WO2015183049A1 - 옵티컬 트래킹 시스템 및 옵티컬 트래킹 시스템의 마커부 자세 산출방법 - Google Patents
옵티컬 트래킹 시스템 및 옵티컬 트래킹 시스템의 마커부 자세 산출방법 Download PDFInfo
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T7/00—Image analysis
- G06T7/20—Analysis of motion
- G06T7/246—Analysis of motion using feature-based methods, e.g. the tracking of corners or segments
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T7/00—Image analysis
- G06T7/20—Analysis of motion
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T7/00—Image analysis
- G06T7/70—Determining position or orientation of objects or cameras
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T7/00—Image analysis
- G06T7/70—Determining position or orientation of objects or cameras
- G06T7/73—Determining position or orientation of objects or cameras using feature-based methods
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T2207/00—Indexing scheme for image analysis or image enhancement
- G06T2207/10—Image acquisition modality
- G06T2207/10056—Microscopic image
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T2207/00—Indexing scheme for image analysis or image enhancement
- G06T2207/30—Subject of image; Context of image processing
- G06T2207/30204—Marker
Definitions
- the present invention relates to an optical tracking system and a method of calculating a marker part of an optical tracking system, and more particularly, to an optical tracking system and a method of calculating a marker part of an optical tracking system using pattern information.
- an optical tracking system is used to track the position of a given object.
- the optical tracking system can be utilized to track an object in real time in equipment such as surgical robots.
- the optical tracking system typically includes a plurality of markers attached to a target object and imaging units for imaging light emitted by the markers, and mathematically calculating information obtained from the imaging units to obtain position information and the like. do.
- the conventional optical tracking system has a disadvantage in that the size of the equipment is increased by including a plurality of markers, and thus may be inappropriate in the case of tracking requiring small precision.
- an object of the present invention is to provide an optical tracking system that can accurately and easily track markers.
- Another problem to be solved by the present invention is to provide a method of calculating a marker part of an optical tracking system applicable to the optical tracking system.
- the optical tracking system includes a marker part, an imaging part, and a processing part.
- the marker unit includes a pattern having specific information and a first lens disposed to be spaced apart from the pattern and having a first focal length.
- the imaging unit includes a second lens having a second focal length and an imaging unit disposed to be spaced apart from the second lens, and the image of the pattern being formed by the first lens and the second lens.
- the processor determines a pose of the marker unit from a coordinate conversion equation between coordinates on the pattern surface of the pattern and pixel coordinates on the image of the pattern, and tracks the marker unit using the determined pose of the marker unit.
- the processing unit a first transformation for converting a first coordinate corresponding to the actual coordinates on the pattern surface of the pattern to a second coordinate corresponding to the three-dimensional local coordinates for the first lens of the marker unit Obtain a second transformation matrix for converting a matrix and a third coordinate corresponding to a three-dimensional local coordinate with respect to the second lens of the second coordinate to a fourth coordinate corresponding to a pixel coordinate on an image of the pattern of the imaging unit
- the coordinate transformation equation may be defined to convert the first coordinate into the fourth coordinate including the first transformation matrix and the second transformation matrix, and the processing unit may generate the posture of the marker unit from the coordinate transformation equation. It is possible to obtain a posture definition matrix that defines.
- the coordinate transformation equation may be defined by the following equation.
- the first transformation matrix may be defined by the following equation.
- the processor may obtain data of the first coordinate and the fourth coordinate from at least three captured images, and apply the obtained data to the following equation to calibrate values of u c , v c, and f b .
- the first transform matrix can be obtained by obtaining.
- the second transformation matrix may be defined by the following equation.
- the processing unit may obtain data of the first coordinates and the fourth coordinates from at least three captured images, and apply the obtained data to the following equation to obtain calibration values of f c , pw and ph. By doing so, the second transform matrix can be obtained.
- the processor may acquire a plurality of data for the first coordinate and the fourth coordinate, and obtain the posture definition matrix by the following equation to which the obtained plurality of data is applied.
- the processor may acquire a plurality of data for the first coordinate and the fourth coordinate, and obtain the posture definition matrix by the following equation to which the obtained plurality of data is applied.
