Patent Publication Number: US-2017361188-A1

Title: Baseball game system

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application claims priority under 35 U.S.C. §119 to Korean Patent Application No. 10-2016-0074300, filed on Jun. 15, 2016, in the Korean Intellectual Property Office (KIPO), the disclosure of which is incorporated by reference herein in its entirety. 
     1. TECHNICAL FIELD 
     Embodiments of the present invention relate to a baseball game system, and more particularly, to a baseball game system capable of accurately determining a location of a ball using a single camera. 
     2. DISCUSSION OF RELATED ART 
     A conventional baseball system determines an accurate location of a ball in a determination area by photographing the ball at various angles using a plurality of cameras. Since the conventional baseball system requires the plurality of cameras, it costs a lot to implement the system. 
     It is to be understood that this background of the technology section is intend portioned to provide useful background for understanding the technology and as such disclosed herein, the technology background section may include ideas, concepts or recognitions that were not part of what was known or appreciated by those skilled in the pertinent art prior to a corresponding effective filing date of subject matter disclosed herein. 
     SUMMARY 
     Exemplary embodiments of the present invention may be directed to a baseball game system capable of accurately determining a location of a ball using a single camera. 
     According to an exemplary embodiment, a baseball game system includes: a pitching unit pitching a ball toward a determination area including a strike zone; a photographing unit positioned in a space between the determination area and the pitching unit; and a location detector detecting a location of a ball based on a plurality of images from the photographing unit. The location detector includes a non-stroke processor detecting a location of a non-struck ball and a stroke processor detecting a location of a struck ball. The non-stroke processor sets first, second, third and fourth straight lines defining the strike zone; calculates, when the ball in the image passes between the first straight line and the second straight line, an average size of the balls between the first straight line and the second straight line; and detects a vertical location of the ball in the determination area based on the average size. 
     The strike zone defined by the first, second, third and fourth straight lines may have a trapezoidal shape. 
     The non-stroke processor may detect the vertical location of the ball in the determination area by comparing the average size with a predetermined reference value. 
     The reference value may include a lower limit value defining a size of the ball located at a lower side of the strike zone; and an upper limit value defining a size of the ball located at an upper side of the strike zone. 
     The non-stroke processor may calculate coordinates of a first point representing a vertical location of the ball on the third straight line based on the comparison between the average size and the reference value; calculate coordinates of a second point representing a vertical location of the ball on the fourth straight line based on the comparison between the average size and the reference value; and set a fifth straight line passing through the first point and the second point. 
     The non-stroke processor may set a sixth straight line based on a trajectory of the ball and calculate a horizontal location of the ball in the determination area based on coordinates of a point at which the sixth straight line meets the fifth straight line. 
     The non-stroke processor may set a size of the ball closest to the first straight line as the average size when the ball in the image does not pass between the first straight line and the second straight line. 
     The non-stroke processor may estimate the average size of the balls between the first straight line and the second straight line based on at least one of a degree of size change of the ball approaching the first straight line and a distance between the first straight line and the ball closest to the first straight line. 
     The non-stroke processor may adjust the upper limit value, the lower limit value and a height of the strike zone based on a height of a batter. 
     The baseball game system may further include a height input unit for inputting the height of the batter. 
     The non-stroke processor may adjust the upper limit value, the lower limit value and the height of the strike zone based on the height input to the height input unit. 
     The baseball game system may further include a human body sensor positioned on batter&#39;s boxes defining the determination area, the human body sensor determining presence of a batter and detecting a height of the batter. 
     The stroke processor may include a stroke coordinate converter calculating three-dimensional coordinates of the ball based on: a ball size determined, from one of the plurality of images, according to coordinates of a reference plane of a maximum projection angle area defined by a maximum projection angle of the photographing unit; a size of the ball displayed in the image; XY coordinates of the ball displayed in the image; and the maximum projection angle of the photographing unit. 
     The coordinate converter may include a ratio calculator calculating a coordinate conversion ratio by dividing the size of the ball displayed in the image by the ball size determined according to the coordinates of the reference plane of the maximum projection angle area. 
     The coordinate converter may further include a coordinate calculator calculating a Z coordinate of the ball by dividing a value obtained by multiplying the coordinate conversion ratio and a length of one side of the reference plane of the maximum projection angle area by a tangent value corresponding to the maximum projection angle of the photographing unit. 
     The coordinate calculator may calculate the XY coordinates of the ball by multiplying the coordinate conversion ratio and the XY coordinates of the ball displayed in the image. 
     The stroke processor may further include a trajectory calculator calculating a final location of the ball by analyzing the plurality of images. 
     The trajectory calculator may calculate a distance by which the ball moves for a predetermined time based on the three-dimensional coordinates of the ball and a time difference between the plurality of images and calculates a velocity of the ball based on the time difference and the moving distance. 
     The trajectory calculator may determine a result value, such as a foul, an out, a hit, a two-base hit, a three-base hit and a home run, of a struck ball based on the three-dimensional coordinates of the ball and the velocity of the ball. 
     The baseball game system may further include a swing determination unit determining whether or not a batter on one of batter&#39;s boxes on opposite sides of the strike zone has swung a baseball bat based on the image from the photographing unit. The swing determination unit may detect a batter&#39;s box on which the batter is positioned based on a degree of change in the image and determines whether or not a swing of the baseball bat has been made based on the detected batter&#39;s box and a trajectory of an end portion of the baseball bat. 
     The swing determination unit may set a first vector connecting two temporally adjacent end portions and sets a second vector perpendicular to the first vector, determine whether the number of second vectors toward the detected batter&#39;s box among the second vectors is within a first reference range, and determine whether an average length of the second vectors is within a second reference range, so as to determine whether or not a swing of the baseball bat has been made. 
     The swing determination unit may determine that a swing of the baseball bat has been made when the number of second vectors toward the detected batter&#39;s box among the second vectors is within the first reference range and the average length of the second vectors is within the second reference range. 
     The swing determination unit may further determine whether a sum of lengths of the first vectors is within a third reference range. 
     The swing determination unit may determine that a swing of the baseball bat has been made when the number of second vectors toward the detected batter&#39;s box among the second vectors is within the first reference range, the average length of the second vectors is within the second reference range, and the sum of the lengths of the first vectors is within the third reference range. 
     The baseball bat may further include a marking pattern. 
     The marking pattern may be positioned at an end portion of the baseball bat. 
     The marking pattern may surround the end portion. 
     The marking pattern may have a lighter color than a color of the baseball bat. 
     The baseball game system may further include a determination unit determining a ball and a strike based on the determination result from the swing determination unit and the detection result from the non-stroke processor. 
     The foregoing is illustrative only and is not intend portioned to be in any way limiting. In addition to the illustrative aspects, exemplary embodiments and features described above, further aspects, exemplary embodiments and features will become apparent by reference to the drawings and the following detailed description. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       A more complete appreciation of the present invention will become more apparent by describing in detail exemplary embodiments thereof with reference to the accompanying drawings, wherein: 
         FIG. 1  is a schematic perspective view illustrating a baseball game system according to an exemplary embodiment; 
         FIG. 2  is a side view of  FIG. 1 ; 
         FIG. 3  is a view illustrating an image photographed by a photographing unit; 
         FIGS. 4A, 4B and 4C  are explanatory views illustrating an operation of a non-stroke processor; 
         FIG. 5  is a flowchart illustrating an operation sequence of the non-stroke processor in  FIGS. 4A, 4B and 4C ; 
         FIG. 6  is a view illustrating a location of a ball in a standardized strike zone; 
         FIGS. 7A, 7B and 7C  are another explanatory views illustrating the operation of the non-stroke processor; 
         FIGS. 8A, 8B and 8C  are still another explanatory views illustrating the operation of the non-stroke processor; 
         FIG. 9  is a view illustrating a height input unit; 
         FIG. 10  is an explanatory view illustrating an operation of a human body sensor; 
         FIG. 11  is another side view of  FIG. 1 ; 
         FIG. 12  is a perspective view illustrating that a ball is photographed according to a maximum projection angle of the photographing unit; 
         FIGS. 13, 14 and 15  are views illustrating an operation of a coordinate converter; 
         FIGS. 16, 17, 18 and 19  are views illustrating an operation of a trajectory calculator; 
         FIG. 20  is a flowchart illustrating an operation sequence of a stroke processor; 
         FIG. 21  is still another side view of  FIG. 1 ; 
         FIG. 22  is a view illustrating an image photographed by a photographing unit; 
         FIGS. 23A and 23B  are explanatory views illustrating an operation of a swing determination unit based on the image of  FIG. 22 ; 
         FIG. 24  is a flowchart illustrating an operation sequence of the swing determination unit in  FIGS. 23A and 23B ; 
         FIG. 25  is a view illustrating a trajectory of a baseball bat in the case of a check swing; 
         FIG. 26  is a perspective view illustrating a baseball bat used in the baseball game system of  FIG. 1 ; 
         FIG. 27  is a cross-sectional view taken along line I-P of  FIG. 1 ; 
         FIG. 28  is a view illustrating an algorithm applied to the non-stroke processor; 
         FIG. 29  is a view illustrating an algorithm applied to the stroke processor; and 
         FIG. 30  is a view illustrating an algorithm applied to the swing determination unit. 
     
