Patent Publication Number: US-10771771-B2

Title: Method of determining calibration parameter for three-dimensional (3D) display device and 3D display device using the method

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application claims the priority benefit of Korean Patent Application No. 10-2014-0164755, filed on Nov. 24, 2014, in the Korean Intellectual Property Office, the entire contents of which are incorporated herein by reference in its entirety. 
     BACKGROUND 
     1. Field 
     At least one example embodiment relate to a method of determining a calibration parameter for a three-dimensional (3D) display device, and a 3D display device using the method. 
     2. Description of the Related Art 
     Among factors related to three-dimensional (3D) image recognition, the foremost factor is a disparity between images viewed by both eyes of a user. Methods of providing different images to both eyes of a user may be classified into a stereoscopic type and an autostereoscopic type. The stereoscopic type method may filter a desired image through division methods that involve using a polarized light, time division, and wavelength division for differentiating a wavelength of a primary color. The autostereoscopic type method may enable images to be viewed only in a desired (or alternatively, predetermined) space using a 3D converter, for example, a parallax barrier, a lenticular lens, or a directional backlight unit. 
     The autostereoscopic type method may alleviate an inconvenience of wearing glasses. However, in the autostereoscopic type method, when an error differing from a design value occurs in a process of producing a 3D display device or a process of installing a 3D converter, an image quality may deteriorate due to crosstalk. 
     SUMMARY 
     At least one example embodiment relates to methods of determining a calibration parameter for a three-dimensional (3D) display device. 
     In at least one example embodiment, the method may include acquiring an image of a second pattern output through a panel and an optical layer as an image of a second pattern, and determining a calibration parameter for the 3D display device based on the first pattern and the second pattern. 
     The first pattern may be displayed using subpixels aligned in the panel. The first pattern may be a pattern in which continuous lines of an identical brightness are disposed at desired intervals. The second pattern may be a pattern in which lines including a plurality of points are disposed at desired intervals. The image of the second pattern may be a single image. 
     The optical layer may include at least one of a lens array, a parallax barrier, and a directional backlight unit. 
     The calibration parameter may include at least one of a parameter associated with a size of the optical layer, and a parameter associated with a position of the optical layer. The parameter associated with the size of the optical layer may include a pitch of the optical layer. The parameter associated with the position of the optical layer may include a rotation angle between the optical layer and the panel. 
     The determining may include obtaining a parameter corresponding to a period of the first pattern based on a subpixel structure of the panel. The parameter corresponding to the period of the first pattern may include an interval between lines included in the first pattern. The subpixel structure of the panel may include an interval between subpixels of a color used for the first pattern in the panel. 
     The determining may include at least one of measuring a parameter corresponding to a gradient of the second pattern, and measuring a parameter corresponding to a period of the second pattern. The parameter corresponding to the gradient of the second pattern may include a slope of a line included in the second pattern. The parameter corresponding to the period of the second pattern may include an interval between lines included in the second pattern. 
     The determining may include performing a Fourier transform on the image of the second pattern, measuring a parameter corresponding to a gradient of the second pattern based on the Fourier-transformed image, and measuring a parameter corresponding to a period of the second pattern based on the Fourier-transformed image. 
     The measuring of the parameter corresponding to the period of the second pattern may include calculating a height difference between pixels having highest intensities in the Fourier-transformed image, and calculating an interval between lines included in the second pattern based on the calculated height difference and a height of the Fourier-transformed image. 
     The measuring of the parameter corresponding to the gradient of the second pattern may include calculating a slope of a first line connecting pixels having highest intensities in the Fourier-transformed image, and calculating a slope of a second line included in the second pattern based on the calculated slope of the first line. 
     The measuring of the parameter corresponding to the gradient of the second pattern may further include detecting a point that is horizontally closest to an origin of the Fourier-transformed image, and calculating a slope of a third line connecting the origin and the detected point. The slope of the second line included in the second pattern may be calibrated based on the calculated slope of the third line connecting the origin and the detected point. 
     The determining may include calculating the calibration parameter based on a parameter corresponding to a period of the first pattern, a parameter corresponding to a gradient of the second pattern, and a parameter corresponding to a period of the second pattern. 
     The determining may include calculating a rotation angle between the optical layer and the panel and a pitch of the optical layer based on Equations 1 and 2, 
     
       
         
           
             
               
                 
                   
                     
