “connected to” or “coupled to” another element or layer, it can be directly on, connected or coupled to the other element or layer or intervening elements or layers may be present. Like numbers may refer to like elements throughout. 
         [0044]    Hereinafter, embodiments of the present disclosure will be explained in detail with reference to the accompanying drawings. 
         [0045]      FIG. 1  is a block diagram of an auto-stereoscopic display apparatus  1000  according to an exemplary embodiment of the present disclosure. 
         [0046]    Referring to  FIG. 1 , the auto-stereoscopic display apparatus  1000  includes a display unit  100  to display an image, a multi-viewpoint forming unit  200  disposed in front of the display unit  100 , gate and data drivers  300  and  400  to drive the display unit  100 , a timing controller  500  to control the gate and data drivers  300  and  400 , and a backlight unit  600  to supply light to the display unit  100 . 
         [0047]    The timing controller  500  receives externally supplied image information RGB and control signals CS. The timing controller  500  converts a data format of the image information RGB to a data format appropriate to an interface between the data driver  400  and the timing controller  500  and generates image data Idata. 
         [0048]    The timing controller  500  generates a data control signal DCS, such as an output start signal, a horizontal start signal, etc., and a gate control signal GCS, such as a vertical start signal, a vertical clock signal, a vertical clock bar signal, etc., on the basis of the control signals CS. The data control signal DCS is applied to the data driver  400  and the gate control signal GCS is applied to the gate driver  300 . 
         [0049]    The gate driver  300  sequentially outputs gate signals in response to the gate control signal GCS received from the timing controller  500 . 
         [0050]    The auto-stereoscopic display apparatus  1000  includes a tracking part  700  that detects a position of a user and outputs user position information about the user and a mapping part  800  that processes the image data Idata on the basis of the user position information and outputs the image data Idata′ to the data driver  400 . 
         [0051]    In more detail, the mapping part  800  includes a calculating unit  810  and a mapping unit  820 . The calculating unit  810  receives user position information from the tracking part  700 , determines a target visible distance based on the user position information, and outputs a compared result of the target visible distance and a reference visible distance. The mapping unit  820  maps the image data Idata on the basis of the image data Idata and generates the mapped image data Idata′. 
         [0052]      FIG. 2  illustrates a method of displaying a three-dimensional image using an auto-stereoscopic display apparatus according to an exemplary embodiment of the present disclosure. 
         [0053]    The image displayed through the display unit  100  includes a plurality of viewpoints. As an example, the image includes first, second, third, and fourth viewpoints, however, embodiments are not limited to four viewpoints. 
         [0054]    The display unit  100  displays the first to fourth viewpoints. The multi-viewpoint forming unit  200  receives the first to fourth viewpoints and refracts the first to fourth viewpoints to project the first to fourth viewpoints to a plurality of reference viewing sets defined at a reference visible distance OVD 1 . The reference visible distance OVD 1  corresponds to a distance between the multi-viewpoint forming unit  200  and the reference viewing sets. 
         [0055]    The reference viewing sets include a first reference viewing set VS 1  and second and third reference viewing sets VS 2  and VS 3 , which are respectively disposed at each side of the first reference viewing set VS 1 , but the number of the reference viewing sets is not limited thereto. Since the first to third reference viewing sets VS 1  to VS 3  are similar to each other, hereinafter, only the first reference viewing set VS 1  will be described in detail and details of the second and third reference viewing sets VS 2  and VS 3  will be omitted. 
         [0056]    The first reference viewing set VS 1  includes first, second, third, and fourth viewing zones VZ 1 , VZ 2 , VZ 3 , and VZ 4  sequentially arranged in a row. The multi-viewpoint forming unit  200  refracts the first to fourth viewpoints and projects the first to fourth viewpoints to the first to fourth viewing zones VZ 1  to VZ 4 , respectively. 
         [0057]    In  FIG. 2 , a left eye of a first user P 1  perceives the first viewpoint in the first viewing zone VZ 1  and a right eye of the first user P 1  perceives the second viewpoint in the second viewing zone VZ 2 . Accordingly, the first user P 1  perceives the first and second viewpoints respectively through the left and right eyes, and thus the first user P 1  can perceive a three-dimensional image due to binocular disparity. Similarly, a left eye of a second user P 2  perceives the second viewpoint in the second viewing zone VZ 2  and a right eye of the second user P 2  perceives the third viewpoint in the third viewing zone VZ 3 . Therefore, since the second user P 2  perceives the second and third viewpoints respectively through the left and right eyes, the second user P 2  can perceive a three-dimensional image due to binocular disparity. The first and second users P 1  and P 2  perceive the three-dimensional image through different pairs of images, and thus the first and second users P 1  and P 2  perceive three-dimensional images that are different from each other. As described above, a user perceives different viewpoints through the left and right eyes along a horizontal direction in the first reference viewing set VS 1 , so that the user can perceive different three-dimensional images in one direction in the first reference viewing set VS 1 . However, when the user perceives adjacent viewpoints in different reference viewing sets on either side of a boundary between adjacent reference viewing sets through the left and right eyes, the user perceives an abnormal image. When a user perceives an abnormal image, the user may get eyestrain from the three-dimensional effect and depth differences between images opposite to each other. 
         [0058]    The tracking part  700  (refer to  FIG. 1 ) tracks the positions of the first and second users P 1  and P 2  who perceive the image displayed in the display unit  100 . To this end, the tracking part  700  may include a stereo IR camera. 