    
    
     DETAILED DESCRIPTION 
     Exemplary embodiments will now be described more fully hereinafter with reference to the accompanying drawings. Although the invention may be modified in various manners and have several exemplary embodiments, exemplary embodiments are illustrated in the accompanying drawings and will be mainly described in the specification. However, the scope of the invention is not limited to the exemplary embodiments and should be construed as including all the changes, equivalents and substitutions included in the spirit and scope of the invention. 
     In the drawings, thicknesses of a plurality of layers and areas are illustrated in an enlarged manner for clarity and ease of description thereof. When a layer, area, or batter&#39;s box is referred to as being “on” another layer, area, or batter&#39;s box, it may be directly on the other layer, area, or batter&#39;s box, or intervening layers, areas, or batter&#39;s boxes may be present therebetween. Conversely, when a layer, area, or batter&#39;s box is referred to as being “directly on” another layer, area, or batter&#39;s box, intervening layers, areas, or batter&#39;s boxes may be absent therebetween. Further when a layer, area, or batter&#39;s box is referred to as being “below” another layer, area, or batter&#39;s box, it may be directly below the other layer, area, or batter&#39;s box, or intervening layers, areas, or batter&#39;s boxes may be present therebetween. Conversely, when a layer, area, or batter&#39;s box is referred to as being “directly below” another layer, area, or batter&#39;s box, intervening layers, areas, or batter&#39;s boxes may be absent therebetween. 
     The spatially relative terms “below”, “beneath”, “less”, “above”, “upper” and the like, may be used herein for ease of description to describe the relations between one element or component and another element or component as illustrated in the drawings. It will be understood that the spatially relative terms are intend portioned to encompass different orientations of the device in use or operation, in addition to the orientation depicted in the drawings. For example, in the case where a device illustrated in the drawing is turned over, the device locationed “below” or “beneath” another device may be placed “above” another device. Accordingly, the illustrative term “below” may include both the lower and upper locations. The device may also be oriented in the other direction and thus the spatially relative terms may be interpreted differently depend portioning on the orientations. 
     Throughout the specification, when an element is referred to as being “connected” to another element, the element is “directly connected” to the other element, or “electrically connected” to the other element with one or more intervening elements interposed therebetween. It will be further understood that the terms “comprises,” “comprising,” “includes” and/or “including,” when used in this specification, 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 will be understood that, although the terms “first,” “second,” “third,” and the like may be used herein to describe various elements, these elements should not be limited by these terms. These terms are only used to distinguish one element from another element. Thus, “a first element” discussed below could be termed “a second element” or “a third element,” and “a second element” and “a third element” may be termed likewise without departing from the teachings herein. 
     “About” or “approximately” as used herein is inclusive of the stated value and means within an acceptable range of deviation for the particular value as determined by one of ordinary skill in the art, considering the measurement in question and the error associated with measurement of the particular quantity (i.e., the limitations of the measurement system). For example, “about” may mean within one or more standard deviations, or within +30%, 20%, 10%, 5% of the stated value. 
     Unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by those skilled in the art to which this invention pertains. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the relevant art and will not be interpreted in an ideal or excessively formal sense unless clearly defined in the present specification. 
     Some of the parts which are not associated with the description may not be provided in order to specifically describe exemplary embodiments of the present invention and like reference numerals refer to like elements throughout the specification. 
     Hereinafter, a baseball game system according to an exemplary embodiment will be described in detail with reference to  FIGS. 1 to 30 . 
       FIG. 1  is a schematic perspective view illustrating a baseball game system according to an exemplary embodiment, and  FIG. 2  is a side view of  FIG. 1 . 
     As illustrated in  FIGS. 1 and 2 , the baseball game system  100  according to an exemplary embodiment includes a pitching unit  700 , a photographing unit  430 , a projector  555 , a location detector  666 , a first batter&#39;s box  241 , a second batter&#39;s box  242 , a groove plate  230  and a swing determination unit  644 . 
     The pitching unit  700  pitches a ball  888  toward a determination area  340  between the first batter&#39;s box  241  and the second batter&#39;s box  242 . 
     The determination area  340  includes a strike zone  333 . That is, a part of the determination area  340  is the strike zone  333 . For example, the determination area  340  may be positioned between the first batter&#39;s box  241  and the second batter&#39;s box  242 . 
     A width of the determination area  340  may be defined by a distance between the first batter&#39;s box  241  and the second batter&#39;s box  242 , and a length of the determination area  340  may be defined by a distance between the groove plate  230  and an imaginary side above the groove plate  230 . Herein, the imaginary side is positioned higher than an upper side of the strike zone  333 . 
     The pitching unit  700  includes a screen  780  and a pitching machine  760 . 
     The screen  780  is positioned between the determination area  340  and the pitching machine  760 . The screen  780  displays an image projected from the projector  555 . The image is displayed on a display surface of the screen  780 . As illustrated in  FIG. 2 , the screen  780  has at least one hole  768 . 
     The pitching machine  760  is positioned behind the screen  780 . That is, the pitching machine  760  is positioned opposite the display surface of the screen  780 . The pitching machine  760  throws the ball  888 . The ball  888  pitched from the pitching machine  760  passes through the hole  768  of the screen  780  and advances toward the determination area  340 . 
     The photographing unit  430  detects a moment when the ball  888  from the pitching unit  700  enters a sensing area  805  and starts photographing. For example, the photographing unit  460  starts tracking all moving objects, including the ball  888 , from the moment when the ball  888  enters the sensing area  805 . To this end, the photographing unit  430  may continuously photograph at a rate of several tens to several hundreds of frames per second from the moment when the ball  888  enters the sensing area  805 . The photographing unit  430  may include a high-speed camera. 
     The photographing unit  430  is positioned above the determination area  340 . For example, as illustrated in  FIG. 2 , the photographing unit  430  may be positioned in a diagonal direction of the determination area  340 , not directly above the determination area  340 . 
     The location detector  666  detects a location of the ball  888  based on the image photographed by the photographing unit  430 . The image provided from the photographing unit  430  includes a plurality of frame images. The location detector  666  may analyze the frame images to calculate coordinates (XY coordinates) of the ball  888  in the determination area  340 . To this end, for example, the location detector  666  may binarize each frame image from the photographing unit  430  based on a corresponding photographing illuminance thereof to generate a black-white image, extract a basic contour (e.g., a contour of a ball) of a subject (e.g., a ball) in the image by scanning the black-white image in the up-and-down direction and the left-and-right direction, determine a center position of the subject from the contour, and determine a location of the subject (e.g., the ball) based on the center position and a trajectory of the subject (e.g., a trajectory of the ball). 
     The location detector  666  includes a non-stroke processor  666   a  and a stroke processor  666   b.    
     The non-stroke processor  666   a  detects a location of the ball  888  that is not struck based on the photographed image from the photographing unit  430 . The stroke processor detects a location of the ball  888  that is struck based on the photographed image from the photographing unit  430 . 
     The coordinate information of the ball detected from the non-stroke processor  666   a  is transmitted to a determination unit (not illustrated). The determination unit determines whether or not the coordinates of the detected ball are located in the strike zone  333  in the determination area. As a result of the determination, in the case where it is determined that the ball  888  is located inside the strike zone  333  or at the boundary thereof, the determination unit declares a strike. On the other hand, in the case where it is determined that the ball is located in the determination area  340  outside the strike zone  300 , the determination unit declares a ball. In an exemplary embodiment, the determination unit determines final ball and strike based on a determination result from a swing determination unit  644  to be described below and the detection result from the non-stroke processor  666   a.    
       FIG. 3  is a view illustrating an image photographed by a photographing unit. 
       FIG. 3  is a view illustrating an image photographed by the photographing unit  430 . A strike zone  300  illustrated in  FIG. 3  is an image of the strike zone  333  in  FIG. 1  described above, a first batter&#39;s box  221  illustrated in  FIG. 3  is an image of the first batter&#39;s box  241  in  FIG. 1  described above, and a second batter&#39;s box  222  illustrated in  FIG. 3  is an image of the second batter&#39;s box  242  in  FIG. 1  described above. 
     The non-stroke processor  666   a  sets the strike zone  300  based on the image photographed by the photographing unit  430 . For example, the strike zone  300  may be defined as an area surrounded by four imaginary straight lines L 1 , L 2 , L 3  and L 4 . 
     A first straight line L 1  and a second straight line L 2  face each other and a third straight line L 3  and a fourth straight line L 4  face each other. The first straight line L 1  and the second straight line L 2  may be arranged parallel to each other. 