- ((u 1 , v 1 ), ..., (u n , v n ) are the data of the first coordinate
- (u ' 1 , v' 1 ), ..., (u ' n , v' n ) are the Data of four coordinates
- (u ' c , v' c ) is the pixel coordinate on the image of the pattern corresponding to the center of the pattern
- f c is the second focal length
- pw is the width of the pixel of the image of the pattern
- ph is the height of the pixels of the image of the pattern
- a method of calculating a marker part attitude of an optical tracking system includes a pattern including a pattern having specific information and a first lens spaced apart from the pattern and having a first focal length ( and an imaging unit including a second lens having a second focal length and an imaging unit disposed to be spaced apart from the second lens and forming an image of the pattern by the first lens and the second lens.
- the method of calculating a marker part attitude of the optical tracking system includes converting a first coordinate corresponding to an actual coordinate on a pattern surface of the pattern into a second coordinate corresponding to a three-dimensional local coordinate with respect to the first lens of the marker part.
- the coordinate transformation equation may be defined by the following equation.
- the first transformation matrix may be defined by the following equation,
- the second transformation matrix may be defined by the following equation.
- the marker portion in an optical tracking system for tracking a marker portion, can be miniaturized by including a pattern of specific information so as to enable tracking, and by modeling the optical system of the marker portion and the image forming portion by coordinate transformation formula, Since the posture of the marker unit can be determined, accurate tracking of the marker unit can be possible in a simpler and easier way.
- FIG. 1 is a conceptual diagram illustrating an optical tracking system according to an embodiment of the present invention.
- FIG. 2 is a flowchart schematically illustrating a problem solving process required for a processing unit of the optical tracking system of FIG. 1 to determine a posture of a marker unit.
- FIG. 3 is a flowchart illustrating a process of modeling a system in the problem solving process of FIG. 2.
- FIG. 4 is a conceptual diagram illustrating a process of modeling the system of FIG. 3.
- FIG. 5 is a flowchart illustrating a process of calibrating a second transform matrix during the problem solving process of FIG. 2.
- FIG. 6 is a flowchart illustrating a process of calibrating a first transform matrix in the problem solving process of FIG. 2.
- FIG. 7 is a flowchart illustrating an example of a process of obtaining a posture definition matrix in the problem solving process of FIG. 2.
- FIG. 8 is a flowchart illustrating another example of a process of obtaining a posture definition matrix in the problem solving process of FIG. 2.
- FIG. 9 is a flowchart illustrating a method of calculating a marker posture of an optical tracking system according to an exemplary embodiment of the present invention.
- first and second may be used to describe various components, but the components should not be limited by the terms. The terms are used only for the purpose of distinguishing one component from another.
- the first component may be referred to as the second component, and similarly, the second component may also be referred to as the first component.
- FIG. 1 is a conceptual diagram illustrating an optical tracking system according to an embodiment of the present invention.
- the optical tracking system 100 includes a marker unit 110, an image forming unit 120, and a processing unit 130.
- the marker unit 110 includes a pattern 112 and a first lens 114.
- the pattern 112 has specific information.
- the specific information is information that can be recognized for tracking in the imaging unit 120, which will be described later.
- the one-dimensional pattern similar to a bar code and two similar to a QR code Dimensional patterns and the like.
- the first lens 114 is spaced apart from the pattern 112 and has a first focal length.
- the separation distance between the first lens 114 and the pattern 112 may allow the imaging unit 120, which will be described later, to image and track the pattern 112 even at a distance. It may be equal to the first focal length of (114).
- bundles of rays with respect to the pattern 112 passing through the first lens 114 may be parallel to each other.
- the first lens 114 may perform a function similar to that of an objective lens of a microscope.
- the marker unit 110 may not include a light source. In this case, the marker unit 110 may be used as a passive marker using an illumination located outside. Alternatively, the marker unit 110 may include a light source. In this case, the marker unit 110 may be used as an active marker using self illumination.
- the imaging unit 120 includes a second lens 122 and an imaging unit 124.
- the second lens 122 has a second focal length.
