Patent Publication Number: US-2016228198-A1

Title: Tracking system and tracking method using the same

Description:
TECHNICAL FIELD 
     Exemplary embodiments of the present invention relate to a tracking system and tracking method using the same. More particularly, exemplary embodiments of the present invention relate to a tracking system and tracking method using the same for surgery capable of detecting a spatial and direction information of a target by tracking coordinates of markers attached on the target, in which the target are markers attached on a patient or surgical instrument. 
     BACKGROUND ART 
     Recently, a robot surgery have been studied and introduced to reduce the pain of patients and to recover faster in an endoscopic surgery or an otolaryngology surgery (ENT surgery). 
     In such a robot surgery, in order to minimize a risk of the surgery and to operate the surgery more precisely, a navigation system is used to navigate to an exact lesion of a patient by tracking and detecting a spatial position and direction of a target such as lesion portion or surgical instrument. 
     The navigation system described above includes a tracking system which is capable of tracking and detecting a spatial position and direction of a target such as lesion or surgical instrument. 
     The tracking system described above includes a plurality of markers attached on a lesion or a surgical instrument, first and second image forming units to form images of lights emitted from the markers, and a processor calculating a 3-dimensional coordinates of the markers which are coupled to the first and second image forming units and calculating a spatial position and a direction of the target by comparing pre-stored information of straight lines connecting the markers adjacent to each other and angle information formed by a pair of straight lines adjacent to each other with the 3-dimensional coordinates of the markers. 
     Herein, in order to calculate the 3-dimensional coordinates of the markers, conventionally, two detectors are required to calculate 3-dimensional coordinates of each marker through a processor, a triangulation method is used in an assumption that a coordinate of marker which is emitted from one marker and formed image in a first image forming unit and a coordinate of marker which is emitted from one marker and formed image in a second image forming unit are identical. 
     Thus, conventional tracking system requires two image forming units to form images of lights which are emitted from each of the markers positioned different to each other, a manufacturing cost increases as well as a whole size also increases, therefore, a restriction of surgical space is generated. 
     DISCLOSURE 
     Technical Problem 
     Therefore, the technical problem of the present invention is to provide a tracking system and method using the same capable of reducing a manufacturing cost as well as minimizing a restriction of a surgical space by achieving compact of the system through calculating 3-dimenstional coordinates for each marker using only one image forming unit. 
     Technical Solution 
     In one embodiment of the present invention, a tracking system includes at least three markers which are attached on a target to emit lights, a pair of light sources which emit lights in different position to each other, a lens portion which passes the lights emitted from the pair of the light sources and reflected by the markers, an image forming unit which forms a pair of maker images for each marker by receiving the lights which have passed by the lens portion, a processor which calculates three-dimensional coordinates of the markers by using the pair of the maker images formed on the image forming unit for each marker and calculates spatial position information and direction information of the target by comparing the three-dimensional coordinates of the markers with pre-stored geometric information between the markers adjacent to each other. 
     Meanwhile, the tracking system may further include a beam splitter which is arranged between the lens portion and the image forming unit to partially reflect the light, which is emitted from one light source of the pair of the light sources, toward a center of the markers, and to partially pass the light, which is emitted toward the center of the markers, re-reflected by the markers, and flowed through the lens unit, toward the image forming unit. 
     Also, the tracking system may further include a diffuser arranged between the light source, which emits light toward the beam splitter, and the beam splitter to diffuse the lights emitted from the light sources. 
     In one embodiment, the image forming unit may be a camera to form a pair of images for each marker by receiving the lights reflected by the markers and having sequentially passed the lens portion and the beam splitter. 
     In one embodiment, the geometric information between the markers may be length information of straight lines connecting the markers adjacent to each other and angle information formed by a pair of straight lines adjacent to each other. 
     In one embodiment of the present invention, a tracking method includes emitting lights from a pair of light sources which are positioned at different position to each other toward at least three markers, reflecting the lights emitted from the pair of the light sources toward a lens portion by the markers, forming a pair of maker images on an image forming unit for each marker through the lights emitted from the markers and have passed the lens portion, calculating three-dimensional coordinates for each marker through a processor by using the pair of maker images formed on the image forming unit for each marker, and calculating spatial position information and direction information of the target by comparing the three-dimensional coordinates of each marker with geometric information which is pre-stored in the processor between the markers adjacent to each other. 
     Herein, one light source of the light sources emits the light toward the beam splitter arranged between the lens portion and the image forming unit, and emits the light towards a center of the markers through the lens portion by partially reflecting the light by the beam splitter, and the other light source directly emits the light toward the markers. 
     Meanwhile, the light emitted toward the beam splitter may be emitted toward the beam splitter by a diffuser arranged between the beam splitter. 
     In one embodiment, the geometric information between the markers may be length information of straight lines connecting the markers adjacent to each other and angle information formed by a pair of the straight lines adjacent to each other. 
     In one embodiment, calculating three-dimensional coordinates of the markers may further include calculating two-dimensional central coordinates for each marker through the processor by using image forming positions of the pair of maker images formed on the image forming unit for each marker, and calculating three-dimensional coordinates of the markers by using the two-dimensional central coordinates of each marker. 
     Advantageous Effects 
     Thus, according to an embodiment of the present invention, in a tracking system and tracking method using the same, one image forming unit is used to calculate spatial position information and direction information of a target by calculating three-dimensional coordinates of the markers through a trigonometry since it is possible to form a pair of maker images for each marker in different image forming positions by a pair of light sources positioned different to each other. 
     Therefore, there is an effect of reducing a manufacturing cost of the tracking system, making small and lightweight, and relatively low restriction of surgical space comparing with conventional tracking system. 
    