     The first straight line L 1  defines a lower side S 1  of the strike zone  300 , the second straight line L 2  defines an upper side S 2  of the strike zone  300 , the third straight line L 3  defines a left side S 3  of the strike zone  300 , and the fourth straight line L 4  defines a right side S 4  of the strike zone  300 . 
     The photographing unit  430  photographs the strike zone  300  from a diagonal direction thereof rather than immediately above the strike zone  300 . The strike zone  300  is shaped like a trapezoid to reflect the perspective phenomenon depending on the shooting angle. For example, the strike zone  300  may have a trapezoidal shape as illustrated in  FIG. 3 . Since the upper side S 2  of the strike zone  300  is positioned relatively closer to the photographing unit  430  than the lower side S 1  of the strike zone  300  is thereto, the upper side S 2  has a longer length than the lower side S 1 . 
     The ball in the image has a larger size as it approaches the photographing unit  430  due to the perspective phenomenon. That is, a size of a ball  800  (see  FIG. 4A ) in the image tells how high the ball  800  is from the ground (or the groove plate  230 ). In other words, a vertical location of the ball  800  may be determined from the size of the ball  800  in the image. 
     The non-stroke processor  666   a  may determine the size of the ball  800  using a predetermined reference value. The reference value may include a lower limit value and an upper limit value. 
     The first straight line L 1  defining the lower side S 1  of the strike zone  300  represents a location of the ball  800  at a lowest position in the strike zone  300  and the second straight line L 2  defining the upper side S 2  of the strike zone  300  represents a location of the ball  800  at a highest position in the strike zone  300   
     A size (hereinafter, a lower limit value) of the ball  800  when the ball  800  is positioned on the first straight line L 1  and a size (hereinafter, an upper limit value) of the ball  800  when the ball  800  is positioned on the second straight line L 2  may be set to predetermined values. The lower limit value is less than the upper limit value. The lower limit value and the upper limit value may be input from the outside. 
     Hereinafter, an operation of the non-stroke processor  666   a  will be described in detail. 
       FIGS. 4A, 4B and 4C  are explanatory views illustrating the operation of the non-stroke processor  666   a , and  FIG. 5  is a flowchart illustrating an operation sequence of the non-stroke processor  666   a  in  FIGS. 4A, 4B and 4C . In an exemplary embodiment, the ball  800  in  FIG. 4A  is an image of the ball  888  in  FIG. 1  described above. In  FIGS. 4A, 4B and 4C , for ease of explanation, the first batter&#39;s box  221  and the second batter&#39;s box  222  are omitted. 
     First, suppose that the balls  800  in a plurality of continuously photographed images pass through the determination area  340  with a trajectory as illustrated in  FIG. 4A . 
     The non-stroke processor  666   a  selects balls  800  located between the first straight line L 1  and the second straight line L 2  in the plurality of continuously photographed images and calculates an average size of the balls  800  ( 501 ). As an example, as illustrated in  FIG. 4A , there are four balls  800  (hatched balls) positioned between the first straight line L 1  and the second straight line L 2  and the four balls  800  each have different sizes. That is, the ball  800  has a less size as it approaches the second straight line L 2 . The non-stroke processor  666   a  individually obtains respective diameters of the four balls  800  and then calculates an average size of the diameters. In an exemplary embodiment, the ball between the first straight line L 1  and the second straight line L 2  may include a ball crossing the first straight line L 1  or the second straight line L 2 . 
     Subsequently, as illustrated in  FIG. 4B , the non-stroke processor  666   a  detects a vertical location of the ball  800  in the determination area  340  based on the average size ( 502 ). In other words, the non-stroke processor  666   a  detects a Y coordinate of the ball in the determination area  340  having a two-dimensional planar shape. 
     To this end, the non-stroke processor  666   a  may detect the vertical location of the ball  800  by, for example, comparing the average size with a predetermined reference value. The reference value includes the lower limit value and the upper limit value described above. 
     A reference number  16  in  FIG. 4  means a size of a ball corresponding to the lower limit value, a reference number  17  in  FIG. 4  means a size of a ball corresponding to the upper limit value, and a reference number  18  in  FIG. 4  means a size of a ball corresponding to the average size of the balls described above, which may or may not be illustrated in the image. 
     As such, the non-stroke processor  666   a  may compare the average size, the upper limit value and the lower limit value to calculate coordinates of a point indicating the vertical location of the ball  800  on the third straight line L 3  based on the comparison result, which will be described in detail below. 
     For example, the non-stroke processor  666   a  divides the third straight line L 3  into a plurality of sections based on the location of the lower limit value and the location of the upper limit value. In such an exemplary embodiment, the third straight line L 3  may be divided into the plurality of sections so that one of points at a boundary between the sections corresponds to the location of the aforementioned lower limit value and another of the points at the boundary corresponds to the location of the upper limit value. 
     Each point is assigned with a different location value. Each location value is determined according to a ratio between the lower limit value and the upper limit value. The location value has a tendency to increase along a Y axis. 
     The non-stroke processor  666   a  finds a location value having a size coinciding with or closest to the average size and selects a point P 1  (hereinafter, “a first point”) given the location value. A Y coordinate of the selected first point P 1  means the vertical location of the ball  800  on the third straight line L 3 . 
     In such a manner, the non-stroke processor  666   a  may calculate coordinates of a point representing a vertical location of the ball on the fourth straight line L 4 , which will be described in detail below. 
     For example, the non-stroke processor  666   a  divides the fourth straight line L 4  into a plurality of sections based on the location of the lower limit value and the location of the upper limit value. In such an exemplary embodiment, the fourth straight line L 4  may be divided into the plurality of sections so that one of points at a boundary between the sections corresponds to the location of the aforementioned lower limit value and another of the points at the boundary corresponds to the location of the upper limit value. 
     Each point is assigned with a different location value. Each location value is determined according to a ratio between the lower limit value and the upper limit value. The location value has a tendency to increase along a Y axis. 
     The non-stroke processor  666   a  finds a location value having a size coinciding with or closest to the average size and selects a point P 2  (hereinafter, “a second point”) given the location value. A Y coordinate of the selected second point P 2  means the vertical location of the ball  800  on the fourth straight line L 4 . 
     The Y coordinate value of the first point P 1  and the Y coordinate value of the second point P 2  indicating the height of the ball  800  may be substantially the same. 
     In the case as in an example illustrated in  FIG. 4B  in which the average size is greater than the lower limit value and less than the upper limit value, the first point P 1  is located on the left side S 3  of the strike zone  300  and the second point P 2  is located on the right side S 4  of the strike zone  300 . 
     Next, the non-stroke processor  666   a  sets a fifth straight line L 5  passing through the first point P 1  and the second point P 2  ( 503 ). 
     Next, the non-stroke processor  666   a  sets a sixth straight line L 6  based on a trajectory of the ball  800  as illustrated in  FIG. 4C  ( 504 ). 
     Subsequently, the non-stroke processor  666   a  calculates a horizontal location of the ball  800  in the determination area  340  based on coordinates of a point P 3  (hereinafter, “a third point”) at which the sixth straight line L 6  meets the fifth straight line L 5 . The coordinates of the third point P 3  may be calculated based on an equation of the sixth straight line L 6  and an equation of the fifth straight line L 5 . The XY coordinates of the third point P 3  is a location of the ball  800  in the determination area  340  ( 506 ). 
     When the third point P 3  is located in the strike zone  300 , as illustrated in  FIG. 4C , the determination unit determines this as a strike regardless of whether a swing of a baseball bat has been made ( 507 ). 
     In an exemplary embodiment, based on the determination result from the determination unit, the projector  555  may display the location of the ball in the standardized strike zone on the screen, which will be described in detail with reference to  FIG. 6 . 
       FIG. 6  is a view illustrating the location of the ball in the standardized strike zone. 
     The projector  555  may project an image as illustrated in  FIG. 6  on the screen  780 . The image of  FIG. 6  includes images of a strike zone  444 , a batter  618  and a ball  803 . The location of the ball  803  in  FIG. 6  corresponds to the XY coordinates of the aforementioned third point P 3 . 
     The strike zone  444  illustrated in  FIG. 6  has a quadrangular shape. A lower side S 11 , an upper side S 22 , a left side S 33  and a right side S 44  of the strike zone in  FIG. 6  correspond to the lower side S 1 , the upper side S 2 , the left side S 3  and the right side S 4  of the strike zone  300  illustrated in  FIG. 3 , respectively. 
     In an exemplary embodiment, the strike zone  444  may include a horizontal grid line  61  and a vertical grid line  62  intersecting each other. The horizontal grid line  61  and the vertical grid line  62  divide the strike zone  444  into a plurality of areas. An approximate location of the ball in the strike zone  444  may be easily determined by the horizontal grid line  61  and the vertical grid line  62 . 
       FIGS. 7A, 7B and 7C  are another explanatory views illustrating the operation of the non-stroke processor  666   a . In an exemplary embodiment, the ball  800  in  FIG. 7A  is an image of the ball  888  illustrated in  FIG. 1  described above. In  FIGS. 7A, 7B, and 7C , for ease of explanation, the first batter&#39;s box  221  and the second batter&#39;s box  222  are omitted. 
     First, suppose that the balls  800  in a plurality of continuously photographed images pass through the determination area  340  with a trajectory as illustrated in  FIG. 7A . 