- the second lens 122 may perform a function similar to that of the eyepiece of the microscope, for example.
- the imaging unit 124 is spaced apart from the second lens 122 and the image of the pattern 112 is formed by the first lens 114 and the second lens 122.
- the separation distance between the imaging unit 124 and the second lens 122 may form an optical bundle for the pattern 112 parallel to each other through the first lens 114.
- the second focal length may be the same as the second focal length of the second lens 122.
- the imaging unit 124 may include an image sensor such as a charge coupled device (CCD), a complementary metal-oxide semiconductor (CMOS), or the like.
- the processor 130 determines the posture of the marker unit 110 from a coordinate conversion equation between coordinates on the pattern surface of the pattern 112 and pixel coordinates on the image of the pattern 112.
- the processor 130 tracks the marker unit 110 using the determined posture of the marker unit 110.
- the processing unit 130 may include, for example, a computer or more specifically a central processing unit (CPU).
- FIG. 2 is a flowchart schematically illustrating a problem solving process required for a processing unit of the optical tracking system of FIG. 1 to determine a posture of a marker unit.
- system modeling is performed on the optical tracking system 100 having the above-described configuration (S100).
- the coordinate transformation between the coordinates on the pattern surface of the pattern 112 and the pixel coordinates on the image of the pattern 112 is based on the optical system of the optical tracking system 100. Since it is made by, by modeling the coordinate transformation according to the optical system of the optical tracking system 100 can set the coordinate transformation equation. In this case, the coordinate transformation according to the optical system of the optical tracking system 100 may be modeled by the optical system of each of the marker unit 110 and the image forming unit 120 and the relationship between them.
- Coordinates on the pattern surface of the pattern 112 shown in FIG. 1 are first coordinates, three-dimensional coordinates of the first lens 114 of the first coordinates are second coordinates, and the second coordinates of the second coordinates.
- the first transformation matrix is The matrix transforms the first coordinates into the second coordinates
- the second transform matrix is a matrix converting the third coordinates into the fourth coordinates.
- the coordinate transformation equation obtained as a result of the system modeling is determined by equations for various parameters of the optical system of the marker unit 110 and the imaging unit 120 shown in FIG. 1, but the parameters cannot be accurately obtained. Since the value may change due to mechanical arrangement, etc., more accurate system modeling may be possible by calibrating the first and second transformation matrices.
- the posture refers to the direction in which the marker unit 110 is directed
- the posture definition matrix is a matrix that provides information on the posture of the marker unit 110, and the marker unit 110 from the posture definition matrix. Roll, pitch, yaw, and the like.
- FIG. 3 is a flowchart illustrating a system modeling process of the problem solving process of FIG. 2, and FIG. 4 is a conceptual diagram illustrating a process of modeling the system of FIG. 3.
- the center point of the first lens 114 is referred to as the first center point A
- the center point of the second lens 122 is called the second center point O
- any point on the pattern 112 is referred to as B.
- the light passing through the first center point A of the first lens 114 goes straight and the light passing through the first center point A meets the second lens 122.
- the point D is refracted by the second lens 122 at the point D and formed at the imaging unit 124 is E.
- the light passing through the first center point A of the first lens 114 and passing through the second center point O of the second lens 122 goes straight, and the point where the light meets the extension line of the line segment DE is referred to as C. .
- the equation of a straight line for the line segment AO (or line AC)
- the coordinate of the first center point A is set to (X, Y, Z), and the coordinate of the second center point O is set to (0,0,0), which is the origin. Since the coordinate of the second center point O of the second lens 122 is set as the origin, the three-dimensional local coordinate system for the second lens 122 is the same as the world coordinate system.
- the coordinates of the pixels (corresponding to the point E) of the image of the pattern 112 formed in the phase are set to (u ', v').
- the coordinates (u, v) and (u c , v c ) may be set based on, for example, the upper left side of the pattern 112, and the coordinates (u ′, v ′) are, for example, the pattern ( 112 may be set based on the upper left side of the image.
- the imaging unit 124 when the imaging unit 124 is positioned at the focal length f c of the second lens 122, the z-axis coordinate of the imaging unit 124 is -f c .