         [0059]      FIG. 3  is a cross-sectional view of an auto-stereoscopic display apparatus shown in  FIG. 2 . 
         [0060]    Referring to  FIG. 3 , the display unit  100  includes a liquid crystal display panel  110  that includes a plurality of pixels PX arranged in rows and columns. The liquid crystal display panel  110  includes a first substrate  111 , a second substrate  112 , and a liquid crystal layer  113  interposed between the first substrate  111  and the second substrate  112 . 
         [0061]    The display unit  100  may include an organic light emitting display panel or an electrophoretic display panel instead of the liquid crystal display panel  110 . 
         [0062]    The pixels PX are disposed on the first substrate  111  and include pixel electrodes, respectively. Although not shown in figures, the first substrate  111  includes gate lines extending in a first direction, data lines extending in a second direction substantially perpendicular to the first direction, and thin film transistors connected to the pixel electrodes in a one-to-one correspondence. 
         [0063]    In addition, each pixel PX may further include a color filter layer configured to include red, green, and blue color pixels. The pixel electrodes may be disposed to correspond to the color filter layers in a one-to-one correspondence. 
         [0064]    The liquid crystal layer  113  includes liquid crystal molecules that align in response to an electric field formed between the first and second substrates  111  and  112 . 
         [0065]    The display unit  100  may further include first and second polarizers  121  and  122  respectively attached to upper and lower surfaces of the liquid crystal display panel  110 . The first and second polarizers  121  and  122  have optical axes substantially perpendicular to each other. 
         [0066]    The multi-viewpoint forming unit  200  is a film disposed on the display unit  100  that includes a plurality of lenticular lenses  210 . The lenticular lenses  210  are arranged in the first direction of the pixel PX and each lenticular lens  210  has a semi-cylinder shape that extends in the second direction of the pixel PX. 
         [0067]    In a present exemplary embodiment, the multi-viewpoint forming unit  200  includes the lenticular lenses  210 , but is not limited thereto. That is, the multi-viewpoint forming unit  200  may include a lenticular device configured to include two substrates and a liquid crystal lens layer interposed between the two substrates. The lenticular device controls the liquid crystal lens layer using electrodes respectively applied to the two substrates to switch between a two-dimensional mode and a three-dimensional mode or vice versa. The display unit  100  transmits the image displayed therethrough to display a two-dimensional image during the two-dimensional mode and refracts the image displayed therethrough to display a three-dimensional image during the three-dimensional mode. 
         [0068]    The backlight unit  600  is disposed at a rear side of the display unit  100  to supply the light to the display unit  100 . The backlight unit  600  includes light emitting diodes or a cold cathode fluorescent lamp as its light source. The light generated by the backlight unit  600  is polarized by the second polarizer  122 , and thus only a component of the polarized light that is substantially parallel to the polarizing axis of the second polarizer  122  is supplied to the liquid crystal display panel  110 . 
         [0069]      FIG. 4  is a cross-sectional view of an auto-stereoscopic display apparatus that projects a three-dimensional image to viewing zones at a reference visible distance according to an exemplary embodiment of the present disclosure. 
         [0070]    Referring to  FIG. 4 , the display unit  100  includes first to ninth pixel sets PS 1  to PS 9  sequentially arranged in a row. Each of the first to ninth pixel sets PS 1  to PS 9  includes first to fourth viewpoint pixels  1  to  4  that respectively display the first to fourth viewpoints. The first to ninth pixel sets PS 1  to PS 9  display viewpoint sets defined by the first to fourth viewpoints through the first to fourth viewpoint pixels  1  to  4 . For example, the second pixel set PS 2  displays a second viewpoint set TS 2 , the fifth pixel set PS 5  displays a fifth viewpoint set TS 5 , and the eighth pixel set PS 8  displays an eighth viewpoint set TS 8 . 
         [0071]    Viewpoint images of each viewpoint set form corresponding viewpoints. In more detail, the first viewpoint is defined by first viewpoint images of the first to ninth pixel sets PS 1  to PS 9 . Similarly, the second to fourth viewpoints are defined by the second to fourth viewpoint images of the first to ninth pixel sets PS 1  to PS 9 , respectively. 
         [0072]    The lenticular lens  210  and the display unit  100  are spaced apart from each other by a gap Dgap. The lenticular lens  210  refracts the viewpoint sets provided from the first to ninth pixel sets PS 1  to PS 9  and projects the viewpoint sets to the first reference viewing set VS 1 , spaced apart by the reference visible distance OVD 1 . 
         [0073]    For example, the lenticular lens  210  refracts the second viewpoint set TS 2  displayed by the second pixel set PS 2  and projects the second viewpoint set TS 2  to the first reference viewing set VS 1 . As a result, the first to fourth viewpoint images of the second pixel set PS 2  are projected to the first to fourth viewing zones VZ 1  to VZ 4 . Similarly, the lenticular lens  210  refracts the fifth and eighth viewpoint sets TS 5  and TS 8  respectively displayed by the fifth and eighth pixel sets PS 5  and PS 8  and projects the fifth and eighth viewpoint sets TS 5  and TS 8  to the first reference viewing set VS 1 . As a result, the first to fourth viewpoint images of the fifth and eighth sets TS 5  and TS 8  are projected to the first to fourth viewing zones VZ 1  to VZ 4 , respectively. 
         [0074]    To allow a user to perceive a three-dimensional image at the reference viewing set VS 1 , the reference visible distance OVD 1 , the gap Dgap, a period P 1  in the row direction of the lenticular lens  210 , a number N of the viewpoints, a width Wp of the pixel are adjusted to satisfy the following Equation 1. In a present exemplary embodiment, the number of viewpoints N is 4. 
         [0000]    
       