     The non-stroke processor  666   a  selects balls  800  located between the first straight line L 1  and the second straight line L 2  in the plurality of continuously photographed images and calculates an average size of the balls  800 . As an example, as illustrated in  FIG. 7A , there are four balls  800  (hatched balls) positioned between the first straight line L 1  and the second straight line L 2 , and the four balls  800  each have different sizes. That is, the ball  800  has a larger size as it approaches the second straight line L 2 . The non-stroke processor  666   a  individually obtains respective diameters of the four balls  800  and then calculates an average size of the diameters. In an exemplary embodiment, the ball between the first straight line L 1  and the second straight line L 2  may include a ball crossing the first straight line L 1  or the second straight line L 2 . 
     Subsequently, as illustrated in  FIG. 7B , the non-stroke processor  666   a  detects a vertical location of the ball  800  in the determination area  340  based on the average size. In other words, the non-stroke processor  666   a  detects a Y coordinate of the ball in the determination area  340  having a two-dimensional planar shape. 
     To this end, the non-stroke processor  666   a  may detect the vertical location of the ball  800  by, for example, comparing the average size with a predetermined reference value. The reference value includes the lower limit value and the upper limit value described above. 
     A reference number  16  in  FIG. 7B  means a size of a ball corresponding to the lower limit value, a reference number  17  in  FIG. 7B  means a size of a ball corresponding to the upper limit value, and a reference number  19  in  FIG. 7B  means a size of a ball corresponding to the average size of the balls described above, which may or may not be illustrated in the image. 
     As such, the non-stroke processor  666   a  may compare the average size, the upper limit value and the lower limit value to calculate coordinates of a point indicating a vertical location of the ball  800  on the third straight line L 3  based on the comparison result, which will be described in detail below. 
     For example, the non-stroke processor  666   a  divides the third straight line L 3  into a plurality of sections based on the location of the lower limit value and the location of the upper limit value. In such an exemplary embodiment, the third straight line L 3  may be divided into the plurality of sections so that one of points at a boundary between the sections corresponds to the location of the aforementioned lower limit value and another of the points at the boundary corresponds to the location of the upper limit value. 
     Each point is assigned with a different location value. Each location value is determined according to a ratio between the lower limit value and the upper limit value. The location value has a tendency to increase along a Y axis. 
     The non-stroke processor  666   a  finds a location value having a size coinciding with or closest to the average size and selects a point P 1  (hereinafter, “a first point”) given the location value. A Y coordinate of the selected first point P 1  means the vertical location of the ball  800  on the third straight line L 3 . 
     In such a manner, coordinates of a point indicating a vertical location of the ball on the fourth straight line L 4  may be calculated, which will be described in detail below. 
     For example, the non-stroke processor  666   a  divides the fourth straight line L 4  into a plurality of sections based on the location of the lower limit value and the location of the upper limit value. In such an exemplary embodiment, the fourth straight line L 4  may be divided into the plurality of sections so that one of points at a boundary between the sections corresponds to the location of the aforementioned lower limit value and another of the points at the boundary corresponds to the location of the upper limit value. 
     Each point is assigned with a different location value. Each location value is determined according to a ratio between the lower limit value and the upper limit value. The location value has a tendency to increase along a Y axis. 
     The non-stroke processor  666   a  finds a location value having a size coinciding with or closest to the average size and selects a point P 2  (hereinafter, “a second point”) given the location value. A Y coordinate of the selected second point P 2  means the vertical location of the ball  800  on the fourth straight line L 4 . 
     The Y coordinate value of the first point P 1  and the Y coordinate value of the second point P 2  indicating the height of the ball  800  may be substantially the same. 
     In the case as in an example illustrated in  FIG. 7B  in which the average size is greater than the upper limit value, the first point P 1  is located on the third straight line L 3  higher than the upper side S 2  of the strike zone  300  and the second point P 2  is located on the fourth straight line IA higher than the upper side S 2  of the strike zone  300 . 
     Next, the non-stroke processor  666   a  sets a fifth straight line L 5  passing through the first point P 1  and the second point P 2 . 
     Next, the non-stroke processor  666   a  sets a sixth straight line L 6  based on a trajectory of the ball  800  as illustrated in  FIG. 7C . 
     Subsequently, the non-stroke processor  666   a  calculates a horizontal location of the ball  800  in the determination area  340  based on coordinates of a point P 3  (hereinafter, “a third point”) at which the sixth straight line L 6  meets the fifth straight line L 5  ( 505 ). The coordinates of the third point P 3  may be calculated based on an equation of the sixth straight line L 6  and an equation of the fifth straight line L 5 . The XY coordinates of the third point P 3  is a location of the ball  800  in the determination area  340 . 
     As illustrated in  FIG. 7C , in the case where the third point P 3  is located outside the strike zone  300  and the swing of the baseball bat is not made, the determination unit determines this as a ball. On the other hand, as illustrated in  FIG. 7C , in the case where the third point P 3  is located outside the strike zone  300  and the swing of the baseball bat has been made, the determination unit determines this as a strike. 
       FIGS. 8A, 8B and 8C  are still another explanatory views illustrating the operation of the non-stroke processor  666   a . Meanwhile, a ball  800  in  FIG. 8A  is an image of the ball  888  in  FIG. 1  described above. In  FIGS. 8A, 8B and 8C , for convenience of explanation, the first batter&#39;s box  221  and the second batter&#39;s box  222  are omitted. 
     First, suppose that the balls in a plurality of continuously photographed images proceed toward the determination area  340  with a trajectory as illustrated in  FIG. 8A , and the proceeding direction changes by a stroke. In such an exemplary embodiment, the ball may not pass through the determination area  340 . In other words, there is no ball between the first straight line L 1  and the second straight line L 2 . 
     The non-stroke processor  666   a  may even predict or estimate a location of the struck ball in the determination area  340  through a ball trajectory before the striking. To this end, the non-stroke processor  666   a  sets a size of a ball closest to the first straight line L 1  as the aforementioned average size. For example, the non-stroke processor  666   a  may set a diameter of a ball  801  emphasized by a hatched portion in  FIG. 8A  as the average size. Alternatively, the non-stroke processor  666   a  may set a diameter of the ball  801  closest to the first straight line L 1  and several balls  802  and  803  close to the ball  801  as the average size. For example, the non-stroke processor  666   a  may set an average size of the three balls  801 ,  802  and  803  illustrated in  FIG. 8A  as the aforementioned average size. 
     For a more accurate size calculation, the non-stroke processor  666   a  may estimate the average size based on a degree of size change of the balls  801 ,  802  and  803  gradually approaching the first straight line L 1  a distance between the first straight line L 1  and the ball closest to the first straight line L 1 . In other words, the non-stroke processor  666   a  may correct the average size based on the degree of size change of the balls  801 ,  802  and  803  gradually approaching the first straight line L 1  and the distance between the first straight line L 1  and the ball closest to the first straight line L 1 . 
     For example, in the case where the degree of size change of the balls  801 ,  802  and  803  gradually increases, the non-stroke processor  666   a  may increase a correction value for correcting the average size. On the other hand, in the case where the degree of size change of the balls  801 ,  802  and  803  gradually decreases, the non-stroke processor  666   a  may reduce the correction value for correcting the average size. 
     In addition, for example, in the case where the distance between the first straight line L 1  and the ball  801  closest to the first straight line L 1  is small, the non-stroke processor  666   a  may reduce the correction value for correcting the average size. On the other hand, in the case where the distance between the first straight line L 1  and the ball  801  closest to the first straight line L 1  is large, the non-stroke processor  666   a  may increase the correction value for correcting the average size. 
     Such a correction operation may be omitted. 
     Next, as illustrated in  FIG. 8B , the non-stroke processor  666   a  detects a vertical location of the ball  800  in the determination area  340  based on the average size. In other words, the non-stroke processor  666   a  detects a Y coordinate of the ball in the determination area  340  having a two-dimensional planar shape. 
     To this end, the non-stroke processor  666   a  may detect the vertical location of the ball  800  by, for example, comparing the average size with a predetermined reference value. The reference value includes the lower limit value and the upper limit value described above. 
     A reference number  16  in  FIG. 8B  means a size of a ball corresponding to the lower limit value, a reference number  17  in  FIG. 8B  means a size of a ball corresponding to the upper limit value, and a reference number  20  in  FIG. 8B  means a size of a ball corresponding to the average size of the balls described above, which′ may or may not be illustrated in the image. 
     As such, the non-stroke processor  666   a  may compare the average size, the upper limit value and the lower limit value to calculate coordinates of a point indicating the vertical location of the ball  800  on a third straight line L 3  based on the comparison result, which will be described in detail below. 