    
     
       DESCRIPTION OF DRAWINGS 
         FIG. 1  is a schematic diagram of a tracking system according to an embodiment of the present invention; 
         FIG. 2  is an example diagram of markers attached on a target; 
         FIG. 3  is an example diagram explaining a method of tracking according to an embodiment of the present invention; 
         FIG. 4  is a block diagram explaining a method of calculating three-dimensional coordinates of markers; 
         FIG. 5  is an example diagram explaining a state of an image forming of markers formed on an image forming unit in case that at least three markers are arranged horizontally to a lens; 
         FIG. 6  is an example diagram of a change of image forming positions according to a distance between the markers and the lens portion; 
         FIG. 7  is an example diagram explaining a method of calculating two-dimensional central coordinates of a first marker; 
         FIG. 8  is an example diagram of explaining a relationship between a reflection position in which light is reflected on a surface of markers and a center position of marker; and 
         FIG. 9  is an example diagram of explaining a method of calculating a coordinate of a reflection position in which light is reflected on a surface of marker. 
     
    
    
     MODE FOR INVENTION 
     The present invention is described more fully hereinafter with reference to the accompanying drawings, in which example embodiments of the present invention are shown. The present invention may, however, be embodied in many different forms and should not be construed as limited to the example embodiments set forth herein. Rather, these example embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the present invention to those skilled in the art. In the drawings, the sizes and relative sizes of layers and regions may be exaggerated for clarity. 
     It will be understood that, although the terms first, second, third etc. may be used herein to describe various elements, components, regions, layers and/or sections, these elements, components, and/or sections should not be limited by these terms. These terms are only used to distinguish one element, component, region, layer or section from another region, layer or section. Thus, a first element, component, or section discussed below could be termed a second element, component, or section without departing from the teachings of the present invention. 
     The terminology used herein is for the purpose of describing particular example embodiments only and is not intended to be limiting of the present invention. 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” and/or “comprising,” 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. 
     Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. 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 idealized or overly formal sense unless expressly so defined herein. 
     Hereinafter, with reference to the drawings, preferred embodiments of the present invention will be described in detail. 
     A tracking system and method using the same according to an embodiment of the present invention attaches at least three markers at a target such as a lesion or a surgical instrument and calculates 3-dimenstional coordinates of the markers, compares geometric information of markers adjacent to each other which are pre-stored in a processor with the 3-dimenstional coordinates of the markers through the processor, and therefore, is capable of calculating spatial position information and direction information of a target such as a lesion or surgical instrument. The detailed description is explained referencing figures. 
       FIG. 1  is a schematic diagram of a tracking system according to an embodiment of the present invention, and  FIG. 2  is an example diagram of markers attached on a target. 
     Referring to  FIGS. 1 to 2 , a tracking system according to an embodiment of the present invention includes at least three markers  110   111  and  112 , at least two light sources, a first light source  150  and a second light source  151 , a lens portion  120 , a beam splitter  160 , an image forming unit  140 , and a processor  140 . 
     The at least three markers  110   111  and  112  are attached on a target  200  such as a lesion of a patient or a surgical instrument. Herein, the at least three markers  110   111  and  112  are separated to adjacent markers  110   111  and  112  to each other at a predetermined interval and the markers are attached on the target  200  such as a lesion or a surgical instrument such that a pair of straight lines L 1  L 2  and L 3  in which each of the markers are virtually connected to adjacent markers forming specific angles A 1  A 2  and A 3 . 
     Herein, geometric information between the markers  110   111  and  112  which are adjacent to each other, in other words, length information of straight lines L 1  L 2  and L 3  which connect the markers  112  which are adjacent to each other and angle information A 1  A 2  and A 3  which are formed by a pair of the straight lines connecting the adjacent markers, are stored in a memory  141  of the processor  140 . 