         
           
             
               
                 
                   
                     Wp 
                     × 
                     N 
                   
                   = 
                   
                     
                       Pl 
                       × 
                       
                         ( 
                         
                           
                             OVD 
                              
                             
                                 
                             
                              
                             1 
                           
                           + 
                           Dgap 
                         
                         ) 
                       
                     
                     
                       OVD 
                        
                       
                           
                       
                        
                       1 
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   1 
                 
               
             
           
         
       
     
         [0075]    A distance Weye between the left and right eyes of the user and a width Wref of each of the first to fourth viewing zones VZ 1  to VZ 4  satisfy the following Equation 2. In a present exemplary embodiment, the distance Weye is about 65 mm. 
         [0000]        Wref&lt;Weye   Equation 2
 
         [0076]    In  FIG. 4 , a third user P 3  perceives a three-dimensional image displayed by the display unit  100  at the reference visible distance OVD 1 , but a fourth user P 4  who perceives the image displayed by the display unit  100  at a target visible distance OVD 2  shorter than the reference visible distance OVD 1  may not perceive the three-dimensional image. 
         [0077]    In more detail, the left eye of the third user P 3  perceives the second viewpoint in the second viewing zone VZ 2  and the right eye of the third user P 3  perceives the third viewpoint in the third viewing zone VZ 3 . However, the left and right eyes of the fourth user P 4  perceive different viewpoints from the third to ninth pixel sets PS 3  to PS 9 . For example, the left eye of the fourth user P 4  perceives the second viewpoint image from the third pixel set PS 3 , but perceives the first viewpoint image from the second pixel set PS 2 . Similarly, the right eye of the fourth user P 4  perceives the third viewpoint image from the seventh pixel set PS 7 , but perceives the fourth viewpoint image from the eighth pixel set PS 8 . 
         [0078]      FIGS. 5A and 5B  are cross-sectional views that illustrate a method of projecting a three-dimensional view to viewing zones at the target visible distance according to an exemplary embodiment of the present disclosure. 
         [0079]    Referring to  FIG. 5A , the auto-stereoscopic display apparatus  1000  projects a three-dimensional image to viewing zones at the reference visible distance OVD 1  and fifth to seventh users P 5  to P 7  perceive the image displayed in the display apparatus  1000  at positions different from each other. 
         [0080]    A first original normal image area RV 1  in which a user perceives a three-dimensional effect may be defined with respect to the reference visible distance OVD 1 . The first original normal image area RV 1  decreases in size with increasing distance from the reference visible distance OVD 1 . Second and third original normal image areas RV 2  and RV 3  that respectively correspond to the second and third viewing sets VS 2  and VS 3  are provided at each side of the first original normal image area RV 1 . When a user perceives viewpoints that are adjacent to each other but are included in different original normal image areas, the user perceives an abnormal image at a boundary between any two of the first to third original normal image areas RV 1  to RV 3  respectively through the left and right eyes. 
         [0081]    As described above, when the auto-stereoscopic display apparatus  1000  projects a three-dimensional image to viewing zones at the reference visible distance OVD 1 , a range in which a user can perceive a three-dimensional image from the display unit  100  is determined with reference to the reference visible distance OVD 1 . 
         [0082]    Meanwhile, the fifth to seventh users P 5  to P 7  perceive the image at a distance less than the reference visible distance OVD 1 . The fifth user P 5  perceives a three-dimensional image in the first original normal image area RV 1 , but the sixth and seventh users P 6  and P 7  perceive an abnormal image at the boundary of the second and third original normal image areas RV 2  and RV 3 . 
         [0083]    The tracking part  700  (see  FIG. 1 ) detects positions of the fifth to seventh users P 5  to P 7  and outputs user position information of the fifth to seventh users P 5  to P 7 . 
         [0084]    The calculating unit  810  (see  FIG. 1 ) calculates distances between the lenticular lens  210  and the fifth to seventh users P 5  to P 7  based on the user position information. 
         [0085]    Then, the calculating unit  810  calculates the target visible distance OVD 2  from the distances between the lenticular lens  210  and the fifth to seventh users P 5  to P 7 . The target visible distance OVD 2  may be, but is not limited to, an average value of the distances between the lenticular lens  210  and the fifth to seventh users P 5  to P 7 . Since the fifth to seventh users P 5  to P 7  are positioned at a distance less than the reference visible distance OVD 1 , the target visible distance OVD 2  may be less than the reference visible distance OVD 1 . 
         [0086]    The calculating unit  810  compares the target visible distance OVD 2  and the reference visible distance OVD 1  and outputs the comparison result. 
         [0087]    The auto-stereoscopic display apparatus  1000  processes signals applied to the display unit  100  on the basis of the comparison result, and thus the fifth to seventh users P 5  to P 7  perceive an undistorted three-dimensional image. 
         [0088]    In more detail, the mapping unit  820  (see  FIG. 1 ) maps the image data Idata (see  FIG. 1 ) on the basis of the comparison result and generates mapped image data Idata′ to divide the pixel sets into L original pixel units and convert the original pixel units into compensated pixel units. A method of processing the image data Idata will be described in detail with reference to  FIGS. 6 to 8 . 
         [0089]    Each original pixel unit is defined to include M pixel sets. “M” is a natural number that satisfies the following Equation 3. 
         [0000]    
       