     For example, the non-stroke processor  666   a  divides the third straight line L 3  into a plurality of sections based on the location of the lower limit value and the location of the upper limit value. In such an exemplary embodiment, the third straight line L 3  may be divided into the plurality of sections so that one of points at a boundary between the sections corresponds to the location of the aforementioned lower limit value and another of the points at the boundary corresponds to the location of the upper limit value. 
     Each point is assigned with a different location value. Each location value is determined according to a ratio between the lower limit value and the upper limit value. The location value has a tendency to increase along a Y axis. 
     The non-stroke processor  666   a  finds a location value having a size coinciding with or closest to the average size and selects a point P 1  (hereinafter, “a first point”) given the location value. A Y coordinate of the selected first point P 1  means the vertical location of the ball  800  on the third straight line L 3 . 
     In such a manner, the non-stroke processor  666   a  may calculate coordinates of a point indicating a vertical location of the ball on a fourth straight line L 4 , which will be described in detail below. 
     For example, the non-stroke processor  666   a  divides the fourth straight line L 4  into a plurality of sections based on the location of the lower limit value and the location of the upper limit value. In such an exemplary embodiment, the fourth straight line L 4  may be divided into the plurality of sections so that one of points at a boundary between the sections corresponds to the location of the aforementioned lower limit value and another of the points at the boundary corresponds to the location of the upper limit value. 
     Each point is assigned with a different location value. Each location value is determined according to a ratio between the lower limit value and the upper limit value. The location value has a tendency to increase along a Y axis. 
     The non-stroke processor  666   a  finds a location value having a size coinciding with or closest to the average size and selects a point P 2  (hereinafter, “a second point”) given the location value. A Y coordinate of the selected second point P 2  means the vertical location of the ball  800  on the fourth straight line L 4 . 
     The Y coordinate value of the first point P 1  and the Y coordinate value of the second point P 2  indicating the height of the ball  800  may be substantially the same. 
     In the case as in an example illustrated in  FIG. 8B  in which the average size is greater than the lower limit value and less than the upper limit value, the first point P 1  is located on the left side S 3  of a strike zone  300  and the second point P 2  is located on the right side S 4  of the strike zone  300 . 
     Next, the non-stroke processor  666   a  sets a fifth straight line L 5  passing through the first point P 1  and the second point P 2 . 
     Next, the non-stroke processor  666   a  sets a sixth straight line L 6  based on a trajectory of the balls  801 ,  802  and  803  as illustrated in  FIG. 8C . 
     Subsequently, the non-stroke processor  666   a  calculates a horizontal location of the ball in the determination area  340  based on coordinates of a point P 3  (hereinafter, “a third point”) at which the sixth straight line L 6  meets the fifth straight line L 5 . The coordinates of the third point P 3  may be calculated based on an equation of the sixth straight line L 6  and an equation of the fifth straight line L 5 . The XY coordinates of the third point P 3  is a location of the ball in the determination area  340  ( 506 ). 
       FIG. 9  is a view illustrating a height input unit. 
     As illustrated in  FIG. 9 , the baseball game system  100  according to an exemplary embodiment may further include a height input unit  987 . 
     A height of a batter is input to the height input unit  987 , and to this end, the height input unit  987  may include a display window  911  and an input means  912 . 
     The input means  912  may be, for example, a keypad. A numerical value input by the input means  912  is displayed on the display window  911 .  FIG. 9  shows an example in which a height of 175.7 cm is input. 
     The non-stroke processor  666   a  adjusts the upper limit value and the lower limit value based on the height input to the height input unit  987 , and sets a height of the strike zone  300  having the adjusted upper and lower limit values. For example, the non-stroke processor  666   a  may include a lookup table therein. In such an exemplary embodiment, the upper limit value, the lower limit value and the height of the strike zone  300  according to the height may be stored in advance in the lookup table. The non-stroke processor  666   a  finds an upper limit value, a lower limit value and a height of the strike zone  300  corresponding to the input height from the look-up table and sets the found values as the upper limit value, the lower limit value and the height of the strike zone  300 . 
       FIG. 10  is an explanatory view illustrating an operation of a human body sensor. 
     As illustrated in  FIG. 10 , the baseball game system  100  according to an exemplary embodiment may further include a human body sensor  111 . 
     The human body sensor  111  may be positioned on at least one of the first batter&#39;s box  221  and the second batter&#39;s box  222 . The human body sensor  111  irradiates a laser to the first batter&#39;s box  221  and the second batter&#39;s box  222  to determine the presence or absence of a user (hereinafter, a batter)  633 . 
     The human body sensor  111  may further perform an operation of detecting a height of the batter  633  on the first batter&#39;s box  221  or the second batter&#39;s box  222 . In such an exemplary embodiment, the human body sensor  111  may replace the aforementioned height input unit  987 . 
     The non-stroke processor  666   a  adjusts the lower limit value, the upper limit value and the height of the strike zone  300  based on the height of the batter  633  detected by the human body sensor  111 . In such an exemplary embodiment, the non-stroke processor  666   a  may include the aforementioned lookup table. 
     In an exemplary embodiment, the non-stroke processor  666   a  may further detect a time when the ball  800  is closest to the first straight line L 1  and a time when the ball is closest to the second straight line L 2 . The non-stroke processor  666   a  may calculate a ball velocity based on the times. 
       FIG. 11  is another side view of  FIG. 1  to explain a maximum projection angle of the photographing unit  430 .  FIG. 12  is a perspective view illustrating that a ball is photographed according to the maximum projection angle of the photographing unit  430 .  FIGS. 13, 14 and 15  are views illustrating an operation of a coordinate converter. 
     Referring to  FIGS. 11, 12 and 13 , the photographing unit  430  photographs a maximum projection angle area  431  and transmits a plurality of images. In  FIG. 12 , the maximum projection angle of the photographing unit  430  is 2θ. That is, the photographing unit  430  may set the maximum projection angle unconstrainedly according to a place where the baseball game system is installed and the maximum projection angle area  431  that may be photographed by the photographing unit  430  is determined in accordance with the set maximum projection angle. The photographing unit  430  may photograph the ball  888  that entered the maximum projection angle area  431 . 
     The stroke processor  666   b  detects a location of the ball  888  based on the plurality of images. The stroke processor  666   b  includes a coordinate converter  667  and a trajectory calculator  668 . 
     The coordinate converter  667  calculates three-dimensional coordinates of the ball based on a ball size determined, from one of the plurality of images, according to coordinates of a reference plane  110  of the maximum projection angle area  431 , a size of the ball displayed in the image, XY coordinates of the ball displayed in the image and the maximum projection angle of the photographing unit  430 . 
     The trajectory calculator  667  analyzes the plurality of images and calculates a final location of the ball. 
     First, a process of the coordinate converter  667  calculating the three-dimensional coordinates of the ball will be described in detail. 
     The coordinate converter  667  includes a ratio calculator  667   a  and a coordinate calculator  667   b.    
     The ratio calculator  667   a  calculates a coordinate conversion ratio by dividing the size of the ball displayed in the image by the size of the ball determined according to the coordinates of the reference plane  110  of the maximum projection angle area  431 . 
     The coordinate calculator  667   b  divides a value obtained by multiplying the coordinate conversion ratio and a length of one side of the reference plane  110  of the maximum projection angle area  431  by a tangent value according to the maximum projection angle of the photographing unit  430 , thus calculating a Z coordinate of the ball. In addition, the coordinate calculator  667   b  calculates the XY coordinates of the ball by multiplying the coordinate conversion ratio and the XY coordinates of the ball displayed in the image. 
     Referring to  FIG. 13 , first, a reference point 0 of the Z coordinate is defined as the photographing unit  430 . In addition, the reference point 0 overlaps a center of the reference plane  110 . Alternatively, an actual bottom surface on which the ball stroke occurs may be set as the reference point of the Z coordinate. The reference plane  110  of the maximum projection angle area  431  may be a bottom surface of a space to which the actual baseball system is applied. Alternatively, the reference plane  110  may be set as an imaginary plane of a different height. A plane that is set parallel to the reference plane  110  with respect to the Z coordinate of the actual three-dimensional coordinates of the ball  880  is defined as a photographing plane  120 . Accordingly, the three-dimensional coordinates of the ball  880  positioned on the photographing plane  120  are three-dimensional coordinates of the ball desired to obtain. 
     When located on the reference plane  110 , the Z coordinate of the ball is Z1, and when located on the photographing plane  120 , the  7  coordinate of the ball is Z2. The maximum projection angle of the photographing unit  430  is 2θ. Since the reference plane  110  is an actual bottom surface, a length t1 of one side of the reference plane  110  may be measured. A length t2 corresponding to a half of one side of the reference plane  110  may also be obtained through the measured length t1 of the one side. 
     Accordingly, Z1 is defined as the following Equation 1 according to the law of trigonometric function. 
         Z 1=length of one side of a reference plane/2/Tan θ= t 2/Tan θ  [Equation 1]
 