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     g denotes a parameter corresponding to a period of the first pattern, a denotes a parameter corresponding to a gradient of the second pattern, c denotes a parameter corresponding to a period of the second pattern, n denotes a number of elements of the optical layer corresponding to a single period of the first pattern, θ denotes the rotation angle between the optical layer and the panel, and p denotes the pitch of the optical layer. 
     The calculating of the rotation angle between the optical layer and the panel and the pitch of the optical layer may include calculating (n, θ) candidates having n being a positive integer, and θ being an angle within a desired (or alternatively, predetermined) range, selecting one of the (n, θ) candidates based on an initial parameter, and calculating p corresponding to the selected (n, θ) candidate. 
     When a subpixel structure of the panel corresponds to a red, green, and blue (RGB) stripe structure, the first pattern may correspond to a stripe pattern having one of red, green, and blue colors, and a direction in which subpixels of an identical color are continuously disposed in the panel. 
     At least one example embodiment relates to a 3D display device. 
     In at least one example embodiment, the 3D display device may include a calibrator configured to calibrate mapping information of a subpixel included in a panel based on a calibration parameter for the 3D display device, and a renderer configured to perform rendering for a 3D image based on the calibrated mapping information. The calibration parameter may be determined based on an image of a second pattern output through a combination of the panel and an optical layer when an image of a first pattern is applied to the panel. 
     According to at least one example embodiment, a device includes a determiner configured to determine a calibration parameter for a three-dimensional (3D) display device based on a first image having a first pattern and a second image having a second pattern. The second image is a version of the first image that is displayed with a panel and an optical layer of the 3D display device. The device includes a calibrator configured to calibrate subpixels of the panel based on the calibration parameter to indicate a propagation direction of light from each subpixel. 
     The first pattern is a pattern in which continuous lines of an identical brightness are at desired intervals. 
     The second pattern is a pattern in which lines comprising a plurality of points are at desired intervals. 
     The optical layer comprises at least one of a lens array, a parallax barrier, and a directional backlight. 
     The calibration parameter comprises at least one of a parameter associated with a size of the optical layer and a parameter associated with a position of the optical layer. 
     The device includes a renderer configured to render a calibrated image based on the calibrated subpixels. 
     Additional aspects of example embodiments will be set forth in part in the description which follows and, in part, will be apparent from the description, or may be learned by practice of the disclosure. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       These and/or other aspects will become apparent and more readily appreciated from the following description of example embodiments, taken in conjunction with the accompanying drawings of which: 
         FIG. 1  illustrates an apparatus for determining a calibration parameter for a three-dimensional (3D) display device according to at least one example embodiment; 
         FIG. 2  illustrates a relationship between an image of a first pattern and an image of a second pattern according to at least one example embodiment; 
         FIG. 3  illustrates a method of displaying an image of a first pattern according to at least one example embodiment; 
         FIG. 4  illustrates a principle of generating an image of a second pattern according to at least one example embodiment; 
         FIGS. 5A through 5C  illustrate a principle of determining slopes of lines included in an image of a second pattern according to at least one example embodiment; 
         FIG. 6  illustrates a principle of determining an interval between lines included in an image of a second pattern according to at least one example embodiment; 
         FIGS. 7 through 9  illustrate a geometric relationship between an image of a second pattern and a calibration parameter for a 3D display device; 
         FIGS. 10A and 10B  illustrate cases corresponding to various solutions according to at least one example embodiment; 
         FIGS. 11A and 11B  illustrate a method of deducing candidate solutions according to at least one example embodiment; 
         FIG. 12  illustrates a scheme of measuring a parameter corresponding to a gradient of a second pattern and a parameter corresponding to a period of the second pattern by performing a Fourier transform on an image of the second pattern according to at least one example embodiment; 
         FIGS. 13 and 14  illustrate display devices, each including an apparatus for determining a calibration parameter according to at least one example embodiment; 
         FIG. 15  illustrates a 3D display device configured to perform a calibration operation based on a calibration parameter according to at least one example embodiment; 
         FIG. 16  is a flowchart illustrating a method of determining a calibration parameter according to at least one example embodiment; 
         FIGS. 17A and 17B  illustrate examples of applications of an image of a first pattern; and 
         FIG. 18  illustrates a method of normalizing an image of a second pattern according to at least one example embodiment. 
     
    
    