     For example, the markers  110   111  and  112  may be attached on the target  200  such as a lesion and a surgical instrument in a triangle shape, straight lines information L 1  L 2  and L 3  forming sides of the triangle in which the markers are used as vertices and angle information A 1  A 2  and A 3  which are formed by a pair of adjacent and virtual straight lines which connect the markers  110   111  and  112  may be pre-stored in the memory  141  included in a processor  140 . 
     Meanwhile, the markers  110   111  and  112  may be passive markers which reflect the lights emitted from the first and second light sources  150  and  151 . 
     The first and second light sources  150  and  151  emit the lights toward the markers  110   111  and  112  at different position to each other. For example, the first light source  150  may directly emit the light toward the markers  110   111  and  112 , and the second light source  151  may emit the light toward the beam splitter  160 , which is arranged between the lens portion  120  and the image forming unit  130 . The light emitted from second light source  151  is partially reflected by the beam splitter  160 , and is emitted toward a center of the markers  110   111  and  112  after passing the lens portion  120 . 
     In other words, a portion of the light emitted from the second light source  151  is reflected by the beam splitter  160  and emitted toward the center of the markers  110   111  and  112  through the lens portion  120 , and the rest of the light passes the beam splitter  160 . 
     Alternatively, the second light source  151  may directly emit the light toward the makers  110   111  and  112 , and the first light source  150  may emit the light toward the beam splitter  160  such that the light is emitted toward the center of the markers  110   111  and  112  through the beam splitter  160 . 
     For example, it may be preferable to use a spot illumination as the first and second light sources  150  and  151  such that the lights are reflected at one point within the whole surface of the markers  110   111  and  112 . 
     The lens portion  120  passes the lights which is directly reflected by the markers  110   111  and  112 , which is emitted from one of the selected light source among the first and second light sources  150  and  151 , and the re-reflected light which is emitted from the other light source, reflected by the beam splitter  160  and emitted toward the center of the markers  110   111  and  112  through the lens potion  120   
     The beam splitter is arranged on a rear portion of the lens portion  120 . The beam splitter  160  partially passes the light emitted from one light source which is selected among the first and second light sources  150  and  151 , and reflects and emits the remaining light toward the center of the markers  110   111  and  112  after passing the lens portion  120 . 
     In other words, the image forming unit  130  is arranged on a rear portion of the beam splitter  160  and forms a pair of maker images for each of the markers  110   111  and  112  by receiving the lights which is directly emitted from one light source which is selected among the first and second light sources  150  and  151 , reflected by the markers  110   111  and  112 , and have sequentially passed the lens portion  120  and the beam splitter  160 , and the light which is emitted from the other light source toward the beam splitter  160 , reflected by the beam splitter  160  and have passed the lens portion  120 , emitted and re-reflected toward the center of the markers  110   111  and  112 , and have sequentially passed the lens portion  120  and the beam splitter  160 . 
     Herein, a portion of the light which is emitted from the first and second light sources  150  and  151 , re-reflected by the markers  110   111  and  112  and have passed the lens portion  120  and flowed in the beam splitter  160 , is reflected by the beam splitter  160  and the rest of the light is flowed into the image forming unit  130  after passing the beam splitter and forms a pair of maker images for each of the markers  110   111  and  112 . 
     For example, the image forming unit  130  may be a camera integrating an image sensor  131  which forms a pair of maker images for each of the markers  110   111  and  112  by receiving the lights which are emitted from the first and second light sources  150  and  151 , reflected by the markers  110   111  and  112 , sequentially have passed the lens portion  120  and the beam splitter  160 . 
     Meanwhile, a diffuser  170  may be arranged between the light source which emits light toward the beam splitter  160  among the first and second light sources  150  and  151  and the beam splitter  160  to diffuse the light toward the beam splitter  160 . 
     The processor  140  calculates three-dimensional coordinates of the markers  110   111  and  112  by using the pair of the maker images for each of the markers  110   111  and  112  which are formed on the image forming unit  130 , in which the lights are emitted from the first and second light sources  150  and  151 , reflected by the markers  110   111  and  112  and are formed on the image forming unit  130 , and calculates spatial position information and direction information of the markers  110   111  and  112  which are attached on the target  200  such as a lesion or a surgical instrument by comparing the three-dimensional coordinates of the markers  110   111  and  112  with geometric information between the markers  110   111  and  112  adjacent to each other. 