     In an exemplary embodiment, a size of the balls  880  and  890  in the image photographed by the photographing unit  430  vary depending on the height of actual location. That is, as the balls  880  and  890  are further away from the photographing unit  430 , the size of the balls  880  and  890  photographed in the image is reduced. For example, a first image  11  illustrated in  FIG. 14  is an image illustrating a ball  880  on the reference plane  110  of  FIG. 13 . A second image  21  illustrated in  FIG. 15  is an image illustrating a ball  890  on the photographing plane  120 . Since the ball  880  on the reference plane  110  is farther away from the photographing unit  430  than the ball on the photographing plane  120  is therefrom, the ball  880  on the reference plane  110  in the first image  11  is less in size than the ball  890  of the second image  21 . 
     Accordingly, actual heights of the balls  880  and  890 , that is, the Z coordinate, may be determined based on the size of the balls  880  and  890  photographed in the image. For example, in the case where the size of the ball in the image is substantially equal to the size of the ball  880  in the first image  11  of  FIG. 14 , the Z coordinate of the ball in the image is substantially the same as the Z coordinate of the ball  880  in the first image  11 . Accordingly, the size of the ball  880  photographed in the first image  11  becomes a reference value according to the coordinates of the reference plane  11  and the size of the ball  890  photographed by the photographing unit  430  is compared with the reference value to calculate the coordinate conversion ratio. The coordinate conversion ratio is as follows. 
     A coordinate conversion ratio=size of a ball displayed in an image/a reference value=size of the ball displayed in the image/size of the ball determined according to coordinates of a reference plane 
     For example, referring to  FIGS. 14 and 15 , the coordinate conversion ratio is the ball size of the second image/the ball size of the first image. In an exemplary embodiment, the size of the ball may be determined based on a diameter of the ball, for example. 
     Accordingly, when the coordinate conversion ratio is calculated using the size of the ball  880  determined according to the coordinates of the reference plane  11  and the size of the ball  890  displayed in the image and then the coordinate conversion ratio is multiplied by Equation 1, the actual Z coordinate of the ball may be obtained as in the following Equation 2. 
         Z 2= Z 1*a coordinate conversion ratio 
       = T 2/tan θ*a coordinate conversion ratio
 