     DETAILED DESCRIPTION OF EXAMPLE EMBODIMENTS 
     Hereinafter, some example embodiments will be described in detail with reference to the accompanying drawings. 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. Also, in the description of embodiments, detailed description of well-known related structures or functions will be omitted when it is deemed that such description will cause ambiguous interpretation of the present disclosure. 
     It should be understood, however, that there is no intent to limit this disclosure to the particular example embodiments disclosed. On the contrary, example embodiments are to cover all modifications, equivalents, and alternatives falling within the scope of the example embodiments. Like numbers refer to like elements throughout the description of the figures. 
     In addition, terms such as first, second, A, B, (a), (b), and the like may be used herein to describe components. Each of these terminologies is not used to define an essence, order or sequence of a corresponding component but used merely to distinguish the corresponding component from other component(s). It should be noted that if it is described in the specification that one component is “connected”, “coupled”, or “joined” to another component, a third component may be “connected”, “coupled”, and “joined” between the first and second components, although the first component may be directly connected, coupled or joined to the second component. 
     The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting. As used herein, the singular forms “a,” “an,” and “the,” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms “comprises,” “comprising,” “includes,” and/or “including,” when used herein, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. 
     It should also be noted that in some alternative implementations, the functions/acts noted may occur out of the order noted in the figures. For example, two figures shown in succession may in fact be executed substantially concurrently or may sometimes be executed in the reverse order, depending upon the functionality/acts involved. 
     Various example embodiments will now be described more fully with reference to the accompanying drawings in which some example embodiments are shown. In the drawings, the thicknesses of layers and regions are exaggerated for clarity. 
     Hereinafter, reference will now be made in detail to embodiments, examples of which are illustrated in the accompanying drawings, wherein like reference numerals refer to like elements throughout. The following example embodiments may be applied to various display devices. For example, the example embodiments may be applied to display devices attached to, for example, televisions, digital signage, tablet computers, and smart phones. 
       FIG. 1  illustrates an apparatus for determining a calibration parameter for a three-dimensional (3D) display device according to at least one example embodiment. Referring to  FIG. 1 , an apparatus  110  for determining a calibration parameter according to at least one example embodiment may determine a calibration parameter for a 3D display device  120 . The 3D display device  120  may be a device configured to display a 3D image, and may include, for example, a glasses-free 3D display device. 
     The glasses-free 3D display device may be a device that enables a user to view a 3D image without wearing an additional device, for example, glasses. The glasses-free 3D display device may also be referred to as an autostereoscopic display device or a multi-view display device. 
     Light output from pixels included in a two-dimensional (2D) display device may propagate in all directions, whereas light output from pixels included in the glasses-free 3D display device may propagate in limited (e.g., desired) directions through an optical layer. Thus, different images may be incident to both eyes of a user, and the user may experience 3D effects. The optical layer may be used as a 3D converter. 
     The glasses-free 3D display device may be implemented in a form in which an optical layer is attached to a front surface or a rear surface of a panel. The optical layer may control a propagation direction of light passing through the panel. The panel may include a liquid crystal display (LCD) panel, a light emitting diode (LED) panel, and an organic light emitting diode (OLED) panel, and the optical layer may include a lens array, a parallax barrier, and a directional backlight unit. For example, pixels of the panel may output light in all directions. When the optical layer is a lens array, light may be refracted by the lens array and output only in desired (or alternatively, predetermined) directions. When the optical layer is a parallax barrier, the parallax barrier may allow light of a desired (or alternatively, predetermined) direction to pass, and block light of other directions. 
     In a case of a glasses-type 3D display device, a left image and a right image may be filtered by glasses worn by a user using, for example, a time difference, a polarization of light, and a color filter. Thus, stereo images are divided based on a time or a space and may be displayed in all directions. Conversely, in a case of the glasses-free 3D display device, a direction of light may be determined at a point in time at which the light is output from the glasses-free 3D display device. Accordingly, when an error occurs between an actual direction of light and a designed direction of light, crosstalk may occur. When crosstalk occurs, the user may view blurred images. When a serious error occurs, the user may view distorted images that may cause dizziness. 
     In general, two factors may cause an error between an actual direction of light and a designed direction of light. First, an error in a size of an optical layer may cause an error between an actual direction of light and a designed direction of light. The error in the size of the optical layer refers to a difference between a size of a manufactured optical layer and a designed value (i.e., a manufacturing error). A representative example of the size may be a pitch of the optical layer. The glasses-free 3D display device may handle subpixel units, and a size thereof may be a unit of millimeters or smaller. A 3D image may change due to a size error of micrometers or smaller. Such a size error may occur in a stage of processing or manufacturing the optical layer. 
     Second, an error in a position of an optical layer may cause an error between an actual direction of light and a designed direction of light. The error in the position of the optical layer refers to a difference between an actual position in which the optical layer is attached to a panel and a designed position in which the optical layer should be attached to the panel. The position of the optical layer may include a height and an angle at which the optical layer is attached to the panel. A representative example of the position may be a rotation angle between the optical layer and the panel. When designing a glasses-free 3D display device, an arrangement of pixels included in a panel and a position of an optical layer may be considered. However, when actually attaching the optical layer to the panel, a position error may occur. A minute change in an angle caused by the position error may result in a drastic change in a 3D image. 
     At least one example embodiment may reduce (or alternatively, prevent) an occurrence of a crosstalk by calibrating an arrangement of pixels of a panel based on a current size and a current position of an optical layer although a size error and a position error exist. For example, at least one example embodiment may calibrate mapping information of a subpixel included in the panel, and render a 3D image based on the calibrated mapping information. 
     For such calibration, an accurate estimation of a size error and a position error may be required. At least one example embodiment may provide technology that displays an image  121  of a desired (or alternatively, predetermined) first pattern on a panel  122  of the 3D display device  120 , captures an image  130  of a second pattern played at a position of a user, and determines a calibration parameter for the 3D display device  120  based on the captured image  130  of the second pattern. 
     As will be described in detail below, at least one example embodiment may use a single image to determine the calibration parameter for the 3D display device  120 . Further, at least one example embodiment may not require an accurate viewpoint, an accurate positioning of optical layer  123 , and/or a position of an image sensor to be used to capture the image  130  of the second pattern. For example, to capture the image  130  of the second pattern, a general image sensor or a general camera may be used. 