         
           
             
               
                 
                   
                     L 
                     + 
                     1 
                   
                   &gt; 
                   
                     
                       M 
                       × 
                       
                         N 
                          
                         
                           ( 
                           
                             Wref 
                             - 
                             
                               Wt 
                                
                               
                                   
                               
                                
                               1 
                             
                           
                           ) 
                         
                       
                     
                     
                       Wt 
                        
                       
                           
                       
                        
                       1 
                     
                   
                   &gt; 
                   L 
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   3 
                 
               
             
           
         
       
     
         [0090]    In Equation 3, “N” denotes the number of viewpoints, “Wref” denotes the width of the viewpoint image projected to the viewing zones at the reference visible distance OVD 1 , “Wt 1 ” denotes the width of the viewpoint image projected to the viewing zones at the target visible distance OVD 2 , and “L” denotes the number of the original pixel units. The width Wref of the viewpoint image projected to the reference visible distance OVD 1  may be substantially the same as the width of the first to fourth viewing zones VZ 1  to VZ 4  at the reference visible distance OVD 1 , and the width Wt 1  of the viewpoint image projected to the target visible distance OVD 2  may be substantially the same as the width of the fifth to eighth viewing zones VZ 5  to VZ 8  (see  FIG. 5B ) at the target visible distance OVD 2 . Since the target visible distance OVD 2  is less than the reference visible distance OVD 1 , the width Wref of the viewpoint image projected to the reference visible distance OVD 1  is greater than the width Wt 1  of the viewpoint image projected to the target visible distance OVD 2 . 
         [0091]    As an example, the first to ninth pixel sets PS 1  to PS 9  may be divided into first to third original pixel units PU 1  to PU 3 . That is, in a present exemplary embodiment, “M” and “L” is each equal to 3. Each of the first to third original pixel units PU 1  to PU 3  has a first unit width WU 1 . 
         [0092]    Referring to  FIG. 5B , the first to third original pixel units PU 1  to PU 3  (see  FIG. 5A ) are respectively converted to first to third compensated pixel units PU 1 ′ to PU 3 ′ each having a second unit width WU 2  different from the first unit width WU 1 . The second unit width WU 2  may be greater than the first unit width WU 1 . 
         [0093]    To convert the first to third original pixel units PU 1  to PU 3  to the first to third compensated pixel units PU 1 ′ to PU 3 ′, the first to third original pixel units PU 1  to PU 3  include first to third dummy pixels DP 1  to DP 3 , respectively. Accordingly, the second unit width WU 2  is greater than the first unit width WU 1  by the width of each of the first to third dummy pixels DP 1  to DP 3 . 
         [0094]    In a present exemplary embodiment, the first to third dummy pixels DP 1  to DP 3  are end portions of the first to third compensated pixel units PU 1 ′ to PU 3 ′, respectively. Therefore, the first to third dummy pixels DP 1  to DP 3  are not disposed between pixel sets in the same compensated pixel unit. 
         [0095]    In a present exemplary embodiment, each of the first to third dummy pixels DP 1  to DP 3  may display the same viewpoint image as the viewpoint image displayed by the pixel adjacent thereto. For example, the first dummy pixel DP 1  displays the same image as the fourth pixel  4  of the third pixel set PS 3 , the second dummy pixel DP 2  displays the same image as the fourth pixel  4  of the sixth pixel set PS 6 , and the third dummy pixel DP 3  displays the same image as the fourth pixel  4  of the ninth pixel set PS 9 . Thus, although the first to third dummy pixels DP 1  to DP 3  are used, the user perceives an undistorted three-dimensional image. 
         [0096]    As described above, when the first to third original pixel units PU 1  to PU 3  are converted to the first to third compensated pixel units PU 1 ′ to PU 3 ′ each having a second unit width WU 2  on the basis of the comparison result, the image displayed in the display unit  100  is refracted by the lenticular lens  210  and projected to a plurality of target viewing sets at the target visible distance OVD 2 . Here, the target visible distance OVD 2  corresponds to the distance between the lenticular lens  210  and the target viewing sets. 
         [0097]    The target viewing sets include a first target viewing set VS 1  and second and third target viewing sets VS 2  and VS 3  disposed at each side of the first target viewing set VS 1 . 