       = T 2/tan θ*size of the ball displayed in the image/size of the ball determined according to coordinates of a reference plane
 
       = T 2/Tan θ*a diameter of the ball in the image/a diameter of the ball determined according to the coordinates of the reference plane  [Equation 2]
 
     As such, the ratio calculator  667   a  calculates the coordinate conversion ratio based on the ball size determined according to the coordinates of the reference plane  110  of the maximum projection angle area  431  and the size of the ball displayed in the image. Then, the coordinate calculator  667   b  calculates the Z coordinate Z2 of the ball based on the coordinate conversion ratio, the maximum projection angle of the photographing unit  430 , the Z coordinate Z1 of the ball when it is located on the reference plane  110  and the length t1 of one side of the reference plane  110 . In an exemplary embodiment, when a bottom surface is set as a reference point O, the Z coordinate of the ball may use Z3. 
     In an exemplary embodiment, the XY coordinates of the ball  890  may be calculated based on the second image  21 . First, a center of the second image  21  is set as the reference point O. According to the set reference point O, the XY coordinates of the ball  890  displayed in the second image  21  is determined with respect to a center of the ball  890 . For example, as illustrated in  FIG. 15 , the XY coordinates of the ball  890  becomes (5, −5). 
     As such, when the aforementioned coordinate conversion ratio is applied to the XY coordinates of the ball  890  obtained based on the second image  21  as below, actual XY coordinates of the ball  890  may be obtained. The XY coordinates of the ball  890  displayed in the second image  21  are different from the actual XY coordinates of the ball and when the previously obtained coordinate conversion ratio is applied, the actual XY coordinates of the ball  890  displayed in the second image  21  may be obtained. 
     Actual X coordinate=X*a coordinate conversion ratio=X*size of the ball displayed in the image/size of the ball determined according to the coordinates of the reference plane 
     Actual Y coordinate=Y*a coordinate conversion ratio=Y*size of the ball displayed in the image/size of the ball determined according to the coordinates of the reference plane 
     As such, according to an exemplary embodiment, the three-dimensional coordinates of the ball  890  may be more accurately calculated based on the maximum projection angle of the photographing unit  430  and the coordinate conversion ratio. An algorithm for obtaining the three-dimensional coordinates according to an exemplary embodiment is as follows. 
     
