Abstract:
An eyeglass-less 3D display device, and a device and method that compensate for a displayed margin of error are provided. The display device acquires an image of an integral image display (IID) image captured by a single camera, and compensates for a margin of error which arises due to a discrepancy between the designed position of a micro lens array located on one surface of a 2D panel and the actual position thereof, so as to provide a high-quality 3D image.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
       [0001]    This is a National Stage application of International Application No. PCT/KR2015/003849 filed Apr. 16, 2015, which claims priority from Chinese Patent Application No. 201410157743.X filed Apr. 18, 2014, and Korean Patent Application No. 10-2015-0052393 filed Apr. 14, 2015, the disclosures of which are incorporated herein in their entireties. 
     
    
     FIELD 
       [0002]    Apparatuses and methods consistent with example embodiments relate to a three-dimensional (3D) display device, and more particularly, to a device and method for correcting an error in a glassless-type integral image display (IID). 
       BACKGROUND 
       [0003]    Integral image display (IID)-type three-dimensional (3D) display technology may involve a display with a high brightness and enable a user to view a 3D image with a naked eye. Such an IID-type technology may generate a 3D image by refracting a two-dimensional (2D) elemental image array (EIA) image in different directions through a refraction implemented by a microlens array located on a 2D display, for example, a liquid crystal display (LCD) panel. 
         [0004]    An actual location of the microlens array may deviate from a designed location of the microlens array due to a characteristic quality (e.g., accuracy) of the microlens array, or an environmental characteristic (e.g., temperature) of a location at which the microlens array is disposed. Thus, correcting an error in the actual location of the microlens array may be needed for a high-quality IID-type 3D display. 
       SUMMARY 
       [0005]    According to an aspect of one or more example embodiments, there is provided a device for correcting a display error, the device including an image acquirer configured to obtain a first image by capturing an integral image display (IID) image by using a single camera, and an error estimator configured to optimize an error algorithm indicating an error that corresponds to a discrepancy between an actual location of a microlens array located on one surface of a two-dimensional (2D) panel and an intended location of the microlens array, and to estimate the error based on the optimized error algorithm. 
         [0006]    The error estimator may optimize the error algorithm by generating an initial error algorithm based on a preset initial error parameter value, and updating the initial error parameter value based on a mapping location to which a point of the first image is to be mapped on the 2D panel. 
         [0007]    The error estimator may include a virtual mapping location determiner configured to determine the virtual mapping location to which the point of the first image is to be mapped on a virtual image plane which lies between the single camera and the microlens array by each microlens of the microlens array and a central location of the single camera, a first mapping location determiner configured to determine a first mapping location to which the virtual mapping location is to be mapped on the 2D panel by analyzing a respective relationship between each respective pixel point of the first image and a corresponding pixel point of the 2D panel, a second mapping location determiner configured to determine a second mapping location to which a connection line connecting the central location of the single camera and the virtual mapping location is to be mapped on the 2D panel, and an optimizer configured to optimize the error algorithm based on a locational difference between the first mapping location and the second mapping location. 
         [0008]    The optimizer may optimize the error algorithm by updating the initial error parameter value to minimize the locational difference between the first mapping location and the second mapping location. 
         [0009]    The optimizer may also optimize the error algorithm by determining a respective distance from each of at least one microlens of the microlens array to the first mapping location and a respective distance from each of the at least one microlens to the second mapping location, and determining that the initial error parameter value is optimized based on a minimal sum of the determined distances. 
         [0010]    According to an aspect of one or more example embodiments, there is provided a display device including an image acquirer configured to obtain a first image by capturing an IID image by using a single camera, an error estimator configured to optimize an error algorithm indicating an error between an actual location of a microlens array located on one surface of a 2D panel and an intended location of the microlens array and to estimate the error based on the optimized error algorithm, and a renderer configured to render the first image to be an Elemental Image Array (EIA)-type second image based on an error associated with the microlens array. 
         [0011]    The error estimator may include a virtual mapping location determiner configured to determine a virtual mapping location to which a point of the first image is to be mapped on a virtual image plane which lies between the single camera and the microlens array by each microlens of the microlens array and a central location of the single camera, a first mapping location determiner configured to determine a first mapping location to which the virtual mapping location is to be mapped on the 2D panel by analyzing a respective relationship between each respective pixel point of the first image and a corresponding pixel point of the 2D panel, a second mapping location determiner configured to determine a second mapping location to which a connection line connecting the central location of the single camera and the virtual mapping location is to be mapped on the 2D panel, and an optimizer configured to optimize the error algorithm based on a locational difference between the first mapping location and the second mapping location. 
         [0012]    The optimizer may optimize the error algorithm by updating a preset initial error parameter value to minimize the locational difference between the first mapping location and the second mapping location. 