     The apparatus  110  for determining a calibration parameter may include an acquirer  111  and a determiner  112 . The acquirer  111  may acquire the image  130  of the second pattern output through the panel  122  and an optical layer  123  when the image  121  of the first pattern is applied to the panel  122 . Each of the acquirer  111  and the determiner  112  may be implemented as software, hardware, or a combination thereof. 
     Referring to  FIG. 2 , the image  121  of the first pattern may include a pattern in which continuous lines of an identical brightness are disposed at desired (or alternatively, predetermined) intervals. For example, the first pattern may be a stripe pattern. The image  121  of the first pattern may pass through the optical layer  123  and be displayed to a viewer as the image  130  of the second pattern. The image  130  of the second pattern may be a ray image passing through a central point of the optical layer  123 , for example, a central axis of a lens, or a slit. The image  130  of the second pattern may include a pattern in which lines including a plurality of points are disposed at desired (or alternatively, predetermined) intervals. For example, the image  130  of the second pattern may include repetitive lines having a single principal direction. 
     A slope of each line included in the image  130  of the second pattern may differ from a slope of each line included in the image  121  of the first pattern. For example, lines included in the image  121  of the first pattern may be vertical lines, and lines included in the image  130  of the second pattern may be inclined lines. Further, an interval between the lines included in the image  130  of the second pattern may differ from an interval between the lines included in the image  121  of the first pattern. As will be described in detail below, the determiner  112  may determine the calibration parameter for the 3D display device  120  by analyzing two adjacent lines  131  and  132  from among the lines included in the image  130  of the second pattern. For example, the determiner  112  may determine a position and a pitch of the optical layer  123  based on the interval between the line  131  and the line  132 , and slopes of the line  131  and the line  132 . 
     The image  121  of the first pattern may be displayed using subpixels continuously disposed (or aligned) in the panel  122 . Referring to  FIG. 3 , a panel  300  of a 3D display device may include a plurality of pixels  310  with a plurality of subpixels. For example, a pixel  310  may include a red (R) subpixel  311  corresponding to a red color, a green (G) subpixel  312  corresponding to a green color, and a blue (B) subpixel  313  corresponding to a blue color. The subpixels of the pixel  310  may be disposed in a stripe structure. 
     The lines included in the image  121  of the first pattern may be displayed by turning on subpixels disposed at desired (or alternatively, predetermined) intervals in an identical column. The subpixels disposed in the identical column may correspond to an identical color. By adjusting an interval at which the subpixels in the identical column are to be turned on or a period for which the subpixels in the identical column are to be turned on, an interval between the lines included in the image  121  of the first pattern or a period may be adjusted. Hereinafter, for ease of description, example embodiments in which pixels included in the panel of the 3D display device may include RGB subpixels of a stripe structure. However, various modifications may be made to a subpixel structure of the panel. 
       FIG. 4  illustrates a principle of generating an image of a second pattern according to at least one example embodiment. Referring to  FIG. 4 , light output through subpixels included in the panel  122  and the optical layer  123  may propagate in limited or desired directions. 
     In an example, the optical layer  123  may include a lens array  420 . The lens array  420  may be a lenticular lens. Light output from subpixels  411  and  412  may be refracted by the lens array  420 , and propagate only in directions from the subpixels  411  and  412  toward centers of corresponding lenses, respectively. 
     In another example, the optical layer  123  may include a parallax barrier  430 . The light output from the subpixels  411  and  412  may be blocked by the parallax barrier  430 , and propagate only in directions passing through slits of the parallax barrier  430 . 
     When the panel  122  is an LCD panel, backlight units may be attached to a surface to which the lens array  420  is attached and an opposite surface. In this example, the light output from the subpixels  411  and  412  may be light emitted from the backlight units and passing through the subpixels  411  and  412 . When the panel  122  is an LED panel or an OLED panel, the subpixels  411  and  412  may independently emit light. 
     In still another example, the optical layer  123  may include a directional backlight unit  440 . The directional backlight unit  440  may be attached to a bottom surface of the panel  122 . In this example, the panel  122  may be an LED panel. A general backlight unit may emit light to propagate in all directions, whereas the directional backlight unit  440  may emit light to propagate in limited directions. The light emitted from the directional backlight unit  440  may pass through the subpixels  411  and  412  and propagate. 
     In describing a point on an optical layer through which light emitted from a subpixel passes and is output, or a point on an optical layer from which light is generated, passes through a subpixel, and is output, a position of a focal point of the lens array  420 , a position of a slit of the parallax barrier  430 , and a position of a light source of the directional backlight unit  440  may play an identical role. For example, a position of a point included in the image  130  of the second pattern may correspond to the position of the focal point of the lens array  420 , the position of the slit of the parallax barrier  430 , or the position of the light source of the directional backlight unit  440 . Thus, when the lens array  420 , the parallax barrier  430 , and the directional backlight unit  440  have identical pitches, identical images  130  of the second pattern may be captured. Hereinafter, for ease of description, a case in which the lens array  420  is used will be described. However, example embodiments may be applicable to a case in which the parallax barrier  430  or the directional backlight unit  440  is used. 
       FIGS. 5A through 5C  illustrate a principle of determining slopes of lines included in an image of a second pattern according to at least one example embodiment. Referring to  FIGS. 5A through 5C , slopes or principal directions of lines included in an image of a second pattern may be determined based on a relationship between an interval between lines included in an image of a first pattern and a horizontal pitch of an optical layer. The horizontal pitch of the optical layer may be a horizontal component of a pitch of the optical layer. 
     A first case  510  of  FIG. 5A , a second case  520  of  FIG. 5B , and a third case  530  of  FIG. 5C  are plane views of a 3D display device viewed from desired (or alternatively, predetermined) points of view. Hereinafter, for ease of description, the points of view from which the 3D display device is viewed in the first case  510 , the second case  520 , and the third case  530  will be referred to as a first point of view, a second point of view, and a third point of view, respectively. 
     Referring to the first case  510  of  FIG. 5A , lines  515  and  516  may be lines included in an image of a first pattern displayed on a panel. An optical layer may not allow all light output through the lines  515  and  516  to reach the first point of view. Only light output through a point  511  at which the line  515  meets a central axis of a lens  513 , and light output through a point  512  at which the line  516  meets a central axis of a lens  514  may reach the first point of view. When points similar to the points  511  and  512  gather together, an image of a second pattern may be generated. 