         [0098]    The first target viewing set VS 1  includes the first to fourth viewing zones VZ 1  to VZ 4  sequentially arranged in a row. The lenticular lens  210  refracts the first to fourth viewpoints of the image and projects the first to fourth viewpoints to the first to fourth viewing zones VZ 1  to VZ 4 , respectively. 
         [0099]    As described above, when each of the first to third compensated pixel units PU 1 ′ to PU 3 ′ has the second unit width WU 2 , the first to third original normal image areas RV 1  to RV 3  (see  FIG. 5A ) corresponding to the first to third original pixel units PU 1  to PU 3  are converted to first to third compensated normal image areas CV 1  to CV 3 , respectively. The first to third compensated normal image areas CV 1  to CV 3  respectively correspond to the first to third target viewing sets VS 1  to VS 3 . The width of the first to third compensated normal image areas CV 1  to CV 3  at the target visible distance OVD 2  is greater than the width of the first to third original normal image areas RV 1  to RV 3  at the target visible distance OVD 2 . 
         [0100]    As described with reference to  FIG. 5A , when the auto-stereoscopic display apparatus  1000  provides the first to third original normal image areas RV 1  to RV 3 , the sixth and seventh users P 6  and P 7  perceive an abnormal image, but the sixth and seventh users P 6  and P 7 , together with the fifth user P 5 , perceive a three-dimensional image when the auto-stereoscopic display apparatus  1000  provides the first to third compensated normal image areas CV 1  to CV 3 . That is, the visible distance changes depending on the positions of the users, and a viewing distance and a viewing range of the auto-stereoscopic display apparatus  1000  may be broadened. 
         [0101]      FIG. 6  is a cross-sectional view of a display unit that projects a three-dimensional image to viewing zones at the reference visible distance according to an exemplary embodiment of the present disclosure. 
         [0102]    Hereinafter, an operation of the auto-stereoscopic display apparatus  1000  will be described in detail with reference to  FIGS. 1 ,  5 A, and  6  when a three-dimensional image is projected at the reference visible distance OVD 1 . 
         [0103]    When the auto-stereoscopic display apparatus  1000  projects the three-dimensional image at the reference visible distance OVD 1 , the mapping unit  800  is not operated and the data driver  400  converts the image data Idata provided from the timing controller  500  to data voltages and applies the data voltages to the display unit  100 . The display unit  100  includes pixels PX arranged in a row. For the convenience of explanation, the pixels PX are arranged in a first direction DX 1  substantially parallel to the row direction and are referred to as first to thirty-sixth pixels PN 1  to PN 36 . 
         [0104]    The image data Idata includes first to thirty-sixth pixel data PD 1  to PD 36  sequentially received from the timing controller  500 . The first to thirty-sixth pixel data PD 1  to PD 36  respectively correspond to the first to thirty-sixth pixels PN 1  to PN 36 . In more detail, the first to thirty-sixth pixel data PD 1  to PD 36  are supplied to the data driver  400 , the data driver  400  sequentially supplies first to thirty-sixth data voltages respectively corresponding to the first to thirty-sixth pixels PN 1  to PN 36  to the first to thirty-sixth pixels PN 1  to PN 36 , and the first to thirty-sixth pixels PN 1  to PN 36  display the image in response to the first to thirty-sixth data voltages to project the three-dimensional image to the viewing zones at the reference visible distance OVD 1 . 
         [0105]    In this case, the first original pixel unit PU 1  includes the first to twelfth pixels PN 1  to PN 12 , the second original pixel unit PU 2  includes the thirteenth to twenty-fourth pixels PN 13  to PN 24 , and the third original pixel unit PU 3  includes the twenty-fifth to thirty-sixth pixels PN 25  to PN 36 . 
         [0106]      FIG. 7  is a cross-sectional view of a display unit that projects a three-dimensional image to the viewing zones at the target visible distance according to an exemplary embodiment of the present disclosure and  FIG. 8  illustrates a process of generating the mapping image data shown in  FIG. 7 . 
         [0107]    Hereinafter, the operation of the auto-stereoscopic display apparatus  1000  will be described in detail with reference to  FIGS. 1 ,  5 B,  7 , and  8  when a three-dimensional image is projected to the viewing zones at the target visible distance OVD 2 . 
         [0108]    The mapping unit  820  maps the image data Idata on the basis of the comparison result and outputs the mapping image data Idata′. In more detail, the mapping unit  820  writes the first to twelfth pixel data PD 1  to PD 12  in first to twelfth addresses A 1  to A 12  and writes a first dummy pixel data DD 1  in a thirteenth address A 13 . 
         [0109]    Then, the mapping unit  820  writes the thirteenth to twenty-fourth pixel data PD 13  to PD 24  in fourteenth to twenty-fifth addresses A 14  to A 25  and writes a second dummy pixel data DD 2  in a twenty-sixth address A 26 . 
         [0110]    The mapping unit  820  writes the twenty-fifth to thirty-sixth pixel data PD 25  to PD 36  in twenty-seventh to thirty-eighth addresses A 27  to A 38  and writes a third dummy pixel data DD 3  in a thirty-ninth address A 39 . 