         [0013]    The renderer may render the first image to be the second image based on a ray algorithm generated based on an actual respective location of each microlens of the microlens array determined based on the estimated error associated with the microlens array. 
         [0014]    The renderer may include a location determiner configured to determine the actual respective location of each microlens based on the error associated with the microlens array, a ray algorithm generator configured to generate the ray algorithm indicating a three-dimensional (3D) ray corresponding to each pixel of the 2D panel based on the determined actual respective location of each microlens, and an EIA renderer configured to render the first image to be the second image using the generated ray algorithm. 
         [0015]    The ray algorithm generator may include an initializer configured to initialize a respective relationship between a pixel of the 2D panel and each respective microlens of the microlens array, an updater configured to update the respective relationship for each respective microlens by using a point obtained by projecting a point of the first image to the 2D panel, and a direction indicator configured to indicate the pixel of the 2D panel and a direction of a microlens corresponding to the pixel by using points on two parallel planes. 
         [0016]    The updater may include a projector configured to obtain a first projection point at which a first observation point included in the first image is projected to the 2D panel through a first microlens of the microlens array, a window arranger configured to form a window of a preset size on the 2D panel centered at the first projection point, and a local updater configured to perform updating on a respective microlens to be mapped to each pixel of the window. 
         [0017]    The local updater may include a verifier configured to verify whether the first microlens through which the first projection point is obtained is a microlens that corresponds to the initialized corresponding relationship, a pixel projector configured to, when the first microlens does not correspond to the initialized respective relationship, obtain a second projection point by projecting a first pixel of the window to the first image based on the initialized respective relationship and obtain a third projection point by projecting the first pixel of the window to the first image based on the first microlens, and a mapping updater configured to determine a first distance between the second projection point and the first observation point and a second distance between the third projection point and the first observation point, and to update a microlens that corresponds to the pixel of the 2D panel for the first projection point to be the first microlens in response to the first distance being greater than or equal to the second distance. 
         [0018]    According to an aspect of one or more example embodiments, there is provided a method for correcting a display error, the method including obtaining a first image by capturing an IID image by using a single camera, generating an error algorithm indicating an error between an actual location of a microlens array located on one surface of a 2D panel and an intended location of the microlens array, and estimating the error by optimizing the error algorithm. 
     
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         [0019]    The above and/or other aspects will become apparent and more readily appreciated from the following description of example embodiments, taken in conjunction with the accompanying drawings of which: 
           [0020]      FIG. 1  is a block diagram illustrating a device for correcting a display error, according to an example embodiment. 
           [0021]      FIG. 2  is a block diagram illustrating an error estimator of a device for correcting a display error, according to an example embodiment. 
           [0022]      FIG. 3  is a diagram illustrating a relationship among a single camera, a two-dimensional (2D) panel, and a microlens array for correcting a display error, according to an example embodiment. 
           [0023]      FIG. 4  is a block diagram illustrating a display device, according to an example embodiment. 
           [0024]      FIG. 5  is a block diagram illustrating a renderer of a display device, according to an example embodiment. 
           [0025]      FIG. 6  is a diagram illustrating a process of rendering performed by a display device, according to an example embodiment. 
           [0026]      FIG. 7  is a block diagram illustrating a ray model generator of a display device, according to an example embodiment. 
           [0027]      FIG. 8  is a block diagram illustrating an updater of the ray model generator of  FIG. 7 . 
           [0028]      FIG. 9  is a flowchart illustrating a method for correcting a display error, according to an example embodiment. 
           [0029]      FIG. 10  is a flowchart illustrating a process of calculating a display error, according to an example embodiment. 
           [0030]      FIG. 11  is a flowchart illustrating a process of rendering based on a display error, according to an example embodiment. 
           [0031]      FIG. 12  is a flowchart illustrating a process of updating a corresponding relationship of a microlens, according to an example embodiment. 
       
    
    
     DETAILED DESCRIPTION 
       [0032]    Hereinafter, some example embodiments will be described in detail with reference to the accompanying drawings. It should be understood, however, that there is no intent to limit this disclosure to the particular example embodiments disclosed. Regarding the reference numerals assigned to the elements in the drawings, it should be noted that the same elements will be designated by the same reference numerals, wherever possible, even though they are shown in different drawings. 
         [0033]    Terms most generally and widely used in a related technical field are used herein. However, other terms may be selected based on development and/or change of related technologies, practices, preferences by one of ordinary skill in the art, and the like. Thus, the terminology used herein is for the purpose of describing particular example embodiments only, and is not intended to limit technical features. 
         [0034]    In addition, terms selected by an applicant are also used herein, and the meanings of such terms are described in the Detailed Description section. The terms used herein are not to be interpreted based solely on the terms themselves, but to be interpreted based on the meanings of the terms as defined herein and the overall context of the present disclosure. 