     When an interval between lines included in the image of the first pattern is identical to a horizontal pitch of the optical layer, slopes of the lines included in the image of the second pattern may be equal to “0”. The horizontal pitch of the optical layer may be a horizontal component of a pitch of the optical layer. For example, the horizontal pitch of the optical layer may be a horizontal interval between the central axis of the lens  513  and the central axis of the lens  514 . In the first case  510 , an interval between the lines  515  and  516  is identical to the horizontal interval between the central axis of the lens  513  and the central axis of the lens  514 . Thus, a slope of a line formed by the points  511  and  512  may be equal to “0”. 
     Referring to the second case  520  of  FIG. 5B , light output through a point  521  at which a line  525  meets a central axis of a lens  523 , and light output through a point  522  at which a line  526  meets a central axis of a lens  524  may reach the second point of view. When the horizontal pitch of the optical layer is greater than the interval between the lines included in the image of the first pattern, the slopes of the lines included in the image of the second pattern may be greater than “0”. In the second case  520 , a horizontal interval between the central axis of the lens  523  and the central axis of the lens  524  is greater than an interval between the lines  525  and  526 . Thus, a slope of a line formed by the points  521  and  522  may be greater than “0”. 
     Referring to the third case  530  of  FIG. 5C , light output through a point  531  at which a line  535  meets a central axis of a lens  533 , and light output through a point  532  at which a line  536  meets a central axis of a lens  534  may reach the third point of view. When the horizontal pitch of the optical layer is less than the interval between the lines included in the image of the first pattern, the slopes of the lines included in the image of the second pattern may be less than “0”. In the third case  530 , a horizontal interval between the central axis of the lens  533  and the central axis of the lens  534  is less than an interval between the lines  535  and  536 . Thus, a slope of a line formed by the points  531  and  532  may be less than “0”. 
     The foregoing cases may correspond to cases in which a lens array is inclined leftward. In a case in which the lens array is inclined rightward, the slopes of the lines included in the image of the second pattern may be reversed. 
     As described above, the slopes of the lines included in the image of the second pattern may be determined based on the relationship between the interval between the lines included in the image of the first pattern and the horizontal pitch of the optical layer. Thus, conversely, when the slopes of the lines included in the image of the second pattern are known, the relationship between the interval between the lines included in the image of the first pattern and the horizontal pitch of the optical layer may be estimated. 
       FIG. 6  illustrates a principle of determining an interval between lines included in an image of a second pattern according to at least one example embodiment. Referring to  FIG. 6 , at least one lens may be provided between adjacent lines included in an image of a second pattern. An interval between the lines included in the image of the second pattern may be determined based on a vertical pitch of an optical layer. The vertical pitch of the optical layer may be a vertical component of a pitch of the optical layer.  FIG. 6  is a plan view of a 3D display device viewed from a desired (or alternatively, predetermined) point of view. Hereinafter, for ease of description, the corresponding point of view will be referred to as a fourth point of view. 
     Lines  610  may be lines included in an image of a first pattern displayed on a panel. As described with reference to  FIGS. 5A through 5C , an optical layer  620  may allow only light output through a plurality of points constituting lines  630  to reach the fourth point of view, rather than allowing all light output through the lines  610  to reach the fourth point of view. In this example, a vertical pitch of the optical layer  620  may correspond to a vertical interval between the lines  630 . 
     As described above, the interval between the lines included in the image of the second pattern may be determined based on the vertical pitch of the optical layer. Thus, conversely, when the interval between the lines included in the image of the second pattern is known, the vertical pitch of the optical layer may be estimated. 
       FIGS. 7 through 9  illustrate a geometric relationship between an image of a second pattern and a calibration parameter for a 3D display device. Referring to  FIG. 7 , an image of a second pattern may include a plurality of points constituting lines  631  and  632 . The determiner  112  of  FIG. 1  may measure a parameter a corresponding to a gradient of the second pattern from the image of the second pattern. For example, the parameter a corresponding to the gradient of the second pattern may correspond to a slope of the line  632 . Further, the determiner  112  may measure a parameter c corresponding to a period of the second pattern from the image of the second pattern. For example, the parameter c corresponding to the period of the second pattern may correspond to a vertical interval between the lines  631  and  632 . 
     A line  611  and a line  612  may be lines included in an image of a first pattern. The determiner  112  may be aware of information on a panel of a 3D display device in advance. For example, the determiner  112  may be aware of a subpixel structure of the panel, a resolution of the panel, and a size of the panel. The subpixel structure of the panel may include an interval between subpixels of a color used for the first pattern in the panel. The determiner  112  may obtain a parameter g corresponding to the period of the first pattern based on the information on the panel. For example, the parameter g corresponding to the period of the first pattern may correspond to an interval between the lines  611  and  612 . 
     The image of the first pattern may be displayed on the panel, and the image of the second pattern may be captured from a desired (or alternatively, predetermined) point of view. Thus, an actual interval between lines displayed on the panel may differ from the interval between the lines  611  and  612  virtually shown on the image of the second pattern. The determiner  112  may obtain the interval between the lines  611  and  612  based on a ratio of the size of the panel to a size of the image of the second pattern. 
     The determiner  112  may determine a calibration parameter for the 3D display device based on the first pattern and the second pattern. For example, the determiner  112  may determine the calibration parameter for the 3D display device based on the parameter a corresponding to the gradient of the second pattern, the parameter c corresponding to the period of the second pattern, and the parameter g corresponding to the period of the first pattern. The calibration parameter for the 3D display device may include a parameter p associated with the size of the optical layer and a parameter  8  associated with a position of the optical layer. 
     The parameter p associated with the size of the optical layer may be a pitch of the optical layer. The pitch of the optical layer may be an interval between elements included in the optical layer. For example, the pitch of the optical layer may be a shortest interval between a central axis  621  of a first lens and a central axis  622  of a second lens. The parameter  8  associated with the position of the optical layer may be a rotation angle of the optical layer. The rotation angle of the optical layer may be an angle at which the optical layer rotates with respect to the panel. For example, the rotation angle of the optical layer may be an angle between a central axis  623  of a third lens and the line  612  displayed on the panel. 
     Referring to  FIG. 8 , a horizontal interval between the central axis  621  of the first lens and the central axis  622  of the second lens may be p/cos θ. p/cos θ may be a horizontal pitch of the optical layer. The horizontal interval between the central axis  621  of the first lens and the central axis  622  of the second lens may be equal to a horizontal interval between the central axis  622  of the second lens and the central axis  623  of the third lens. Thus, a horizontal interval between the central axis  621  of the first lens and the central axis  623  of the third lens may be 2·p/cos θ. 
     Referring to a right triangle  810 , a length of a bottom side may be 2·p/cos θ−g, a height may be g·tan α, and one acute angle may be θ. Based on lengths of two sides and one acute angle of the right triangle  810 , Equation 1 may be deduced. 
     