         [0111]    The data written in the first to thirty-sixth addresses A 1  to A 39  of the mapping image data Idata′ sequentially correspond to the first to thirty-ninth pixels PN 1  to PN 39 . In more detail, the mapping image data Idata′ are sequentially supplied to the data driver  400 , the data driver  400  sequentially supplies the first to thirty-ninth data voltages corresponding to the mapping image data Idata′ to the first to thirty-ninth pixels PN 1  to PN 39 , and the first to thirty-ninth pixels PN 1  to PN 39  display the image in response to the first to thirty-ninth data voltages to project the three-dimensional image to the viewing zones at the target visible distance OVD 2 . 
         [0112]    For example, the first to thirteenth pixels PN 1  to PN 13  of the first compensated pixel unit PU 1 ′ receive the data voltages converted from the first to twelfth pixel data PD 1  to PD 12  and the first dummy pixel data DD 1  written in the first to thirteenth addresses A 1  to A 13  and display the image corresponding to the first to twelfth pixel data PD 1  to PD 12  and the data voltages. 
         [0113]    As a result, the first compensated pixel unit PU 1 ′ includes the first to thirteenth pixels PN 1  to PN 13 , the second compensated pixel unit PU 2 ′ includes the fourteenth to twenty-sixth pixels PN 14  to PN 26 , and the third compensated pixel unit PU 3 ′ includes the twenty-seventh pixel to thirty-ninth pixels PN 27  to PN 39 . In this case, the thirteenth, twenty-sixth, and thirty-ninth pixels PN 13 , PN 26 , and PN 39  may be the first, second, and third dummy pixels DD 1 , DD 2 , and DD 3 , respectively. 
         [0114]    Each of the first to third dummy pixel data DD 1  to DD 3  may be substantially the same as the pixel data written in the addresses adjacent thereto. In more detail, the first dummy pixel data DD 1  may be the same as the twelfth or thirteenth pixel data PD 12  and PD 13  respectively written in the twelfth and fourteenth addresses A 12  and A 14 . Similarly, the second dummy pixel data DD 2  may be the same as the twenty-fourth or twenty-fifth pixel data PD 24  and PD 25  respectively written in the twenty-fifth and twenty-seventh addresses A 25  and A 27 , and the third dummy pixel data DD 3  may be the same as the thirty-sixth pixel data PD 36  written in the thirty-eighth address A 38 . In a present exemplary embodiment, the first dummy pixel data DD 1  is the twelfth pixel data PD 12 , the second dummy pixel data DD 2  is the twenty-fourth pixel data PD 24 , and the third dummy pixel data DD 3  is the thirty-sixth pixel data PD 36 . Accordingly, each of the first to third dummy pixels DD 1  to DD 3  may display the same image as that of the pixel adjacent thereto. 
         [0115]      FIGS. 9A and 9B  are cross-sectional views of a method of projecting a three-dimensional image to the viewing zones at the target visible distance according to an exemplary embodiment of the present disclosure. 
         [0116]    Referring to  FIGS. 9A and 9B , the auto-stereoscopic display apparatus  1000  projects a three-dimensional image to the viewing zones at the reference visible distance OVD 1  and eighth to tenth users P 8  to P 10  at different positions from each other. perceive an image displayed in the display apparatus  1000  The eighth to tenth users P 8  to P 10  perceive the image at a distance greater than the reference visible distance OVD 1 . The eighth user P 8  perceives a three-dimensional image in the first original normal image area RV 1 , but the ninth and tenth users P 9  and P 10  perceive an abnormal image at the boundary of the second and third original normal image areas RV 2  and RV 3 . 
         [0117]    The tracking part  700  (see  FIG. 1 ) detects positions of the eighth to tenth users P 8  to P 10  and outputs the positions of the eighth to tenth users P 8  to P 10 . 
         [0118]    The calculating unit  810  (see  FIG. 1 ) calculates distances between the lenticular lens  210  and the eighth to tenth users P 8  to P 10  based on the user position information. 
         [0119]    Then, the calculating unit  810  calculates a target visible distance OVD 3  from the distances between the lenticular lens  210  and the eighth to tenth users P 8  to P 10 . The target visible distance OVD 2  may be, but is not limited to, an average value of the distances between the lenticular lens  210  and the eighth to tenth users P 8  to P 10 . Since the eighth to tenth users P 8  to P 10  are positioned at a distance greater than the reference visible distance OVD 1 , the target visible distance OVD 3  is greater than the reference visible distance OVD 1 . 
         [0120]    The calculating unit  810  compares the target visible distance OVD 3  and the reference visible distance OVD 1  and outputs a comparison result. 
         [0121]    The auto-stereoscopic display apparatus  1000  processes signals supplied to the display unit  100  on the basis of the comparison result, and thus the eighth to tenth users P 8  to P 10  perceive an undistorted three-dimensional image. 
         [0122]    In more detail, the mapping unit  820  (see  FIG. 1 ) maps the image data Idata (see  FIG. 1 ) on the basis of the comparison result and generates the mapped image data Idata′ to divide the pixel sets into L original pixel units and convert the original pixel units to compensated pixel units. The method of processing the image data Idata will be described in detail with reference to  FIGS. 10 to 12 . 
         [0123]    Each original pixel unit is defined to include M pixel sets. “M” is a natural number that satisfies the following Equation 4. 
         [0000]    
       