         [0035]      FIG. 1  is a block diagram illustrating a device for correcting a display error, according to an example embodiment. The device for correcting a display error will be hereinafter referred to as a display error correcting device for simplicity. The display error correcting device includes an image acquirer  110  and an error estimator  120 . The image acquirer  110  obtains a first image by capturing an internal image display (IID) image with a single camera. For a glassless-type three-dimensional (3D) display, the single camera may capture the IID image, and an error associated with a microlens may be corrected for the obtained image. A microlens array located on one surface of a two-dimensional (2D) panel may display a glassless-type 3D image by refracting the first image in different directions. Here, encoding may be performed on a location of each pixel of the 2D panel with respect to the first image obtained by capturing the IID image. In addition, decoding may be performed on the first image obtained by capturing the IID image in order to obtain a respective relationship between the first image and each pixel of the 2D panel. The first image obtained by capturing the IID image may be a black-and-white image of a 2D Gray code or a sinusoidal fringe-type image including a phase shift. 
         [0036]    Based on the respective relationship between a pixel point of the first image and a pixel of the 2D panel, a corresponding relationship between the pixel of the 2D panel and a point on a virtual image plane of the single camera capturing the first image, for example, an image plane of an image sensor, may be obtained. In particular, as a result of the decoding performed on the first image, a location of the pixel of the 2D panel on the image plane of the single camera may be determined. Based on the corresponding relationship between the pixel of the 2D panel and the location of the pixel on the image plane of the signal camera capturing the first image, a motion parameter of the single camera may be obtained. The motion parameter may include, for example, either or both of a rotation parameter and a parallel translation parameter. The motion parameter may be obtained by using any of various methods well-known in a related technical field to which the present disclosure belongs, and thus a detailed description of the methods will be omitted here. 
         [0037]    The error estimator  120  generates an error model (also referred to herein as an “error algorithm”) indicating an error between an actual location of the microlens array located on one surface of the 2D panel and an intended location (also referred to herein as a “designed location”) of the microlens array, and estimates the error by optimizing the error model. A method of estimating a display error will be described in detail with reference to  FIGS. 2 and 3 . 
         [0038]      FIG. 2  is a block diagram illustrating an error estimator of a display error correcting device, according to an example embodiment. The error estimator  120  of  FIG. 1  may optimize the error model by generating an initial error model based on a preset initial error parameter value and updating the initial error parameter value based on a mapping location to which one point of the first image is to be mapped on the 2D panel. The error estimator  120  includes a mapping location determiner (also referred to herein as a “virtual mapping location determiner”)  121 , a first mapping location determiner  122 , a second mapping location determiner  123 , and an optimizer  124 . 
         [0039]      FIG. 3  is a diagram illustrating a relationship among a single camera  301 , a 2D panel  302 , and a microlens array  303  which is configured for correcting a display error, according to an example embodiment. Referring to  FIG. 3 , an error may be estimated by calculating an actual location of the microlens array  303 . 
         [0040]    Referring back to  FIG. 2 , the mapping location determiner  121  calculates a location of a microlens, for example, L c  in  FIG. 3 , based on an initial error parameter. Here, the location L c  corresponds to a designed location of the microlens. An error parameter φ indicates a locational difference between a designed location of a microlens and an actual location of the microlens, and an error model is a function that indicates an error between the designed location and the actual location of the microlens based on the error parameter φ. 
         [0041]    Equation 1 below expresses an actual location of a microlens that may be defined using a designed location of the microlens and an error model (also referred to herein as an “error algorithm”). 
         [0000]    
       
         
           
             
               
                 
                   
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         [0042]    In Equation 1, [x ij , y ij , z ij ] T  and [x′ ij , y′ ij , z′ ij ] T  denote 3D coordinates of an actual location of a microlens and 3D coordinates of a designed location of the microlens, respectively. 
         [0043]    [e (x)   ij , e (y)   ij , e (z)   ij ] T  denotes an error between the 3D coordinates of the actual location of the microlens and the 3D coordinates of the designed location of the microlens. 
         [0044]    In [e (x)   ij , e (y)   ij , e (z)   ij ] T , a total amount of calculation may be reduced by using different error models, i.e., different error algorithms, for different types of errors. 
         [0045]    For example, an error between a designed location of a microlens and an actual location of the microlens based on a 2D panel may be represented by a rotation angle θ and a parallel translation vector [tx, ty] in the 2D panel. Such an error may be defined as expressed in Equation 2 below based on coordinates of a center of each lens of a lens array. 