       
         
           
             
               
                 
                   
                     tan 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     θ 
                   
                   = 
                   
                     
                       
                         np 
                         
                           cos 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           θ 
                         
                       
                       - 
                       g 
                     
                     
                       g 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       tan 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       α 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                   
                   ] 
                 
               
             
           
         
       
     
     Equation 1 may be arranged as expressed by Equation 2.
 
 g  tan α sin θ+ g  cos θ− np= 0  [Equation 2]
 
     In Equation 2, g denotes a parameter corresponding to a period of a first pattern, and a denotes a parameter corresponding to a gradient of a second pattern.  0  denotes a rotation angle between an optical layer and a panel, and p denotes a pitch of the optical layer. n denotes a number of elements of the optical layer corresponding to a single period of the first pattern. For example, n may correspond to a number of lenses provided between adjacent lines included in an image of the second pattern. 
     Referring to  FIG. 9 , a vertical interval between the central axis  621  of the first lens and the central axis  622  of the second lens may be p/sine. Referring to a right triangle  910 , a length of a bottom side may be p, a height may be sine, and one acute angle may be θ. Based on lengths of two sides and one acute angle of the right triangle  910 , Equation 3 may be deduced. 
     
       
         
           
             
               
                 
                   c 
                   = 
                   
                     p 
                     
                       sin 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       θ 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     3 
                   
                   ] 
                 
               
             
           
         
       
     
     In Equation 3, c denotes a parameter corresponding to a period of the second pattern, p denotes the pitch of the optical layer, and θ denotes the rotation angle between the optical layer and the panel. The determiner  112  of  FIG. 1  may determine the pitch p of the optical layer and the rotation angle θ between the optical layer and the panel based on Equations 2 and 3. 
     For ease of description,  FIGS. 7 through 9  are described assuming a case in which n corresponds to “2”. However, the pitch p of the optical layer and the rotation angle θ between the optical layer and the panel may vary depending on n. In an example, referring to  FIG. 10A , in a situation in which a first pattern and a second pattern are given, a pitch p of an optical layer and a rotation angle θ between the optical layer and a panel satisfying Equations 2 and 3 in a case  1010  of n being “1” may be calculated. In another example, referring to  FIG. 10B , in a situation in which a first pattern and a second pattern are given, a pitch p of an optical layer and a rotation angle θ between the optical layer and a panel satisfying Equations 2 and 3 in a case  1020  of n being “3” may be calculated. 
     In Equations 2 and 3, there are a total of three unknowns n, p, and θ. Since a number of the unknowns is greater than a number of equations, a plurality of solutions satisfying Equations 2 and 3 may exist. For example, a relationship between the number n of the elements of the optical layer corresponding to the single period of the first pattern and the rotation angle θ of the optical layer may be represented as shown in a graph of  FIG. 11A . 
     The number n of the elements of the optical layer corresponding to the single period of the first pattern may be a positive integer greater than or equal to “1”, and the rotation angle θ of the optical layer may be greater than or equal to −90 degrees and less than or equal to +90 degrees. Thus, candidate solutions may be extracted from the graph of  FIG. 11A . For example, when n is “1”, “2”, “3”, or “4”, θ may be 23.2735 degrees, 11.9920 degrees, 8.0214 degrees, or 6.0218 degrees, respectively. When 8 is known, p may be calculated based on Equation 3, as shown in a table of  FIG. 11B . 
     When an initial parameter of a 3D display device is known, an optimal solution may be selected from candidate solutions based on the initial parameter. The initial parameter may be a design value for the 3D display device. The initial parameter may be a pitch of the optical layer. For example, when an optical layer of the 3D display device is designed to have a pitch of 0.5 millimeters (mm), a candidate solution of n=2 having a pitch p most approximate to the design value of 0.5 mm may be finally selected from the candidate solutions. When the optical layer of the 3D display device is designed to have a rotation angle of 12 degrees, a candidate solution of n=2 having a rotation angle θ most approximate to the design value of 12 degrees may be finally selected from the candidate solutions. At least one example embodiment may provide technology that determines a rotation angle of an optical layer and a pitch of the optical layer simultaneously. 
       FIG. 12  illustrates a scheme of measuring a parameter corresponding to a gradient of a second pattern and a parameter corresponding to a period of the second pattern by performing a Fourier transform on an image of the second pattern according to at least one example embodiment. At least one example embodiment may provide technology that measures parameters resistant against noise, irrespective of a gradient of a captured image. 
     A pattern included in an image of a second pattern may include noise, or may be irregular. Thus, an error may occur when measuring a gradient of the second pattern and/or a duration of the second pattern directly from the image of the second pattern. At least one example embodiment may provide technology that accurately measures a parameter corresponding to the gradient of the second pattern and a parameter corresponding to a period of the second pattern in a frequency domain by performing a Fourier transform on the image of the second pattern. 
     Referring to  FIG. 12 , an image  1200  may be a result of performing a Fourier transform on an image of a second pattern. Unlike the image of the second pattern, a gradient and a period of a pattern may be explicitly represented in the image  1200 . Although noise is included in the image of the second pattern, the identical gradient and the identical period may be represented in the image  1200 . 
     The determiner  112  of  FIG. 1  may measure a parameter corresponding to the gradient of the second pattern and a parameter corresponding to the period of the second pattern using the image  1200 . A line  1210  may be a line connecting points horizontally close to a center of the image  1200 . The line  1210  may represent a vertical frequency component in the image of the second pattern, and indicate that the image of the second pattern is inclined. The determiner  112  may calibrate remaining gradients based on the line  1210 . A line  1220  may be a line connecting points having highest intensities in the image  1200 . A slope of the line  1220  may be perpendicular to the gradient of the second pattern. 
     The determiner  112  may measure the parameter corresponding to the gradient of the second pattern using Equation 4. 
     
       
         
           
             
               
                 
                   α 
                   = 
                   
                     b 
                     - 
                     
                       π 
                       2 
                     
                     - 
                     a 
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     4 
                   
                   ] 
                 
               
             
           
         
       
     