- the equation of straight line L1 is found from line segment AO, where the position of point C is obtained.
- the equation of straight line L2 is found from line segment AB, where the position of point D is obtained.
- the equation for straight line L3 is found from line segment DC.
- the attitude definition matrix defining the attitude of the marker unit 110 is defined as a 3 * 3 matrix [R], and each component of the matrix [R] is r 11 , r 12 , r 13 , r 21 , r 22 ,
- the world coordinate of point B is the pattern coordinate (u, v) of point B, and the focal length f b of the matrix [R] and the first lens 114.
- the pixel coordinates (u ', v') of the point E can be represented by the pattern coordinates (u, v) of the point B, the pattern 112 corresponding to the point B and the pattern corresponding to the point E You can define the relationship between images.
- the relational expression may be represented by a matrix equation as shown in Equation 1 below, and the matrix equation regarding the coordinate transformation may be set as the coordinate transformation formula.
- (u, v) is the first coordinate
- (u ', v') is the fourth coordinate
- [C] is the first transformation matrix
- [A] is the second transformation matrix
- [R] Means the posture definition matrix.
- (u c , v c ) is the coordinate on the pattern surface of the center of the pattern
- f b is the first focal length
- f c is the second focal length
- pw is the width of the pixel of the image of the pattern
- ph Is the height of the pixels of the image of the pattern.
- i is a predetermined i-th pattern.
- the coordinate transformation equation consists of the product of the first and second transformation matrices and the attitude definition matrix described in FIG. 1.
- the actual coordinates on the pattern surface of the pattern 112 are the first coordinates ((u, v)), and the first lens of the first coordinates.
- 3D local coordinates (114) for the second coordinates 3D local coordinates (same as the world coordinates) for the second lens 122 of the second coordinates of the third coordinates, and the image forming unit
- the coordinate transformation formula is used to convert the first coordinates to the second coordinates.
- [A] [which is a product of a transformation matrix [C], a posture definition matrix [R] for converting the second coordinates to the third coordinates and a second transformation matrix [A] for converting the third coordinates to the fourth coordinates R] [C].
- the calibration is first performed on the second transform matrix, and then performed on the first transform matrix.
- FIG. 5 is a flowchart illustrating a process of calibrating a second transform matrix during the problem solving process of FIG. 2.
- a matrix [B] and a matrix [H] are defined to facilitate mathematical analysis for calibration (S210).
- Equation 2 when the matrix [B] is defined using the second transform matrix [A], it is represented by Equation 2, and the first transform matrix [C] and the second transform matrix [A] are defined. And a matrix [H] using the posture definition matrix [R], as shown in Equation 3 below.
- Equation 4 is obtained by multiplying both sides of Equation 3 by A ⁇ 1 .
- the matrix [B] can be defined as in Equation 5.
- ⁇ -f c / pw
- ⁇ -f c / ph
- f c is the focal length of the second lens 122 of the imaging unit 120
- pw and ph are the width and height of the pixel, respectively it means.
- the column vectors b and v ij are defined using Equation 6 using nonzero components of the matrix [B].
- Equation 7 Using the orthogonality of the matrix [R] in Equation 6, Equation 7 can be obtained.
- the column vector b may be obtained by using a method such as singular value decomposition (SVD). Finding the column vector b gives us all the components of the matrix [B].
- SVD singular value decomposition
- the matrix through a formula (8) to know all of the components of the [B] v 'c, ⁇ , ⁇ , u' can be obtained c (representing the ⁇ , ⁇ as a parameter).
- the first transform matrix [C] is calibrated using the second transform matrix [A] previously calibrated.
- FIG. 6 is a flowchart illustrating a process of calibrating a first transform matrix in the problem solving process of FIG. 2.
- the calibrated matrix [A] is substituted into the matrix [H] to obtain a matrix [R] (S250).
- Equation 10 is obtained by substituting the second transform matrix [A] of Equation 9 into Equation 3 and arranging [R] [C] of Equation 1.
- the product of the matrix [A] and the matrix [R] is defined as the matrix [HK], substituted into the coordinate transformation equation of Equation 1, and arranged to be composed of the components of the matrix [HK] and the matrix [C].