         [0000]        e   (x)   ij   =x′   ij (cos(θ)−1)−sin(θ) y′   ij   −tx  
 
         [0000]        e   Y   ij   =x′   ij  sin(θ)+(cos(θ)−1) y′   ij   −ty   [Equation 2]
 
         [0046]    In Equation 2, the error parameter φ may be defined by including therein the rotation angle θ and the parallel translation vector [tx, ty]. 
         [0047]    In a presence of a warping phenomenon in the lens array, a light center of the lens array may not be positioned on a single plane. In such a case, an error change in a Z direction may be defined as expressed in Equation 3 below using a single elliptic radial distortion model. 
         [0000]        e   (z)ij =( a ( x′   ij   −x   0 ) 2   +b ( y′   ij   −y   0 ) 2 ) c+d   [Equation 3]
 
         [0048]    In Equation 3, [x 0 , y 0 ] denotes a location of a radial distortion center on a horizontal plane, and [a, b, c, d] denotes lens array distortion type parameters. Here, the error parameter φ may be expressed as [x 0 , y 0 , a, b, c, d]. 
         [0049]    Although Equations 2 and 3 above are equations associated with the error model, the error model may be defined by other methods, and thus the error model is not be limited by Equations 2 and 3. 
         [0050]    The mapping location determiner  121  determines a mapping location based on a location of a microlens. Here, the location of the microlens may be indicated as central coordinates of the microlens. In detail, a point to which a point of the first image on a virtual image plane which lies between the single camera and the microlens array is mapped on an image plane by each microlens and a central location of the single camera may be determined to be the mapping location, for example, L c  in  FIG. 3 . 
         [0051]    Referring to  FIG. 3 , a central location (or central coordinates) O c  of the single camera  301  may be determined based on a motion parameter value, and a virtual mapping location I c  of a microlens corresponding to the first image, for example, a location on the image plane, may be obtained by projecting the designed location L c  of the microlens to the virtual image plane of the single camera  301 . In this aspect, an intersection point at which a connection line connecting the designed location L c  of the microlens and the central location O c  of the single camera  301  meets the image plane may be designated as the virtual mapping location I c . 
         [0052]    The first mapping location determiner  122  determines a first mapping location P SL (c; φ) to which the virtual mapping location I c  is to be mapped on the 2D panel  302  by analyzing a respective relationship between each respective pixel point of the first image and a corresponding pixel point of the 2D panel  302 . The analyzing of the respective relationship may be performed through decoding performed on the first image. Here, a location to which the virtual mapping location I c  is to be mapped on the 2D panel  302  may be indicated by the first mapping location P SL (c; φ). In this manner, coordinates of a point at which a point of first image is to be displayed on the 2D panel  302  may be determined. 
         [0053]    The second mapping location determiner  123  determines, to be a second mapping location P P (c; φ), a location to which the connection line connecting the central location O c  of the single camera  301  and the virtual mapping location I c  is to be mapped on the 2D panel  302 . In particular, coordinates of a point at which the virtual mapping location I c  is located on the 2D panel  302  based on the motion parameter and the designed location L c  of the microlens may be indicated by the second mapping location P P (c; φ). 
         [0054]    The optimizer  124  optimizes the error model based on a locational difference between the first mapping location and the second mapping location. In detail, the locational difference between the first mapping location and the second mapping location may be a distance between the first mapping location and the second mapping location, and the initial error parameter may be optimized based on the distance. According to an example embodiment, a distance between the first mapping location and the second mapping location may be calculated for each of at least one microlens of the microlens array  303 , and the initial error parameter may be considered to be optimized when a sum of calculated distances is minimized. 
         [0055]    A sum of the distances calculated for each of the at least one microlens of the microlens array  303  may be expressed by Equation 4 below. 
         [0000]        E (φ)=Σ c ε CC ( P   p ( c ;φ)− P   SL ( c ;φ)) 2   [Equation 4]
 
         [0056]    In Equation 4,  CC  denotes a central location of a microlens. Here, the microlens may be at least one microlens included in the microlens array  303 , and thus be a subset of the microlens array  303 . P P (c; φ) denotes a second mapping location, where φ denotes an error parameter, L c  denotes a location of the microlens, and c denotes central coordinates of the microlens. P SL (c; φ) denotes a first mapping location, where φ denotes an error parameter, L c  denotes a location of the microlens, and c denotes central coordinates of the microlens. 
         [0057]    (P P (c; φ)−P SL (c; φ)) 2  denotes a distance between the second mapping location P P (c; φ) and the first mapping location P SL (c; φ). 
         [0058]    The error parameter φ may be optimized by minimizing E(φ) For example, an optimal value of the error parameter φ may be obtained using a heuristic nonlinear optimization algorithm such as, for example, a genetic algorithm. 