       
         
           
               
             
               
                   
               
               
                 [Algorithm] 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
            
               
                   
                 float tan = Mathf.Tan(arcOption.fieldOfview/2*Mathf.PI/180); 
               
               
                   
                 float w = imgWidth/2; 
               
               
                   
                 float h = imgHeight/2; 
               
               
                   
                 foreach(ARC_TARGET at in list) 
               
               
                   
                 { 
               
               
                   
                 float r = arcOption.balldiameter/at.size; 
               
               
                   
                 if(r&gt;1) r=1; if(r&lt;0) r=0; 
               
               
                   
                 float d = r/tan 
               
               
                   
                 float x = (at.pos.x−w)*r; 
               
               
                   
                 float y = (at.pos.y−h)*r; 
               
               
                   
                 float z = −d*w; 
               
               
                   
                 at.pos3D = new Vector3 (x,y,x); 
               
               
                   
                 } 
               
               
                   
                   
               
            
           
         
       
     
     Hereinafter, an operation of the trajectory calculator will be described below with reference to  FIGS. 16, 17, 18 and 19 . 
       FIGS. 16, 17, 18 and 19  are views illustrating an operation of a trajectory calculator. 
     Referring to  FIGS. 16, 17, 18 and 19 , the trajectory calculator  668  (see  FIG. 12 ) analyzes a plurality of images to calculate a final location of the ball. For example,  FIG. 16  is a view illustrating overlap of a total of nine images taken at time intervals. A ball  891  relatively close to a center 0 is an image of a previously photographed ball  891  and a ball  892  relatively far from the center 0 is an image of a ball  892  photographed later in time. In the case where a diameter of the ball  892  photographed later is larger than a diameter of the previously photographed ball  891 , the trajectory calculator  668  determines that the ball is gradually ascending. On the other hand, as illustrated in  FIG. 17 , in the case where a diameter of a ball  894  photographed later is less than a diameter of a previously photographed ball  893 , the trajectory calculator  668  determines that the ball is gradually descending. 
     In addition, referring to  FIGS. 18 and 19 , the trajectory calculator  668  calculates a distance by which the ball moves for a predetermined period of time using the three-dimensional coordinates of the ball and a time difference between the plurality of images, and calculates a velocity of the ball based on the time difference and the moving distance. 
     That is, as described above, the coordinate converter  667  calculates respective three-dimensional coordinates of balls  895 ,  896 ,  897  and  898 . The trajectory calculator  668  calculates a distance d by which the ball moves for a predetermined period of time based on the calculated three-dimensional coordinates of the balls  895 ,  896 ,  897  and  898  and the time difference between each image. Then, the trajectory calculator  668  calculates a velocity of the ball based on the time difference between each image and the moving distance d. In addition, the trajectory calculator  668  determines a result value, such as a foul, an out, a hit, a two-base hit, a three-base hit and a home run, of a struck ball based on the three-dimensional coordinates of the ball and the velocity of the ball. 
       FIG. 20  is a flowchart illustrating an operation sequence of the stroke processor  666   b.    
     Referring to  FIG. 20 , the baseball game system according to an exemplary embodiment detects a size of a ball displayed in an image ( 511 ). A coordinate conversion ratio is calculated by comparing a size of the ball determined according to coordinates of a reference plane of an area with the size of the ball displayed in the image ( 512 ). A Z coordinate of the ball is detected based on the coordinate conversion ratio and a maximum projection angle of a photographing unit ( 514 ). A moving distance and a velocity of the ball are calculated ( 515 ). A final location and a result of the ball are determined ( 516 ). 
       FIG. 21  is still another side view of  FIG. 1  for explaining the operation of the swing determination unit  644 . 
     The swing determination unit  644  determines whether or not a swing of a baseball bat  777  has been made based on the image photographed by the photographing unit  430 . The image provided from the photographing unit  430  includes a plurality of frame images. The swing determination unit  644  may detect a degree of change in a specific portion of the image based on the plurality of frame images. For example, the swing determination unit  644  detects a batter&#39;s box where a batter  608  is positioned based on the degree of change in the image and determines whether or not a swing of the baseball bat  777  has been made based on the detected batter&#39;s box and a trajectory of an end portion of the baseball bat  777 . To this end, for example, the swing determination unit  644  may binarize each frame image from the photographing unit  430  based on a corresponding photographing illuminance thereof to generate a black-white image, extract a basic contour (e.g., respective contours of the batter  608  and the baseball bat  777 ) of a subject (e.g., the batter  608  and the baseball bat  777 ) in the image by scanning the black-white image in the up-and-down direction and the left-and-right direction, determine a center position of the subject from the contour, and determine a location of the subject based on the center position. In addition, the swing determination unit  644  may detect a movement and a moving direction of the subject based on a change of the center position of the subject and from this, the degree of change in the image may be calculated. 
       FIG. 22  is a view illustrating the image photographed by the photographing unit  430 . A strike zone  300  in  FIG. 22  is an image of the aforementioned strike zone  333  in  FIG. 1 , a first batter&#39;s box  221  in  FIG. 22  is an image of the aforementioned first batter&#39;s box  241  in  FIG. 1 , a second batter&#39;s box  222  in  FIG. 22  is an image of the aforementioned second batter&#39;s box  242  in  FIG. 1 , a ball  800  in  FIG. 22  is an image of the aforementioned ball  888  in  FIG. 1 , a batter  618  in  FIG. 22  is an image of the aforementioned batter  608  in  FIG. 1 , and a baseball bat  321  in  FIG. 22  is an image of the aforementioned baseball bat  777  in  FIG. 1 . 
     The swing determination unit  644  sets the strike zone  300  based on the image photographed by the photographing unit  430 . For example, the strike zone  300  may be defined as an area surrounded by four imaginary sides L 1 , L 2 , L 3  and L 4 . 
     A lower side L 1  and an upper side L 2  face each other and a left side L 3  and a right side L 4  face each other. The lower side L 1  and the upper side L 2  may be arranged parallel to each other. 
     The photographing unit  430  photographs the strike zone  300  from a diagonal direction thereof rather than immediately above the strike zone  300 . The strike zone  300  is shaped like a trapezoid to reflect the perspective phenomenon depending on the shooting angle. For example, the strike zone  300  may have a trapezoidal shape as illustrated in  FIG. 22 . Since the upper side S 2  of the strike zone  300  is positioned relatively closer to the photographing unit  430  than the lower side S 1  of the strike zone  300  is thereto, the upper side S 2  has a longer length than the lower side S 1 . 
     The ball  800  in the image has a larger size as it approaches the photographing unit  430  due to the perspective phenomenon. That is, the size of the ball  800  in the image tells how high the ball  800  is from the ground (or the groove plate  230 ). In other words, a vertical location of the ball  800  may be determined from the size of the ball  800  in the image. 
     When a swing of the baseball bat  321  is made by the batter  618 , a swing trajectory having a shape of a curve (for example, an arch) as illustrated in  FIG. 3  is formed. 
     The operation of the swing determination unit  644  will be described in detail based on the image illustrated in  FIG. 22 . 
       FIGS. 23A and 23B  are explanatory views illustrating the operation of the swing determination unit based on the image of  FIG. 22 , and  FIG. 24  is a flowchart illustrating an operation sequence of the swing determination unit in  FIGS. 23A and 23B . In  FIGS. 23A and 23B , for convenience of explanation, the first batter&#39;s box  221  and the second batter&#39;s box  222  are omitted. 
     First, the swing determination unit  644  detects a batter&#39;s box where the batter  618  is positioned based on the image of  FIG. 22  ( 521 ). In the image illustrated in  FIG. 22 , a degree of change in the image at the first batter&#39;s box  221  is greater than that at the second batter&#39;s box  222 . This is because the batter  618  is positioned on the first batter&#39;s box  221 . Based on the difference in the degree of image change, the swing determination unit  644  determines which batter&#39;s box the batter  618  is positioned at. That is, since the degree of image change at the first batter&#39;s box  221  is greater than the degree of image change at the second batter&#39;s box  222 , the swing determination unit  644  determines that the batter  618  is on the first batter&#39;s box  221 . Accordingly, the first batter&#39;s box  221  is detected by the swing determination unit  644 . 
     Subsequently, as illustrated in  FIG. 23A , the swing determination unit  644  sets a first vector V 1  connecting two temporally adjacent end portions  322  (end portions of the baseball bat) ( 522 ). For example, as illustrated in  FIG. 23A , when fourteen end portions  322  form a single swing trajectory, thirteen first vectors V 1  connecting two adjacent end portions  322  are set. 
     A length of the first vector V 1  is proportional to a distance between the adjacent end portions  322 . A direction of the first vector V 1  is directed from an end portion  322  that is photographed relatively earlier in time toward an end portion  322  that is photographed later in time. For example, as illustrated in  FIG. 23A , in the case where there are an (n−1)-th photographed end portion (hereinafter, “an (n−1)-th end portion”) and an n-th photographed end portion (hereinafter, “an n-th end portion”), in terms of time sequence, a first vector V 1  connecting the (n−1)-th end portion and the n-th end portion has a point directed from the (n−1)-th end portion toward the n-th end portion. 
     Next, as illustrated in  FIG. 23B , the swing determination unit  644  sets a second vector V 2  extending from a center point of the first vector V 1  perpendicularly to the first vector V 1  ( 523 ). In such an exemplary embodiment, the swing determination unit  644  may set an extending direction of the second vector V 2  based on a shape of a curve forming a swing trajectory. As an example, the swing determination unit  644 —may set a line segment connecting a first end portion and a last end portion, and the second vector V 2  may extend in a direction crossing the line segment. As another example, by the swing determination unit  644 , the second vector V 2  may extend from a convex surface of the curve toward a concave surface of the curve. 
     Next, the swing determination unit  644  determines whether the number of second vectors V 2  that are directed toward the detected batter&#39;s box  221  or pass through the detected batter&#39;s box  221  among the second vectors V 2  is within a first reference range. 
     Subsequently, the swing determination unit  644  determines whether an average length of the second vectors V 2  is within a second reference range. The length of the second vector V 2  is related to a velocity of the end portion  322  of the baseball bat, and as the length of the second vector V 2  increases, it means the velocity of the end portion  322  is faster. 
     The swing determination unit  644  determines whether or not a swing of the baseball bat  777  has been made based on the two determinations ( 524 ). For example, in the case where the number of second vectors V 2  that are directed toward the detected batter&#39;s box  221  or pass through the detected batter&#39;s box  221  among the second vectors V 2  is within the first reference range and the average length of the second vectors V 2  is within the second reference range, the swing determination unit  644  determines that a swing of the baseball bat  321  has been made. 
     On the other hand, in the case where the number of second vectors V 2  that are directed toward the detected batter&#39;s box  221  or pass through the detected batter&#39;s box  221  among the second vectors V 2  is out of the first reference range, or the average length of the second vectors V 2  is out of the second reference range, the swing determination unit  644  determines that the end portions  322  forming such a trajectory are noise. That is, in such an exemplary embodiment, the swing determination unit  644  determines that a swing of the baseball bat  321  has not been made. 
     As such, the swing determination unit  644  determines whether or not a swing of the baseball bat  777  has been made based on the trajectory and velocity of the end portions  322 . 
     In an exemplary embodiment, the swing determination unit  644  may further determine lengths of the first vectors V 1  to detect a check swing. For example, the swing determination unit  644  may further determine whether a sum of lengths of the first vectors V 1  is within a third reference range. In such an exemplary embodiment, in the case where the number of second vectors V 2  that are directed toward the detected batter&#39;s box  221  or pass through the detected batter&#39;s box  221  among the second vectors V 2  is within the first reference range, the average length of the second vectors V 2  is within the second reference range, and the sum of the lengths of the first vectors V 1  is within the third reference range, the swing determination unit  644  determines that a swing of the baseball bat  321  has been made. 
     The first and second vectors V 1  and V 2  in  FIGS. 22, 23A and 23B  have characteristics coinciding with the first, second and third reference ranges, and in such an exemplary embodiment, the swing determination unit  644  determines that a swing of the baseball bat  321  has been made. 
       FIG. 25  is a view illustrating a trajectory of a baseball bat in the case of a check swing. 
     As illustrated in  FIG. 25 , in the case where the baseball bat  321  is not swung properly, the swing determination unit  644  determines it as a check swing. That is, it is not determined as a swing by the swing determination unit  644 . 
     The sum of the lengths of the first vectors V 1  in  FIG. 25  is out of the third reference range. For example, in the case where the sum of the lengths of the first vectors V 1  is less than a predetermined threshold value, the swing determination unit  644  may determine it as a check swing. 
       FIG. 26  is a perspective view illustrating a baseball bat used in the baseball game system of  FIG. 1 , and  FIG. 27  is a cross-sectional view taken along line I-I′ of  FIG. 1 . 
     In order to substantially minimize the effect of noise, the baseball bat  777  may further include a marking pattern  788 , as illustrated in  FIGS. 26 and 27 . 
     As illustrated in  FIG. 26 , the marking pattern  788  may be positioned at an end portion of the baseball bat  777 . 
     As illustrated in  FIG. 27 , the marking pattern  788  may have a shape surrounding the end portion of the baseball bat  777 . 
     The marking pattern  788  may have a bright color so that the end portion of the baseball bat  777  may be clearly visible when generating the black-white image as descried above. For example, the marking pattern  788  may have a lighter color than a color of the baseball bat  777 . 
       FIG. 28  is a view illustrating an algorithm applied to the non-stroke processor,  FIG. 29  is a view illustrating an algorithm applied to the stroke processor, and  FIG. 30  is a view illustrating an algorithm applied to the swing determination unit. 
     The non-stroke processor may detect the coordinates of the ball in the determination area through the algorithm of  FIG. 28 , the stroke processor may detect the coordinates of the struck ball through the algorithm illustrated in  FIG. 29  or the algorithm described above (the algorithm for obtaining the three-dimensional coordinates), and the swing determination unit may determination whether or not a swing has been made through the algorithm of  FIG. 30 . 
     As set forth hereinabove, the baseball game system according to one or more exemplary embodiments may provide the following effects. 
     First, the baseball game system may accurately determine the location of the ball using a single camera by determining the height of the ball based on the size of the ball. 
     Second, the baseball game system may accurately determine whether or not the game is a strike by setting the strike zone in a trapezoidal shape in consideration of the photographing angle of the camera. 
     Third, the baseball game system may even predict the location of a struck ball in the determination area based on the trajectory of the ball before the striking. 
     Fourth, the baseball game system may determine the location of the ball in the determination area more accurately by correcting the average size based on at least one of the degree of size change of the balls before striking and the size change trend of the balls. 
     Fifth, the baseball game system may accurately determine the location of the ball by determining the location of the ball in consideration of the maximum projection angle of the camera. 
     Sixth, the baseball game system may accurately determine whether a swing of a baseball bat has been made in consideration of the position of a batter, the swing trajectory and velocity of the baseball bat, or the like. 
     Seventh, the baseball game system may determine whether a swing of the baseball bat has been made more accurately by determining whether a check swing has been made based on the length of the swing trajectory. 
     Eighth, the baseball game system may detect the trajectory of the baseball bat more accurately by using the baseball bat including a marking pattern. 
     While the present invention has been illustrated and described with reference to the exemplary embodiments thereof, it will be apparent to those of ordinary skill in the art that various changes in form and detail may be made thereto without departing from the spirit and scope of the present invention.