         
           
             
               
                 
                   
                     L 
                     + 
                     1 
                   
                   &gt; 
                   
                     
                       M 
                       × 
                       
                         N 
                          
                         
                           ( 
                           
                             
                               Wt 
                                
                               
                                   
                               
                                
                               2 
                             
                             - 
                             Wref 
                           
                           ) 
                         
                       
                     
                     
                       Wt 
                        
                       
                           
                       
                        
                       2 
                     
                   
                   &gt; 
                   L 
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   4 
                 
               
             
           
         
       
     
         [0124]    In Equation 4, “N” denotes the number of viewpoints, “Wref” denotes the width of the viewpoint image projected to the viewing zones at the reference visible distance OVD 1 , “Wt 2 ” denotes the width of the viewpoint image projected to the viewing zones at the target visible distance OVD 3 , and “L” denotes the number of the original pixel units. The width Wref of the viewpoint image projected to the viewing zones at the reference visible distance OVD 1  may be substantially the same as the width of the first to fourth viewing zones VZ 1  to VZ 4  at the reference visible distance OVD 1 , and the width Wt 2  of the viewpoint image projected to the viewing zones at the target visible distance OVD 3  may be substantially the same as the width of the ninth to twelfth viewing zones VZ 9  to VZ 12  (see  FIG. 9B ) at the target visible distance OVD 3 . Since the reference visible distance OVD 1  is less than the target visible distance OVD 3 , the width Wref of the viewpoint image projected to the viewing zones at the reference visible distance OVD 1  is less than the width Wt 2  of the viewpoint image projected to the viewing zones at the target visible distance OVD 3 . 
         [0125]    As an example, the first to ninth pixel sets PS 1  to PS 9  may be divided into first to third original pixel units PU 1  to PU 3 . That is, in the present exemplary embodiment, each of “M” and “L” is 3. Each of the first to third original pixel units PU 1  to PU 3  has a first unit width WU 1 . 
         [0126]    The first to third original pixel units PU 1  to PU 3  are respectively converted to first to third compensated pixel units PU 1  “to PU 3 ” each having a third unit width WU 3  different from the first unit width WU 1 . The third unit width WU 3  may be greater than the first unit width WU 1 . 
         [0127]    To convert the first to third original pixel units PU 1  to PU 3  to the first to third compensated pixel units PU 1 ″ to PU 3 ″, a pixel in each of the first to third original pixel units PU 1  to PU 3  are defined to be first to third dummy pixels DP 1  to DP 3  and are subsequently excluded from the first to third original pixel units PU 1  to PU 3 . Accordingly, the third unit width WU 3  becomes narrower than the first unit width WU 1  by the width of each of the first to third dummy pixels DP 1  to DP 3 . 
         [0128]    In a present exemplary embodiment, the first to third dummy pixels DP 1  to DP 3  are defined as the pixels respectively provided to end portions of the first to third compensated pixel units PU 1 ″ to PU 3 ″. 
         [0129]    For example, a fourth pixel  4  of the third pixel set PS 3  of the first original pixel unit PU 1  is designated as the first dummy pixel DP 1  and excluded from the first original pixel unit PU 1 . A fourth pixel  4  of the sixth pixel set PS 6  of the second original pixel unit PU 2  is designated as the second dummy pixel DP 2  and excluded from the second original pixel unit PU 2 . A fourth pixel  4  of the ninth pixel set PS 9  of the third original pixel unit PU 3  is designated as the third dummy pixel DP 3  and excluded from the third original pixel unit PU 3 . 
         [0130]    As described above, when the first to third original pixel units PU 1  to PU 3  are converted to the first to third compensated pixel units PU 1 ″ to PU 3 ″ each having a third unit width WU 3  on the basis of the comparison result, the image displayed in the display unit  100  is refracted by the lenticular lens  210  and projected to a plurality of target viewing sets at the target visible distance OVD 3 . Here, the target visible distance OVD 3  corresponds to the distance between the lenticular lens  210  and the target viewing sets. 
         [0131]    The target viewing sets include a fourth target viewing set VS 4  and fifth and sixth target viewing sets VS 5  and VS 6  disposed at each side of the fourth target viewing set VS 4 . 
         [0132]    The fourth target viewing set VS 4  includes the ninth to twelfth viewing zones VZ 9  to VZ 12  sequentially arranged in a row. The lenticular lens  210  refracts the first to fourth viewpoints of the image and projects the first to fourth viewpoints to the ninth to twelfth viewing zones VZ 9  to VZ 12 , respectively. 
         [0133]    As described above, when each of the first to third compensated pixel units PU 1 ″ to PU 3 ″ has a third unit width WU 3 , the first to third original normal image areas RV 1  to RV 3  corresponding to the first to third original pixel units PU 1  to PU 3  are converted to fourth to sixth compensated normal image areas CV 4  to CV 6 , respectively. The fourth to sixth compensated normal image areas CV 4  to CV 6  respectively correspond to the fourth to sixth target viewing sets VS 4  to VS 6 . The width of the fourth to sixth compensated normal image areas CV 4  to CV 6  at the target visible distance OVD 3  is greater than the width of the first to third original normal image areas RV 1  to RV 3  at the target visible distance OVD 3 . Accordingly, as described with reference to  FIG. 9A , when the auto-stereoscopic display apparatus  1000  projects a three-dimensional image to the first to third original normal image areas RV 1  to RV 3 , the ninth and tenth users P 9  and P 10  perceive an abnormal image, but the ninth and tenth users P 9  and P 10  together with the eighth user P 8  perceive a three-dimensional image when the auto-stereoscopic display apparatus  1000  projects a three-dimensional image to the fourth to sixth compensated normal image areas CV 1  to CV 3 . 