         [0059]    A final error value of the microlens array  303  may be calculated based on the optimized error parameter in order to estimate an error associated with the microlens array  303 . An actual location of a microlens may be calculated by applying an error value obtained after the optimization to a relative error model of the actual location of the microlens and a designed location of the microlens, for example, Equations 1, 2, or 3. 
         [0060]    According to another example embodiment, there is provided a display device that may render an image obtained by correcting a display error in an image obtained by capturing an IID image, and display the rendered image.  FIG. 4  is a block diagram illustrating a display device  400  according to an example embodiment. The display device  400  includes an image acquirer  410 , an error estimator  420 , and a renderer  430 . 
         [0061]    The image acquirer  410  obtains a first image by capturing an IID image with a single camera. By decoding the obtained first image, a respective relationship between each respective pixel point of the first image and a corresponding pixel point of a 2D panel may be determined. 
         [0062]    The error estimator  420  estimates an error between an actual location of a microlens array located on one surface of the 2D panel and an intended location of the microlens array by optimizing an error algorithm indicating the error between the intended location and the actual location. The error estimator  420  includes a virtual mapping location determiner, a first mapping location determiner, a second mapping location determiner, and an optimizer, which are described above with reference to  FIG. 2 . In detail, the virtual mapping location determiner determines a virtual mapping location to which a point of the first image is to be mapped on a virtual image plane which lies between the single camera and the microlens array by each microlens of the microlens and a central location of the single camera. Referring back to  FIG. 3 , a virtual mapping location I c  on the virtual image plane may be determined by a location of each microlens of the microlens array, for example, the intended location L c  and a central location O c  of the single camera. 
         [0063]    The first mapping location determiner determines a first mapping location, for example, P SL (c; φ), to which the virtual mapping location I c  is to be mapped on the 2D panel by analyzing a respective relationship between each respective pixel point of the first image and a corresponding pixel point of the 2D panel. Here, φ denotes an initial error parameter, and c denotes a central location of a microlens. The second mapping location determiner determines, to be a second mapping location, for example, P P (c; φ), a location to which a connection line connecting the central location O c  of the single camera and the virtual mapping location I c  is to be mapped on the 2D panel. Here, φ denotes the initial error parameter, and c denotes the central location of the microlens. The optimizer optimizes an error model based on a locational difference, or a distance, between the first mapping location and the second mapping location. The error model may be optimized by updating an error parameter value to minimize the distance between the first mapping location and the second mapping location. 
         [0064]    After an error value associated with a microlens is calculated, the renderer  430  renders the first image to be an elemental image array (EIA)-type second image based on an error associated with the microlens array. The rendering may be performed based on a ray model (also referred to herein as a “ray algorithm”) generated based on an actual location of each microlens of the microlens array calculated based on the estimated error associated with the microlens array. A method of rendering performed by the renderer  430  will be described in detail below with reference to  FIGS. 5 and 6 . 
         [0065]      FIG. 5  is a block diagram illustrating the renderer  430  of the display device  400 , according to an example embodiment. The renderer  430  includes a location determiner  431 , a ray model generator  432 , and an EIA renderer  433 . 
         [0066]    The location determiner  431  calculates an actual respective location of each microlens of a microlens array based on an error associated with the microlens array. For example, the actual respective location of the microlens may be calculated based on Equation 1 above. 
         [0067]    The ray model generator  432  generates a ray model indicating a 3D ray corresponding to each pixel of a 2D panel based on an actual respective location of each microlens. The ray model may be used for rendering to be performed on an EIA image, and may be used to map each pixel of the 2D panel to a single ray in a 3D space. The ray model that is generated as a default in a presence of an error in a location of a microlens of the microlens array may not accurately perform the rendering, and thus generating the ray model based on an actual respective location of a respective microlens of the microlens array may be needed. A process of generating a ray model will be described below in detail with reference to  FIG. 6 . 
         [0068]    The EIA renderer  433  renders the first image to be the EIA-type second image by using the ray model. 
         [0069]      FIG. 6  is a diagram illustrating a process of rendering performed by the display device  400 , according to an example embodiment. A process of generating a ray model in the rendering is illustrated.  FIG. 7  is a block diagram illustrating the ray model generator  432  of the display device  400 , according to an example embodiment. The ray model generator  432  of  FIG. 5  includes an initializer  710 , an updater  720 , and a direction indicator  730 . 
         [0070]    The initializer  710  initializes a respective relationship between a respective pixel of a 2D panel and each corresponding microlens of a microlens array. The respective relationship may be initialized to be a preset value. For example, for the initialization, each pixel of the 2D panel may be mapped to a predetermined microlens, and the first microlens may be indicated by an initial indication sign. The initial indication sign may be different from a respective indication sign of each respective microlens. 