     Herein, the memory  141  is integrated in the processor  140 . Meanwhile, the memory  141  integrated in the processor  140  may pre-store geometric information of the markers  110   111  and  112  adjacent to each other, in other words, length information of straight lines L 1  L 2  and L 3  connecting the markers  110   111  and  112  adjacent to each other, and angle information A 1  A 2  and A 3  formed by a pair of the straight lines connecting the markers  110   111  and  112  adjacent to each other. 
     In addition, the memory  141  integrated in the processor  140  may pre-store spatial position information and direction information of the first and second light sources  150  and  151 . 
     Referring to  FIGS. 1-8 , a tracking process of spatial position information and direction information of a target using a tracking system according to an embodiment of the present invention is described below. 
       FIG. 3  is an example diagram explaining a method of tracking according to an embodiment of the present invention; 
       FIG. 4  is a block diagram explaining a method of calculating three-dimensional coordinates of markers,  FIG. 5  is an example diagram explaining a state of image forming of markers formed on an image forming unit in case that at least three markers are arranged horizontally to a lens,  FIG. 6  is an example diagram of a change of image forming positions according to a distance between markers and a lens portion,  FIG. 7  is an example diagram explaining a method of calculating two-dimensional central coordinates of a first marker,  FIG. 8  is an example diagram of explaining a relationship between a reflection position in which light is reflected on a surface of marker and a center position of marker, and  FIG. 9  is an example diagram of explaining a method of calculating a coordinate of a reflection position in which light is reflected on a surface of marker. 
     For the convenience of explanation, it will be described as an example in the case that a first light source is arranged to directly emit a light toward to markers, and a second light source is arranged to emit a light toward a markers through a beam splitter. 
     Referring to  FIGS. 1-9 , in order to track spatial position information and direction information of a target using a tracking system according to an embodiment of the present invention, first, first and second light sources  150  and  151  positioned different to each other are operated to emit lights toward a first to third markers  110   111  and  112  (S 110 ). 
     In more detail, a spot illumination emitted from the first light source  150  are directly irradiated toward the first to third markers  110   111  and  112 , and a spot illumination emitted from the second light source  151  is irradiated toward a beam splitter  160  such that a portion of the light passes the beam splitter and the remaining light is reflected by the beam splitter, passes a lens portion  120 , and emits toward a center of the first to third markers  110   111  and  112 . 
     The spot illuminations emitted from the first and second light sources  150  and  151 , which are emitted toward the markers  110   111  and  112 , are reflected toward a lens portion  120  by the first to third markers  110   111  and  112  (S 120 ). 
     In more detail, the light emitted from the first light source  150  is directly reflected at one position of a surface of the first to third markers  110   111  and  112 , reflected toward the lens portion  120  through a first to third optical paths AX 1  AX 2  and AX 3 , the light emitted from the second light source  151  is irradiated toward the beam splitter  160 , a portion of the light passes the beam splitter  160  and the remaining is reflected by the beam splitter  160 , passes the lens portion  120  through a fourth to sixth optical paths AX 4  AX 5  and AX 6 , and emits toward the first to third markers  110   111  and  112 . 
     The lights which pass the lens portion  120  through the first to sixth optical paths AX 1  AX 2  AX 3  AX 4  AX 5  and AX 6  form a pair of maker images on an image forming unit  130  for each of the markers  110   111  and  112  (S 130 ). 
     In more detail, the light which is emitted from the first light source  150 , reflected by the first marker  110  through the first optical path AX 1  and have passed the lens portion  120 , forms a first image of the first marker  110  on the image forming unit  130 , and the light which is emitted from the second light source  151 , reflected by the first marker  110  through the fourth optical path AX 4  and have passed the lens portion  120 , forms a second image of the first marker  110  on the image forming unit  130 . Also, the light which is emitted from the first light source  151 , reflected by the second marker  111  through the second optical path AX 2  and have passed the lens portion  120 , forms a first image of the second marker  111  on the image forming unit  130 , and the light which is emitted from the second light source  151 , reflected by the second marker  111  through the fifth optical path AX 5  and have passed the lens portion  120 , forms a second image of the second marker  111  on the image forming unit  130 . Also, the light which is emitted from the first light source  150 , reflected by the third marker  112  through the third optical path AX 3  and have passed the lens portion  120 , forms a first image of the third marker  112  on the image forming unit  130 , and the light which is emitted from the second light source  151 , reflected by the third marker  112  through the sixth optical path AX 6  and have passed the lens portion  120 , forms a second image of the third marker  112  on the image forming unit  130 . 