- the matrix [HK] can be obtained by using the matrix [A] obtained from Equation 9 and the matrix [R] obtained from Equation 11, and when applied to the coordinate conversion equation of Equation 1, the matrix [HK] and the matrix [ Equation 12 consisting of the components of C] is obtained.
- the matrix [AA], the matrix [BB], and the matrix [CC] can be defined using Equation 13 using the matrix [HK].
- FIG. 7 is a flowchart illustrating an example of a process of obtaining a posture definition matrix in the problem solving process of FIG. 2.
- Equation 14 can be obtained by setting this as an equation.
- the matrix [H] is obtained using, for example, a method such as singular value decomposition (SVD) (S320a).
- SVD singular value decomposition
- Equation 15 is obtained.
- Equation 15 2n equations of Equation 15 are obtained using a method such as singular value decomposition (SVD) as an example.
- SVD singular value decomposition
- the posture definition matrix may be obtained in other ways.
- FIG. 8 is a flowchart illustrating another example of a process of obtaining a posture definition matrix in the problem solving process of FIG. 2.
- Equation 16 is obtained.
- the matrix [R] is obtained using, for example, a method such as singular value decomposition (SVD) (S330b).
- SVD singular value decomposition
- Equation 16 2n equations of Equation 16 are obtained using a method such as singular value decomposition (SVD).
- SVD singular value decomposition
- the posture of the marker unit 110 may be calculated by applying the system modeling process and the method of obtaining the posture definition matrix [R] to the optical tracking system 100 shown in FIG. 1.
- FIG. 9 is a flowchart illustrating a method of calculating a marker posture of an optical tracking system according to an exemplary embodiment of the present invention.
- the processor 130 first calibrates first and second transform matrices from at least three images (S510).
- the calibration is substantially the same as the process of step S200 described in FIG. 2 and the steps S210 to S280 described in detail in FIGS. 5 and 6, and the processing unit 130 includes steps S230 and S280 of the process.
- the first and second transformation matrices may be calibrated using only the final equation for calibration.
- an attitude definition matrix is obtained from a coordinate transformation equation including the first and second transformation matrices (S520).
- the attitude definition matrix is substantially the same as the process of step S300 described in FIG. 2, steps S310 to S330a, and steps S310 to S330b described in detail with reference to FIGS. 7 and 8, and the processing unit 130.
- the attitude definition matrix may be obtained using only the final equation for acquiring the attitude definition matrix as in steps S320a and S320a, or step S320b.
- the processor 130 preliminarily obtains a first transformation matrix for converting the first coordinates to the second coordinates and a second transformation matrix for converting the third coordinates to the fourth coordinates in advance. From the coordinate transformation equation, an attitude definition matrix defining the attitude of the marker unit 110 may be obtained.
- the posture of the marker unit 110 may be obtained by obtaining the posture definition matrix.
- the roll, pitch, yaw, and the like of the marker unit 110 may be grasped from the posture defining matrix.
- the marker portion including the pattern of the specific information can be miniaturized so that the tracking is possible, and the optical system of the marker portion and the image forming unit coordinate conversion type Since the posture of the marker may be determined by modeling, it may be possible to accurately track the marker in a simpler and easier manner.
- optical tracking system 110 marker portion
- Pattern 114 First lens
- imaging portion 122 second lens
- imaging unit 130 processing unit
Abstract
Description
Claims (12)
- 특정정보를 갖는 패턴(pattern) 및 상기 패턴으로부터 이격되어 배치되며 제1 초점거리를 갖는 제1 렌즈를 포함하는 마커(marker)부;제2 초점거리를 갖는 제2 렌즈 및 상기 제2 렌즈로부터 이격되어 배치되며 상기 제1 렌즈와 상기 제2 렌즈에 의하여 상기 패턴의 이미지가 결상되는 결상유닛을 포함하는 결상부; 및상기 패턴의 패턴면 상의 좌표와 상기 패턴의 이미지 상의 픽셀좌표 사이의 좌표변환식으로부터 상기 마커부의 자세를 결정하고, 결정된 상기 마커부의 자세를 이용하여 상기 마커부를 트래킹하는 처리부를 포함하는 옵티컬 트래킹 시스템.