         [0071]    For example, a mapping relationship, or the corresponding relationship, between a respective pixel of the 2D panel and a corresponding microlens of the microlens array may be represented through the following method. Under the assumption of coordinates (m, n) of one pixel of the 2D panel, mapping between each respective pixel and a corresponding microlens may be indicated by a respective indication sign, for example, S(m,n),T(m,n),G(m,n). Here, S(m,n),T(m,n),G(m,n) indicate coordinate values on an x, y, and z axis, respectively, with respect to a center of a respective microlens to be mapped to each corresponding pixel. For example, in an absence of a microlens with S(m,n)=0, T(m,n)=0, G(m,n)=0, (0, 0, 0), may be the initial indication sign. Here, central coordinates of a microlens mapped to each pixel through the initialization may be (0, 0, 0). The mapping relationship between the 2D panel and a microlens may also be represented by other types of indication signs, such as, for example, a number. 
         [0072]    The updater  720  updates the respective relationship for each microlens by using a point obtained by projecting a point of the first image to the 2D panel. A method of updating the respective relationship will be described in detail below with reference to  FIGS. 6 and 8 .  FIG. 6  illustrates a 2D panel  601 , a microlens array  602 , and a first image  603  (or an observation plane including a first observation point). 
         [0073]      FIG. 8  is a block diagram illustrating the updater  720  of the ray model generator  432  of  FIG. 7 . The updater  720  includes a projector  721 , a window former (also referred to herein as a “window arranger”)  722 , and a local updater  723 , and may update a value of a ray model indicating a respective relationship between a 2D panel and a respective microlens of a microlens array. 
         [0074]    The projector  721  obtains a first projection point to which a first observation point included in a first image is projected on a 2D panel through a certain microlens of a microlens array. Referring back to  FIG. 6 , a first projection point T 1  to which a first observation point V c  included in the first image  603  or the observation plane is projected on the 2D panel  601  through a certain microlens H (j)  of the microlens array  602  may be obtained. 
         [0075]    The window former  722  forms a window of a preset size, centered at the first projection point, in the 2D panel. Here, various shapes of windows may be formed, for example, a circular, a spherical, a quadrate, or a rectangular window may be formed. Referring back to  FIG. 6 , a rectangular window W including seven pixels is formed to be centered at the first projection point T 1 . 
         [0076]    A length of one side of the window may be expressed as Equation 5 below. 
         [0000]      1.2 p ( D+g )/( D·s )  [Equation 5]
 
         [0077]    In Equation 5, p denotes a size of a microlens, for example, a diameter of the microlens; D denotes a distance from a predetermined observation point to a 2D panel; s denotes a physical dimension of a pixel of the 2D panel, for example, a length of one side of a rectangular pixel; and g denotes a distance from a designed location of a microlens array to the 2D panel. 
         [0078]    The local updater  723  performs updating on a microlens to be mapped to each pixel in the window by using the window on the 2D panel. In detail, the local updater  723  includes a verifier  723 - 1  configured to verify an initial respective relationship, a pixel projector  723 - 2  configured to calculate a second projection point and a third projection point when the initial respective relationship is not verified, and a mapping updater  723 - 3  configured to update the respective relationship by using the second projection point and the third projection point. 
         [0079]    The verifier  723 - 1  verifies whether a certain microlens through which the first projection point is obtained corresponds to an initialized respective relationship. For example, as illustrated in  FIG. 6 , the first observation point V c  may be projected to the first projection point T 1  of the 2D panel  601  through the microlens H (j)  of the microlens array  602 . Here, the verifier  723 - 1  may verify whether the first projection point T 1  among the pixels of the 2D panel  601  and the microlens H (j)  are in a mapping relationship from the initialized respective relationship. When the mapping relationship does not correspond to the initialized respective relationship, two projection points for a first pixel, which is one of the pixels included in the window W, may be obtained. The window W may include at least one pixel of various forms, and thus the first pixel may be a pixel in the window W. 
         [0080]    The pixel projector  723 - 2  obtains a second projection point by projecting the first pixel to the observation plane that includes the first image  603  based on the initialized respective relationship associated with the first pixel, for example, the initialized respective relationship between a pixel of the 2D panel and a microlens. For example, as illustrated in  FIG. 6 , the first pixel may be a pixel that comes first in the window W, and a second projection point P 1  to which the first pixel is projected on the observation plane through a microlens H (j)  may be obtained based on the initialized respective relationship. Subsequently, a certain microlens, for example, the microlens H (j)  through which the first observation point V c  is projected to the first projection point T 1 , may be used to obtain a third projection point P 2  by projecting the first pixel of the window W to the first image  603  or the observation plane. 