     As described above, after forming the first and second images of the first to third markers  110   111  and  112  on the image forming unit  130 , three-dimensional coordinates of the first to third markers  110   111  and  112  are calculated by using the first and second images of the first to third markers  110   111  and  112  formed on the image forming unit  130  through a processor  140  (S 1410 ). 
     Detailed explanation of calculating the three-dimensional coordinates of the first to third markers  110   111  and  112  is described below. 
     In order to calculate the three-dimensional coordinates of the first to third markers  110   111  and  112 , first, two-dimensional central coordinates are calculated through the processor  140  by using image forming positions of the first and second images of the first to third markers  110   111  and  112  formed on the image forming unit  130  (S 141 ). 
     Calculating the two-dimensional central coordinates of each of the markers  110   111  and  112  is explained in detail. For the convenience of explanation, in  FIGS. 5-6 , it will be described as an example in the case that the first to third markers  110   111  and  112  are arranged horizontally to the lens portion. And the beam splitter is omitted in the figure as it is explaining the case that the first to third markers  110   111  and  112  are arranged horizontally to the lens portion. 
     Also, as shown in  FIG. 1 , image forming positions of the second images of the first to third markers  110   111  and  112  is omitted since they are identical to a center line CL of the lens portion  120  in  FIGS. 5-6 , in which the second images are formed by the lights emitted from the second light source  150  toward the center of each of the markers  110   111  and  112 , reflected by the markers  110   111  and  112 , and flowed into the image forming unit  130  through the fourth to sixth optical paths AX 4  AX 5  and AX 6 . 
     As shown in  FIGS. 5-6 , the light emitted from the first light source  150  is reflected in different position of surfaces of each of the markers  110   111  and  112  through the first to third optical paths AX 1  AX 2  and AX 3 , and forms images on the image forming unit  130 . Therefore, the first images of the first to third markers  110   111  and  112  are formed in different positions to each other, in which the first images of the first to third markers  110   111  and  112  are formed by the light flowed in to the lens portion  120  which is emitted from the first light source  150 , reflected in different position of surfaces of each of the markers  110   111  and  112  through the first to third optical paths AX 1  AX 2  and AX 3 . 
     Therefore, the two-dimensional central coordinates of each of the markers  110   111  and  112  are calculated through the processor  140  by using the image forming positions of the first images of the first to third markers  110   111  and  112 , the image forming positions of the second maker images, the position information of the first and second light sources  150  and  151  which are pre-stored in the processor  140 , and radius information of the first to third markers  110   111  and  112 . 
     The process of calculating the two-dimensional central coordinates of the markers by the processor is described below. 
     As shown in  FIG. 7 , the two-dimensional central coordinates of the markers  110   111  and  112  is defined as x,y, a coordinate of a first light source  150  is defined as I 1 , J 1 , a coordinate of a second light source  151  is defined as I 2 , J 2 , a coordinate of a first image which is emitted from the first light source  150 , reflected by a first marker  110  and forming an image on an image forming unit  130 , is defined as U 1 , V 1 , a coordinate of a second image which is emitted from the second light source  151 , reflected by a first marker  110  and forming an image on an image forming unit  130 , is defined as U 2 , V 2 , a coordinate of a reflection position, in which the light emitted from the first light source  150  and reflected by the first marker  110 , is defined as x 1 ,y 1 , a coordinate of a reflection position, in which the light emitted from the second light source  151  and reflected by the first marker  110 , is defined as x 2 ,y 2 , a vector Ū from U 1 , V 1  to x 1 ,y 1 , vector  V  from U 2 , V 2  to x 2 ,y 2 , a vector Ī from I 1 , J 1  to x 1 ,y 1 , and a vector  J  from I 2 , J 2  to x 2 ,y 2  may be represented as a Formula 1. 
     