     In Equation 4, a denotes the parameter corresponding to the gradient of the second pattern, b denotes an angle between an x axis of the image  1200  and the line  1220 , and a denotes an angle between the x axis of the image  1200  and the line  1210 . 
     A height  1230  may be a height difference between the points having the highest intensities in the image  1200 . In another example, the height  1230  may be a height of a point closest to an origin of the image  1200 , among the points having the highest intensities in the image  1200 . The determiner  112  may calculate a number of lines having an identical slope or an identical principal direction in the image of the second pattern by dividing the overall height of the image  1200  by the height  1230 . 
     The determiner  112  may calculate the parameter corresponding to the period of the second pattern by dividing a height of an image of a first pattern displayed on the 3D display device by the calculated number. In this example, the determiner  112  may calculate a parameter corresponding to a period of the first pattern based on an actual interval between lines of the first pattern displayed on a panel. 
     The determiner  112  may calculate the parameter corresponding to the period of the second pattern by dividing a height of the captured image of the second pattern by the calculated number. In this example, the determiner  112  may calculate the parameter corresponding to the period of the first pattern by adjusting the actual interval between the lines of the first pattern displayed on the panel based on a ratio of a size of the panel to a size of the image of the second pattern. 
     The determiner  112  may determine the calibration parameter for the 3D display device more accurately by iteratively performing the foregoing processes. For example, the determiner  112  may determine a final calibration parameter based on statistics of calibration parameters deduced as a result of the iteratively performing. The determiner  112  may also determine the final calibration parameter by excluding a calibration parameter out of a normal distribution, among the calibration parameters. The determiner  112  may determine the final calibration parameter based on the calibration parameters deduced as a result of the iteratively performing, thereby minimizing a degree of inaccuracy of the final calibration parameter caused by an error included in a result of a single iteration. 
     As described with reference to  FIGS. 11A and 11B , the determiner  112  may need to select one candidate solution. The determiner  112  may obtain a plurality of sets of candidate solutions by iteratively performing the foregoing processes. The determiner  112  may finally select a candidate solution included in common sets of candidate solutions. 
     The determiner  112  may increase an accuracy of the calibration parameter based on images of the second pattern iteratively captured with respect to the identical image of the first pattern. In another example, the determiner  112  may increase the accuracy of the calibration parameter based on images of the second pattern captured while changing the image of the first pattern. 
     A method of changing the image of the first pattern may be applied in various manners. For example, the image of the first pattern may be changed sequentially using r subpixels, g subpixels, and b subpixels, while fixing a period of a pattern. In another example, the image of the first pattern may be changed by changing a period of a pattern, for example, an interval between lines in the pattern. 
       FIGS. 13 and 14  illustrate display devices, each including an apparatus for determining a calibration parameter according to at least one example embodiment. Referring to  FIG. 13 , a display device  1300  according to at least one example embodiment may include a display  1310 , an optical layer  1320 , an acquirer  1330 , and a determiner  1340 . The display  1310  may correspond to the panel  122  of  FIG. 1 , the optical layer  1320  may correspond to the optical layer  123  of  FIG. 1 , the acquirer  1330  may correspond to the acquirer  111  of  FIG. 1 , and the determiner  1340  may correspond to the determiner  112  of  FIG. 1 . In  FIG. 13 , light may be output from the display  1310  through the optical layer  1320 . However, when the optical layer  1320  is attached to a rear surface of the display  1310 , for example, when the optical layer  1320  is a directional backlight unit, light may be output from the optical layer  1320  through the display  1310 . 
     An output image of a second pattern may be captured by a camera  1350 , and the acquirer  1330  may receive the captured image. The acquirer  1330  may receive the captured image using various methods, for example, cable connection, wireless connection, and network communication. The descriptions provided with reference to  FIGS. 1 through 12  may be applicable to each module of  FIG. 13  and thus, duplicated descriptions will be omitted for conciseness. 
     Referring to  FIG. 14 , a display device  1400  according to at least one example embodiment may include a display  1410 , an optical layer  1420 , a camera  1430 , and a determiner  1440 . The display  1410  may correspond to the panel  122  of  FIG. 1 , the optical layer  1420  may correspond to the optical layer  123  of  FIG. 1 , and the determiner  1440  may correspond to the determiner  112  of  FIG. 1 . Although not shown in  FIG. 14 , the optical layer  1420  may be attached to a rear surface of the display  1410 . 
     The camera  1430  may capture an image of a second pattern reflected in a minor  1450 . In this example, the determiner  1440  may determine a calibration parameter for the display device  1400 , in view of a left-right reversal of the captured image occurring when the image of the second pattern is reflected in the mirror  1450 . 
       FIG. 15  illustrates a 3D display device configured to perform a calibration operation based on a calibration parameter according to at least one example embodiment. Referring to  FIG. 15 , a 3D display device  1500  according to at least one example embodiment may include a calibrator  1510  and a renderer  1520 . It should be understood that the calibrator  1510  and the renderer  1520  may be included in the same or separate device (e.g., an image processing device) as the acquirer  110  and the determiner  112  from  FIG. 1 . The calibrator  1510  may calibrate mapping information of a subpixel included in a panel based on a calibration parameter for the 3D display device  1500 . The calibration parameter may be determined using the methods described with reference to  FIGS. 1 through 14  and thus, duplicated descriptions will be omitted for conciseness. 
     The mapping information may indicate a propagation direction of light generated from the subpixel or output through the subpixel. For example, the mapping information may be mapping information between subpixels to be used to render a 3D image from a desired (or alternatively, predetermined) point of view and the corresponding point of view. In another example, the mapping information may be mapping information between a subpixel of a panel and an element of an optical layer to be used to render a 3D image. 
     The mapping information may be generated in a form of a matrix. Elements of the matrix may correspond to subpixels of the panel. The elements of the matrix may include at least one index. A value of an index may indicate a position of a point of view divided based on a desired (or alternatively, predetermined) position, for example, a viewing position, an angle indicating a direction of light, or a desired (or alternatively, predetermined) point of view. 
     Initial mapping information may be determined based on an initial parameter or a design value for the 3D display device  1500 . For example, the initial mapping information may be generated from an initial parameter such as a pitch and an angle. The calibrator  1510  may calibrate the initial mapping information based on the calibration parameter. 
     In another example, the calibrator  1510  may generate new mapping information from a pitch and an angle corresponding to the calibration parameter, rather than calibrating the initial mapping information. In this example, the initial mapping information may not be generated. The new mapping information may accurately indicate a propagation direction of light generated from the subpixel or output through the subpixel. 
     The renderer  1520  may perform rendering for a 3D image based on the calibrated mapping information. For example, the renderer  1520  may determine an image to be displayed on the panel based on the calibrated mapping information, thereby reducing (or alternatively, preventing) an occurrence of crosstalk in the 3D image. 