         [0081]    The mapping updater  723 - 3  updates the respective relationship between a microlens and a pixel of the 2D panel by using the two projection points. Here, a distance between the second projection point and the first observation point is referred to as a first distance, and a distance between the third projection point and the first observation point is referred to as a second distance. When the first distance is greater than or equal to the second distance, a microlens that corresponds to a pixel of the 2D panel in association with the first projection point may be updated to be the certain microlens. In this aspect, the pixel of the 2D panel and the first observation point that corresponds to the first projection point may correspond to the microlens through which the first observation point is projected to the first projection point. 
         [0082]    For example, as illustrated in  FIG. 6 , the first distance is |V c −P 1 |, and the second distance is |V c −P 2 |. When Equation 6 below is satisfied, the respective relationship may be updated. 
         [0000]      | V   c   −P   1   |≧|V   c   −P   2 |  [Equation 6]
 
         [0083]    In Equation 6, when the first distance is greater than or equal to the second distance, a microlens in the respective relationship with the pixel of the 2D panel corresponding to the first projection point T 1  may be updated to be the microlens H (j) . Conversely, when the first distance is less than the second distance, the initialized respective relationship may be maintained. The mapping updater  723 - 3  updates a respective relationship between the 2D panel and a microlens of the microlens array by considering one point of the first image to be a first observation point. 
         [0084]    Referring back to  FIG. 7 , the direction indicator  730  indicates a direction of a microlens that corresponds to a pixel of the 2D panel by using points on two parallel planes. In this aspect, the 2D panel and the microlens may be parallel to each other, and thus a ray model that determines a ray proceeding towards a 3D space from the 2D panel may be generated by using the respective points on the planes. 
         [0085]      FIG. 9  is a flowchart illustrating a method for correcting a display error, according to an example embodiment. According to an example embodiment, an error associated with a microlens array may be corrected for a first image obtained by capturing an IID image with a single camera. 
         [0086]    In operation  901 , a first image is obtained by capturing an IID image with a single camera. The IID image may be captured by using the single camera to display a glassless-type 3D image. 
         [0087]    In operation  902 , an error model indicating an error between a designed location of a microlens array located on one surface of a 2D panel and an actual location of the microlens array is generated. The error model may be defined by using a relationship between the actual location and the designed location of the microlens array as represented in Equation 1, and may be expressed using an error parameter as represented in Equations 2 and 3. 
         [0088]    In operation  903 , the error associated with the microlens array is estimated by optimizing the error model. To estimate the error, the error model may be optimized by generating an initial error model based on a preset initial error parameter value and updating the initial error parameter value based on a mapping location to which a point of the first image is to be mapped on the 2D panel. A process of optimizing the error model will be described in detail below with reference to  FIG. 10 . 
         [0089]      FIG. 10  is a flowchart illustrating a process for calculating a display error, according to an example embodiment. In operation  1001 , a virtual mapping location to which a point of a first image is to be mapped on a virtual image plane that lies between a single camera and a microlens array by each microlens of the microlens array and a central location of the single camera is determined. The virtual mapping location may be indicated by I c  as shown in  FIG. 3 . In particular, an intersection point at which a connection line connecting a central location Q c  of the single camera and a location L c  of a microlens of the microlens array meets the virtual image plane parallel to the single camera may become the virtual mapping location I c . 
         [0090]    In operation  1002 , a first mapping location to which the mapping location is to be mapped on a 2D panel is determined by analyzing a respective relationship between each respective pixel point of the first image and a corresponding pixel point of the 2D panel. For example, a first mapping location P SL (c; φ) may be defined based on an error parameter φ and a central location c of a microlens, and the respective relationship with the corresponding pixel point of the 2D panel may be determined by performing decoding on the first image. 
         [0091]    In operation  1003 , a second mapping location to which the connection line connecting the central location of the single camera and the mapping location is to be mapped on the 2D panel is determined. For example, a second mapping location P P (c; φ) may indicate coordinates at which the mapping location I c  is located on the 2D panel based on a motion parameter and the location L c  of the microlens, and may be defined based on the error parameter φ and the central location c of the microlens. 
         [0092]    When the first mapping location and the second mapping location are determined, optimization may be performed on an error model based on a locational difference between the two mapping locations. A distance between the first mapping location and the second mapping location may be calculated. When a sum of calculated distances is a minimum, an initial error parameter may be considered to be optimized, and the error model may thus be optimized. 
         [0093]    According to another example embodiment, a method for correcting a display error may further include rendering the first image to be an EIA-type second image based on an error associated with the microlens array. A process of rendering will be described in detail below with reference to  FIG. 11 .  FIG. 11  is a flowchart illustrating a process of performing rendering based on a display error, according to an example embodiment. 
         [0094]    In operation  1101 , an actual location of each microlens of a microlens array is calculated based on an error associated with the microlens array. For example, an actual location of a microlens of the microlens array may be calculated by using Equation 1 about the error associated with the microlens array, and the actual location and a designed location of the microlens. 