       
         
           
             
               
                 
                   
                     
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                                
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                   [ 
                   
                     Formula 
                      
                     
                         
                     
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                     3 
                   
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                                  
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                     
                 
               
             
           
         
       
     
     And referring to  FIGS. 7-8 , a coordinate x 1 ,y 1  which is the position that the light emitted from the first light source  150  (Referring to  FIG. 7 ) or the second light source  151  (Referring to  FIG. 7 ) is reflected by the first marker  110  may be within a radius r with a center portion x,y, a square of radius r may be represented as a Formula 4 since a summation of the vector which in inputted to x 1 ,y 1  is identical to a direction of a vector which connects x 1 ,y 1  with x,y which is a center portion of the first marker  110 , a vector  P  from x,y to x 1 ,y 1 , and a vector  Q  from x,y, to x 2 ,y 2  may be represented as a Formula 5. 
     
       
         
           
             
               
                 
                   
                     
                       
                         ( 
                         
                           X 
                           - 
                           x 
                         
                         ) 
                       
                       2 
                     
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                         ) 
                       
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                             2 
                           
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                         r 
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                   [ 
                   
                     Formula 
                      
                     
                         
                     
                      
                     4 
                   
                   ] 
                 
               
             
             
               
                 
                   
                     
                       P 
                       _ 
                     
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                                   x 
                                   1 
                                 
                               
                             
                             
                               
                                 
                                   y 
                                   1 
                                 
                               
                             
                           
                           ] 
                         
                         - 
                         
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                       _ 
                     
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                                   y 
                                   2 
                                 
                               
                             
                           
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                         - 
                         
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                     Formula 
                      
                     
                         
                     
                      
                     5 
                   
                   ] 
                 
               
             
           
         
       
     
     Meanwhile, and an error E of x, y, t 1 , and t 2  may be represented as a Formula 6 by using the four equations included in the Formula 4 and Formula 5. 
     
       
         
           
             
               
                 
                   E 
                   = 
                   
                     
                        
                       
                         
                           
                             ( 
                             
                               
                                 
                                   
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                                     _ 
                                   
                                   x 
                                 
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                                   1 
                                 
                               
                               - 
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                             ) 
                           
                           2 
                         
                         + 
                         
                           
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                                     _ 
                                   
                                   y 
                                 
                                 · 
                                 
                                   t 
                                   1 
                                 
                               
                               - 
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                             ) 
                           
                           2 
                         
                         - 
                         
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                           2 
                         
                       
                        
                     
                     + 
                     
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                               ( 
                               
                                 
                                   
                                     
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                                       _ 
                                     
                                     x 
                                   
                                   · 
                                   
                                     t 
                                     2 
                                   
                                 
                                 - 
                                 x 
                               
                               ) 
                             
                             2 
                           
                            
                           
                             
                               ( 
                               
                                 
                                   
                                     
                                       V 
                                       _ 
                                     
                                     y 
                                   
                                   · 
                                   
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                                     2 
                                   
                                 
                                 - 
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                               ) 
                             
                             2 
                           
                         
                         - 
                         
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                           2 
                         
                       
                        
                     
                     + 
                     
                        
                       
                         
                           P 
                           _ 
                         
                         × 
                         
                           
                             
                               U 
                               _ 
                             
                             + 
                             
                               I 
                               _ 
                             
                           
                           2 
                         
                       
                        
                     
                     + 
                     
                        
                       
                         
                           Q 
                           _ 
                         
                         × 
                         
                           
                             
                               V 
                               _ 
                             
                             + 
                             
                               J 
                               _ 
                             
                           
                           2 
                         
                       
                        
                     
                   
                 
               
               
                 
                   [ 
                   
                     Formula 
                      
                     
                         
                     
                      
                     6 
                   
                   ] 
                 
               
             
           
         
       
     