- 제1항에 있어서,상기 처리부는, 상기 패턴의 패턴면 상의 좌표에 해당하는 제1 좌표를 상기 마커부의 상기 제1 렌즈에 대한 3차원적 좌표에 해당하는 제2 좌표로 변환하는 제1 변환행렬 및 상기 제2 좌표의 상기 제2 렌즈에 대한 3차원적 좌표에 해당하는 제3 좌표를 상기 결상부의 상기 패턴의 이미지 상의 픽셀좌표에 해당하는 제4 좌표로 변환하는 제2 변환행렬을 획득하고,상기 좌표변환식은 상기 제1 변환행렬 및 상기 제2 변환행렬을 포함하여 상기 제1 좌표를 상기 제4 좌표로 변환하도록 정의되며,상기 처리부는 상기 좌표변환식으로부터 상기 마커부의 자세를 정의하는 자세정의행렬을 획득하는 것을 특징으로 하는 옵티컬 트래킹 시스템.
- 제4항에 있어서, 상기 처리부는,적어도 3개 이상의 촬영 이미지로부터 uc, vc 및 fb의 캘리브레이션 값을 획득함으로써 상기 제1 변환행렬을 획득하는 것을 특징으로 하는 옵티컬 트래킹 시스템.
- 제6항에 있어서, 상기 처리부는,적어도 3개 이상의 촬영 이미지로부터 fc, pw, ph의 캘리브레이션 값을 획득함으로써 상기 제2 변환행렬을 획득하는 것을 특징으로 하는 옵티컬 트래킹 시스템.
- 제3항에 있어서, 상기 처리부는,상기 제1 좌표 및 상기 제4 좌표에 대한 복수의 데이터를 획득하고, 상기 획득된 복수의 데이터가 적용된 하기 수학식에 의하여 상기 자세정의행렬을 획득하는 것을 특징으로 하는 옵티컬 트래킹 시스템.((u1,v1), …, (un,vn)은 상기 제1 좌표의 데이터, (u'1,v'1), …, (u'n,v'n)은 상기 제4 좌표의 데이터, (u'c,v'c)는 상기 패턴의 중심에 대응하는 상기 패턴의 이미지 상의 픽셀좌표, fc는 상기 제2 초점거리, pw는 상기 패턴의 이미지의 픽셀의 폭, ph는 상기 패턴의 이미지의 픽셀의 높이)
- 특정정보를 갖는 패턴(pattern) 및 상기 패턴으로부터 이격되어 배치되며 제1 초점거리를 갖는 제1 렌즈를 포함하는 마커(marker)부, 및 제2 초점거리를 갖는 제2 렌즈 및 상기 제2 렌즈로부터 이격되어 배치되며 상기 제1 렌즈와 상기 제2 렌즈에 의하여 상기 패턴의 이미지가 결상되는 결상유닛을 포함하는 결상부를 포함하여, 상기 마커부를 트래킹하도록 상기 마커부의 자세를 산출하기 위한 옵티컬 트래킹 시스템의 마커부 자세 산출방법에 있어서,상기 패턴의 패턴면 상의 좌표에 해당하는 제1 좌표를 상기 마커부의 상기 제1 렌즈에 대한 3차원적 좌표에 해당하는 제2 좌표로 변환하는 제1 변환행렬 및 상기 제2 좌표의 상기 제2 렌즈에 대한 3차원적 좌표에 해당하는 제3 좌표를 상기 결상부의 이미지 상의 픽셀좌표에 해당하는 제4 좌표로 변환하는 제2 변환행렬을 획득하는 단계; 및상기 제1 변환행렬 및 상기 제2 변환행렬을 포함하며, 상기 제1 좌표를 상기 제4 좌표로 변환하는 좌표변환식으로부터 상기 마커부의 자세를 정의하는 자세정의행렬을 획득하는 단계를 포함하는 옵티컬 트래킹 시스템의 마커부 자세 산출방법.
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