         [0095]    In operation  1102 , a ray model indicating a 3D ray corresponding to each pixel of a 2D panel is generated. The ray model may be used to perform rendering on an EIA image, and to map each pixel of the 2D panel to a single ray in a 3D space. The ray model may be generated by initializing a respective relationship between a microlens of the microlens array and each pixel of the 2D panel, and updating the respective relationship based on a point obtained by projecting a point of a first image to the 2D panel. A process of updating the respective relationship will be described in detail below with reference to  FIG. 12 . 
         [0096]    In operation  1103 , the first image is rendered to be an EIA-type second image using the generated ray model. The rendering may be performed by using any of various rendering methods, and all the methods of rendering may be applicable here. 
         [0097]      FIG. 12  is a flowchart illustrating a process of updating a respective relationship of a microlens, according to an example embodiment. According to an example embodiment, a ray model may be generated by initializing a respective relationship between a respective pixel of a 2D panel and each corresponding microlens of a microlens array, and updating the respective relationship between the pixel of the 2D panel and the microlens by using a point obtained by projecting a point of a first image to the 2D panel. The ray model may be generated by indicating the respective pixel of the 2D panel and a direction of a microlens corresponding to the respective pixel of the 2D panel by using points on two parallel plans. The updating of the respective relationship based on an initialized respective relationship value may include obtaining a first projection point to which a first observation point included in the first image is projected on the 2D panel through a certain microlens, forming a window of a preset size on the 2D panel centered at the first projection point, and performing updating on a microlens to be mapped to each pixel of the window. Hereinafter, a process of performing updating on a microlens to be mapped to each pixel of the window will be described in detail with reference to  FIG. 12 . 
         [0098]    In operation  1201 , whether a certain microlens of a microlens array, for example, a microlens H(j), through which a first projection point, for example, T 1 , is obtained, is a microlens H (j)  that corresponds to an initialized respective relationship, for example, T 1 −H (j) , is determined. When a respective relationship is determined as the initialized respective relationship, the respective relationship T 1 − (j)  may be appropriate, and the microlens H (j)  may be mapped to the microlens in operation  1202 . Conversely, when the respective relationship does not correspond to the initialized respective relationship, projection may be performed to obtain two projection points in operation  1203 . Referring back to  FIG. 6 , when a window including seven pixels is formed based on a first projection point T 1  obtained by projecting a first observation point V c  to a 2D panel through a certain microlens H (j) , a second projection point P 1  may be obtained by projecting a pixel of the window, for example, a first pixel as illustrated in  FIG. 6 , to an observation plane, for example, a first image  603 , on which the first observation point V c  is located by using an initialized respective relationship. A third projection point P 2  may be obtained by projecting the first pixel to the observation plane through the microlens H (j)  through which the first projection point T 1  is obtained. When the second projection point P 1  and the third projection point P 2  are obtained, a distance between the first observation point V c  and each of the projection points may be calculated. A first distance may be calculated between the second projection point P 1  and the first observation point V c , and a second distance may be calculated between the third projection point P 2  and the first observation point V c . 
         [0099]    In operation  1204 , a comparison between the first distance and the second distance is performed. When the first distance is less than the second distance, for example, No from operation  1204 , the projection through the microlens H (j)  may be more appropriate, and thus a microlens that corresponds to a pixel of the 2D panel at which the first projection point T 1  is located is mapped to the microlens H (j)  in operation  1205  In such a case, the mapping may not be needed because the first projection point T 1  is already mapped to the microlens H (j) . Conversely, when the first distance is greater than or equal to the second distance, for example, Yes from operation  1204 , the projection through the microlens H (i)  may be more appropriate, a microlens corresponding to a pixel of the 2D panel at which the first projection point T 1  is located is mapped to the microlens H (i) . 
         [0100]    When the ray model is generated after the mapping based on a respective relationship between each pixel of the 2D panel and a corresponding microlens is performed, the first image may be rendered to be the EIA-type second image by using the generated ray model. 
         [0101]    While this disclosure includes specific example embodiments, it will be apparent to one of ordinary skill in the art that various changes in form and details may be made in these example embodiments without departing from the spirit and scope of the claims and their equivalents. The example embodiments described herein are to be considered in a descriptive sense only, and not for purposes of limitation. Descriptions of features or aspects in each example embodiment are to be considered as being applicable to similar features or aspects in other example embodiments. Suitable results may be achieved if the described techniques are performed in a different order, and/or if components in a described system, architecture, device, or circuit are combined in a different manner, and/or replaced or supplemented by other components or their equivalents. 
         [0102]    Therefore, the scope of the present disclosure is defined not by the detailed description, but by the claims and their equivalents, and all variations within the scope of the claims and their equivalents are to be construed as being included in the present disclosure.