     Since x, y, t 1 , and t 2  are parameters of the Formula 6, the two-dimensional central coordinate of the first marker  110  is calculated by a processor  140 . 
     Two-dimensional central coordinates of second and third markers  111  and  112  are calculated by the processor  140  by repeating the process described above. 
     Meanwhile, a process of calculating a coordinate of a reflection position of a light which is emitted from the first light source  150  or the second light source  151  and reflected on a surface of a first marker  110  is described below. 
     As shown in  FIG. 9 , a radius of a first marker  110  is defined as r, a center portion of a lens portion  120  is defined as (0, 0), a position of a first light source  150  is defined as (0, d), a center portion of a first marker  110  (e, f), and a reflection position coordinate (x, y) in which a light emitted from the first light source  150  is reflected on a surface of a first marker  110 . 
       [Formula 7] 
       ( x−e ) 2 +( y−f ) 2   =r   2    (1)
 
         y =(tan θ−tan θ′)/(1+tan θ tan θ′)×−(tan θ−tan θ′)/(1+tan θ tan θ′)+ f    (2)
 
       y=tan θx   (3)
 
         y =((tan θ−(2 tan θ′/(1−tan θ′ 2 )))/(1+tan θ(2 tan θ′)/(1−tan θ′ 2 )))) x+d    (4)
 
     Therefore, a square of a radius of a first marker  110  may be represented as a Formula 7, and the Formula 1 is represented as equations (2)-(4) of the Formula 7, a coordinate of y-axis of a reflection position in which a light emitted from a first light source  150  is reflected on a surface of a first marker  110  by solving the equation (4) of the Formula 7. 
     Meanwhile, a coordinate of x-axis of a reflection position in which a light emitted from a first light source  150  is reflected on a surface of a first marker  110  by solving the equation (1) of the Formula 7. 
     Therefore, coordinates of reflection positions in which lights emitted from first and second light sources  150  and  151  and reflected on surfaces of a first to third makers  110   111  and  112  are calculated by repeating the process described above. 
     Then, three-dimensional coordinates of the first to third markers  110   111  and  112  are calculated through the processor  140  by using the two dimensional coordinates of the first to third markers  110   111  and  112  (S 142 ). 
     As described above, after calculating the three-dimensional coordinates of the makers  110   111  and  112 , spatial position information and direction information of a target  200  are calculated by comparing the three-dimensional coordinates of each of the markers  110   111  and  112  with geometric information, which is pre-stored in the processor  140 , between the markers  110   111  and  112  adjacent to each other (S 150 ). 
     Herein, the geometric information between the markers  110   111  and  112  adjacent to each other may be length information L 1  L 2  and L 3  virtually connecting the markers  110   111  and  112  adjacent to each other and angle information A 1  A 2  and A 3  formed by a pair of the straight lines which connect the markers  110   111  and  112  adjacent to each other. 
     In other words, spatial position information and direction information of a target  200  are calculated by comparing three-dimensional coordinates of each of the markers  110   111  and  112  with length information L 1  L 2  and L 3  virtually connecting the markers  110   111  and  112  adjacent to each other and angle information A 1  A 2  and A 3  formed by a pair of the straight lines which connect the markers  110   111  and  112  adjacent to each other, which are pre-stored in the processor  140 . 
     As described above, in a tracking system and a method using the same according to an embodiment of the present invention, one light source of a pair of light sources  150  and  151  which is positioned different to each other directly emits a light toward a specific point of a surface of each of the markers  110   111  and  112  and reflects the light toward a lens portion  120  such that first images of each of markers  110   111  and  112  are formed on an image forming unit  130 , the other light source emits a light such that the light is emitted toward a center of each of the markers  110   111  and  112  through a lens portion  120  and the light is re-reflected toward a lens portion  120 , and second images of each of makers  110   111  and  112  are formed on an image forming unit  130 , and therefore, a pair of images of each of markers  110   111  and  112  are formed on an image forming unit  140 . 
     In other words, three-dimensional coordinates of each of markers  110   111  and  112  are calculated by using one image forming unit  130  through a trigonometry since a pair of images of markers for each of markers  110   111  and  112  are formed on an image forming unit  130  positioned different to each other. 
     Therefore, in a tracking system and a method using the same according to an embodiment of the present invention, spatial position information and direction information of markers  110   111  and  113  which are attached on a target  200  are calculated by using only one image forming unit  130 . 
     Therefore, there is an effect of reducing a manufacturing cost of the tracking system with small and lightweight, and relatively low restriction of surgical space comparing with conventional tracking system. 
     It will be apparent to those skilled in the art that various modifications and variation can be made in the present invention without departing from the spirit or scope of the invention. Thus, it is intended that the present invention cover the modifications and variations of this invention provided they come within the scope of the appended claims and their equivalents.