         [0134]      FIG. 10  is a cross-sectional view of the display unit that projects the three-dimensional image to the viewing zones at the reference visible distance according to an exemplary embodiment of the present disclosure. 
         [0135]    Hereinafter, the operation of the auto-stereoscopic display apparatus  1000  will be described in detail with reference to  FIGS. 1 ,  9 A, and  10  when the three-dimensional image is projected to the viewing zones at the reference visible distance OVD 1 . 
         [0136]    When the auto-stereoscopic display apparatus  1000  projects the three-dimensional image to the viewing zones at the reference visible distance OVD 1 , the mapping unit  800  is not operated and the data driver  400  converts the image data Idata provided from the timing controller  500  to data voltages and applies the data voltages to the display unit  100 . The display unit  100  includes the pixels PX arranged in a row. For the convenience of explanation, the pixels PX are arranged in the first direction DX 1  substantially parallel to the row direction and are referred to as first to thirty-sixth pixels PN 1  to PN 36 . 
         [0137]    The image data Idata includes first to thirty-sixth pixel data PD 1  to PD 36  sequentially received from the timing controller  500 . The first to thirty-sixth pixel data PD 1  to PD 36  respectively correspond to the first to thirty-sixth pixels PN 1  to PN 36 . In more detail, the first to thirty-sixth pixel data PD 1  to PD 36  are supplied to the data driver  400 , the data driver  400  sequentially supplies first to thirty-sixth data voltages respectively corresponding to the first to thirty-sixth pixels PN 1  to PN 36  to the first to thirty-sixth pixels PN 1  to PN 36 , and the first to thirty-sixth pixels PN 1  to PN 36  display the image in response to the first to thirty-sixth data voltages to project the three-dimensional image to the viewing zones at the reference visible distance OVD 1 . 
         [0138]    In this case, the first original pixel unit PU 1  includes the first to twelfth pixels PN 1  to PN 12 , the second original pixel unit PU 2  includes the thirteenth to twenty-fourth pixels PN 13  to PN 24 , and the third original pixel unit PU 3  includes the twenty-fifth to thirty-sixth pixels PN 25  to PN 36 . 
         [0139]    The mapping unit  820  designates the first to third dummy pixels DP 1  to DP 3  on the basis of the comparison result. For example, the mapping unit  820  may designate the twelfth, twenty-fourth, and thirty-sixth pixels as the first, second, and third dummy pixels DP 1 , DP 2 , and PD 3 , respectively. 
         [0140]      FIG. 11  is a cross-sectional view of a display unit that projects a three-dimensional image to the viewing zones at the target visible distance according to an exemplary embodiment of the present disclosure and  FIG. 12  illustrates a process of generating mapping image data shown in  FIG. 11 . 
         [0141]    Hereinafter, the operation of the auto-stereoscopic display apparatus  1000  will be described in detail with reference to  FIGS. 1 ,  9 B,  10 , and  11  when the three-dimensional image is projected to the viewing zones at the target visible distance OVD 3 . 
         [0142]    The mapping unit  820  maps the image data Idata on the basis of the comparison result and outputs the mapping image data Idata′. 
         [0143]    In more detail, the mapping unit  820  designates the first to third dummy pixel data DD 1  to DD 3  among the image data Idata and removes the first to third dummy pixel data DD 1  to DD 3  from the image data Idata to generate the mapping image data Idata′. In a present exemplary embodiment, the first dummy pixel data DD 1  is the twelfth pixel data PD 12 , the second dummy pixel data DD 2  is the twenty-fourth pixel data PD 24 , and the third dummy pixel data DD 3  is the thirty-sixth pixel data PD 36 . 
         [0144]    To this end, the mapping unit  820  writes the first to eleventh pixel data PD 1  to PD 11  in first to eleventh addresses A 1  to A 11  and does not write the twelfth pixel data PD 12  that corresponds to the first dummy pixel data DP 1  in the mapping image data Idata′. 
         [0145]    Then, the mapping unit  820  writes the thirteenth to twenty-third pixel data PD 13  to PD 23  in twelfth to twenty-second addresses A 1  to A 22  and does not write the twenty-fourth pixel data PD 24  that corresponds to the second dummy pixel DP 2  in the mapping image data Idata′. 
         [0146]    The mapping unit  820  writes the twenty-fifth to thirty-fifth pixel data PD 25  to PD 35  in twenty-third to thirty-third addresses A 23  to A 33  and does not write the thirty-sixth pixel data PD 36  that corresponds to the third dummy pixel DP 3  in the mapping image data Idata′. 
         [0147]    The data written in the first to thirty-third addresses A 1  to A 33  of the mapping image data Idata′ sequentially correspond to the first to thirty-third pixels PN 1  to PN 33 . In more detail, the mapping image data Idata′ are sequentially supplied to the data driver  400 , the data driver  400  sequentially supplies the first to thirty-third data voltages corresponding to the mapping image data Idata′ to the first to thirty-third pixels PN 1  to PN 33 , and the first to thirty-third pixels PN 1  to PN 33  display the image in response to the first to thirty-third data voltages to project the three-dimensional image to the viewing zones at the target visible distance OVD 3 . 
         [0148]    As a result, the first to eleventh pixels PN 1  to PN 11  of the first compensated pixel unit PU 1 ″ receive the data voltages converted by the first to eleventh pixel data PD 1  to PD 11  written in the first to eleventh addresses A 1  to A 11  and display the image corresponding to the data voltages. 
         [0149]    In addition, the twelfth to twenty-second pixels PN 12  to PN 22  of the second compensated pixel unit PUT′ receive the data voltages converted by the thirteenth to twenty-third pixel data PD 13  to PD 23  written in the twelfth to twenty-second addresses A 12  to A 22  and display the image corresponding to the data voltages. 
         [0150]    Further, the twenty-third to thirty-third pixels PN 23  to PN 33  of the third compensated pixel unit PU 3 ″ receive the data voltages converted by the twenty-fifth to thirty-fifth pixel data PD 25  to PD 35  written in the twenty-third to thirty-third addresses A 23  to A 33  and display the image corresponding to the data voltages. 
         [0151]    Although exemplary embodiments of the present disclosure have been described, it is understood that embodiments of the present disclosure should not be limited to these exemplary embodiments but various changes and modifications can be made by one ordinary skilled in the art within the spirit and scope of embodiments of the present disclosure as hereinafter claimed.