       FIG. 16  is a flowchart illustrating a method of determining a calibration parameter according at least one example embodiment. Referring to  FIG. 16 , a method of determining a calibration parameter according to at least one example embodiment may include operation  1610  of acquiring an image of a second pattern output through a panel and an optical layer when an image of a first pattern is applied to the panel, and operation  1620  of determining a calibration parameter for a 3D display device based on the first pattern and the second pattern. Operation  1610  may correspond to an operation of the acquirer  111  of  FIG. 1 , and operation  1620  may correspond to an operation of the determiner  112  of  FIG. 1 . The descriptions provided with reference to  FIGS. 1 through 12  may be applicable to each operation of  FIG. 16  and thus, duplicated descriptions will be omitted for conciseness. 
       FIGS. 17A and 17B  illustrate examples of applications of an image of a first pattern. Referring to  FIGS. 17A and 17B , at least two patterns may be included in a single image of a first pattern. Referring to  FIG. 17A , an image  1710  may include two patterns  1711  and  1712  having different periods. The two patterns  1711  and  1712  having different periods may be spatially separated from each other in the image  1710 . Referring to  FIG. 17B , an image  1720  may include two patterns  1721  and  1722  having different colors. Periods of the two patterns  1721  and  1722  having different colors may be different from or identical to each other. 
     When a single image of a first pattern includes a plurality of patterns, the determiner  112  of  FIG. 1  may determine a calibration parameter with respect to each of the plurality of patterns. The determiner  112  may determine a final calibration parameter based on the determined plurality of calibration parameters. 
       FIG. 18  illustrates a method of normalizing an image of a second pattern according to at least one example embodiment. Referring to  FIG. 18 , an image  1810  captured from a predetermined point of view may include a distorted image of a second pattern. When the Fourier transform described with reference to  FIG. 12  is used, parameters used to determine a calibration parameter may be preserved although the distorted image of the second pattern is used. The parameters may include, for example, an interval between points in a Fourier-transformed image, and a gradient with respect to a reference axis. 
     The determiner  112  of  FIG. 1  may convert the distorted image of the second pattern into a normalized image  1820  of a rectangular shape. The normalized image  1820  may have a characteristic robust against a geometric change and/or a photometric change, when compared to the distorted image of the second pattern. For example, the determiner  112  may detect four edges or vertices of the distorted image of the second pattern from the captured image  1810 . The determiner  112  may convert the distorted image of the second pattern into the normalized image  1820  based on the detected four edges or vertices. The normalized image  1820  may have a size identical to that of an image of a first pattern displayed on a panel. The determiner  112  may determine the calibration parameter based on the normalized image  1820 . 
     At least one example embodiment may display, on a panel, a 2D pattern of which a size is known, capture an image reaching a desired (alternatively, predetermined) point of view through a 3D converter such as an optical layer, and determine a calibration parameter for a 3D display device by analyzing the captured image. At least one example embodiment may employ a calibration scheme to determine the calibration parameter. The calibration scheme may be a scheme of determining a parameter of a transform function f(x) by comparing a known value x to a value y obtained through the transform function f(x). 
     According to at least one example embodiment, a pattern displayed on the panel may be x, the 3D converter may be f(x), and the captured image may be y. At least one example embodiment may determine the parameter of the transform function f(x), for example, the calibration parameter for the 3D display device, by analyzing the captured image y. 
     At least one example embodiment may provide automatic calibration technology for a 3D display device. According to at least one example embodiment, when producing 3D display devices in large quantities, a calibration parameter for each individual 3D display device may be determined. Further, when an installation state of a 3D converter changes, the calibration parameter may be re-determined. 
     The units and/or modules described herein may be implemented using hardware components and software components. For example, the hardware components may include microphones, amplifiers, band-pass filters, audio to digital convertors, and processing devices. A processing device may be implemented using one or more hardware device configured to carry out and/or execute program code by performing arithmetical, logical, and input/output operations. The processing device(s) may include a processor (i.e., a special purpose processor), a controller and an arithmetic logic unit, a digital signal processor, a microcomputer, a field programmable array, a programmable logic unit, a microprocessor or any other device capable of responding to and executing instructions in a defined manner. The processing device may run an operating system (OS) and one or more software applications that run on the OS. The processing device also may access, store, manipulate, process, and create data in response to execution of the software. For purpose of simplicity, the description of a processing device is used as singular; however, one skilled in the art will appreciated that a processing device may include multiple processing elements and multiple types of processing elements. For example, a processing device may include multiple processors or a processor and a controller. In addition, different processing configurations are possible, such a parallel processors. 
     The software may include a computer program, a piece of code, an instruction, or some combination thereof, to independently or collectively instruct and/or configure the processing device to operate as desired, thereby transforming the processing device into a special purpose processor. Software and data may be embodied permanently or temporarily in any type of machine, component, physical or virtual equipment, computer storage medium or device, or in a propagated signal wave capable of providing instructions or data to or being interpreted by the processing device. The software also may be distributed over network coupled computer systems so that the software is stored and executed in a distributed fashion. The software and data may be stored by one or more non-transitory computer readable recording mediums. 
     The methods according to the above-described example embodiments may be recorded in non-transitory computer-readable media including program instructions to implement various operations of the above-described example embodiments. The media may also include, alone or in combination with the program instructions, data files, data structures, and the like. The program instructions recorded on the media may be those specially designed and constructed for the purposes of example embodiments, or they may be of the kind well-known and available to those having skill in the computer software arts. Examples of non-transitory computer-readable media include magnetic media such as hard disks, floppy disks, and magnetic tape; optical media such as CD-ROM discs, DVDs, and/or Blue-ray discs; magneto-optical media such as optical discs; and hardware devices that are specially configured to store and perform program instructions, such as read-only memory (ROM), random access memory (RAM), flash memory (e.g., USB flash drives, memory cards, memory sticks, etc.), and the like. Examples of program instructions include both machine code, such as produced by a compiler, and files containing higher level code that may be executed by the computer using an interpreter. The above-described devices may be configured to act as one or more software modules in order to perform the operations of the above-described example embodiments, or vice versa. 
     A number of example embodiments have been described above. Nevertheless, it should be understood that various modifications may be made to these example embodiments. For example, 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. Accordingly, other implementations are within the scope of the following claims.