KR20170123390A - Three-dimensional calibrator for measuring of 3D alignment error and method for measuring of 3D alignment error using thereof - Google Patents

Abstract

The present invention relates to a stereoscopic calibrator where cross sections are formed in a plurality of layers, and a plurality of holes are placed at regular intervals in each layer. The present invention also relates to a three-dimensional (3D) arrangement error calculation method using the stereoscopic calibrator, which can rapidly and easily calculate a 3D arrangement error value to a relevant device by calculating a rotation matrix and a motion vector on a 3D coordinate point where the central line of holes formed on the stereoscopic calibrator meets the top surface thereof. In the stereoscopic calibrator for 3D arrangement error measurement, a plurality of holes are formed on a stereoscopic plate of which cross sections are formed in a plurality of layers. The stereoscopic plate is formed by integrating a second circular plate with a second diameter smaller than a first diameter into a first circular plate with the first diameter, and has a plurality of hole straps, where a fixed number of holes are separately placed at positions separated from the central point of the stereoscopic plate at regular intervals, with different distances from the central point from one another.

Description

TECHNICAL FIELD [0001] The present invention relates to a three-dimensional calibrator for measuring three-dimensional alignment errors, and a three-dimensional alignment error calculation method using the three-

The present invention relates to a three-dimensional calibrator for measuring a three-dimensional alignment error in which a plurality of holes are arranged at regular intervals in a multilayered cross-section, and a three-dimensional calibrator for measuring a three- Dimensional alignment error using a three-dimensional calibrator for calculating a three-dimensional alignment error, which enables a quick and easy calculation of a three-dimensional alignment error value for a corresponding device by calculating a rotation matrix and a movement vector.

Generally, a method of acquiring three-dimensional data of a scan object having a three-dimensional shape includes a method of digitizing a three-dimensional coordinate point by a mechanical method using a touching method,

Optical triangulation, an optical method of obtaining a three-dimensional image by scanning, is well known.

The three-dimensional scanner using the photo-trigonometry generally includes a sensor head that scans (irradiates) a laser beam in the form of a sheet beam to a subject and maintains the laser beam at a constant angle and captures the image with a high-speed image camera, And an image processing unit for receiving the image and generating three-dimensional data through image analysis.

At this time, accurate distance data must be calculated in order to generate three-dimensional data in a three-dimensional scanner. Accordingly, the 3D scanner is provided with a 3D camera that provides a three-dimensional image including distance information.

However, an error due to the mounting of the 3D scanner equipped with the 3D camera and an error due to the offset value of the 3D camera itself may occur.

Accordingly, before obtaining the three-dimensional image of the object in the three-dimensional scanner, the alignment error for the 3D camera is calculated in advance, and a correcting value corresponding to the error is applied to the three- A method of obtaining an image is used.

On the other hand, as a method of calculating a three-dimensional alignment error, a method of photographing a calibrator made of a plane having a chessboard pattern and mathematically calculating a three-dimensional error value from a two-dimensional photographed image of the calibrator is used.

However, in order to calculate the three-dimensional coordinate values using the two-dimensional coordinate values of the calibrator having the chessboard pattern, the mathematical algorithms are complicated and require a large error calculation time.

In addition, when applying to a 3D scanner equipped with a 3D camera using a calibrator having a two-dimensional chessboard pattern, coordinate values corresponding to distance values can not be obtained, so that it is impossible to calculate a three-dimensional error value.

1. Korean Patent Publication No. 2014-0054590 (entitled " Camera Calibration Method and Apparatus) 2. Korean Patent Registration No. 10-1373604 (entitled "Camera Calibration Method Using Multiple Correction Techniques and Image System Applied to It)

Accordingly, the present invention provides a three-dimensional calibrator for three-dimensional alignment error calculation in which a plurality of sections are formed in multiple layers and a plurality of holes are arranged at regular intervals in each layer, Dimensional alignment error using a three-dimensional calibrator which can calculate a three-dimensional alignment error value for a corresponding device by calculating a rotation matrix and a motion vector for a point.

According to an aspect of the present invention, there is provided an apparatus for forming a plurality of holes on a solid plate having a multi-layered cross section, the solid plate having a first diameter smaller than a first diameter on a first circular plate having a first diameter, And a second ring plate having a first diameter and a second diameter are integrally connected to each other, wherein a hole band spaced from the center point of the three-dimensional plate by a predetermined number of holes is spaced apart from the center point of the three- Dimensional calibrated error measurement is provided. The three-dimensional calibator for three-dimensional alignment error measurement is configured to have a plurality of distances.

The stereoscopic plate is configured to form first through third hole bands, and at least one of the first through third hole bands is formed in each layer of the stereoscopic plate. A stereoscopic calibrator for alignment error measurement is provided.

The three-dimensional calibrator for three-dimensional alignment error measurement is characterized in that the holes of the different holes are arranged on straight extension lines with respect to the center point of the three-dimensional plate.

According to another aspect of the present invention, there is provided a stereoscopic calibrator comprising: a stereoscopic calibrator having a plurality of cross-sections and a plurality of holes formed in each layer, A method for calculating a three-dimensional alignment error using a stereoscopic calibrator for calculating a 3D alignment error of a camera provided in an image processing terminal using a captured image of a stereoscopic calibrator, the method comprising: Dimensional coordinate system based on the camera position in the image processing terminal, a point on the rotation axis of the rotation stage on which the three-dimensional calibrator is located at the shortest distance from the origin of the 3D coordinate system, To the origin of the coordinate system, A third step of setting the origin of the 3D coordinate system to be located on the X-axis of the S-coordinate system at the processing terminal, a fourth step of calculating a 3D error matrix for converting the coordinates of the hole based on the stereoscopic- A fifth step of acquiring X-axis and Z-axis coordinate values and a rotation angle with respect to each hole center of the stereoscopic calibrator from the rotation image acquired in the first step at the image processing terminal, A sixth step of calculating a final 3D error matrix based on the coordinate values of the X and Z axes based on the 3D coordinate system for each of the holes, the rotation angle, and the hole coordinate values based on the W coordinate system corresponding thereto, And a seventh step of calculating a 3D alignment error value based on the final 3D error matrix. A method of calculating a column error is provided.

Also, the coordinate value of the hole is set to a specific point coordinate value at which the center vertical center line of the hole meets the horizontal line of the top surface of the stereolithography plate. A three-dimensional alignment error calculating method using the stereoscopic calibrator is provided.

여기서, R은 회전관련 행렬로, 는 S 좌표계를 기준으로 3D 좌표계에서의 회전 행렬이고,

는 S_O 좌표계(회전축 초기상태 좌표계)를 기준으로 W 좌표계에서의 회전 행렬이며, t는 이동벡터 성분으로

는 S 좌표계 원점에서 3D 좌표계의 원점까지의 이동행렬이고,

는 S₀ 좌표계 원점에서 W좌표계 원점까지의 이동행렬임.In the fourth step, the 3D error matrix is composed of a rotation-related matrix R and a motion vector component t, and is set according to the following equation: < EMI ID = do.

Here, R denotes a rotation-related matrix, Is a rotation matrix in the 3D coordinate system with respect to the S coordinate system,

Is a rotation matrix in the W coordinate system based on the S _O coordinate system (initial state coordinate system of the rotation axis), t is a motion vector component

Is the movement matrix from the origin of the S-coordinate system to the origin of the 3D coordinate system,

Is a movement matrix from the origin of the S ₀ coordinate system to the origin of the W coordinate system.

3D 좌표계에서의 좌표값[X,Y,Z,1}은 하기 수학식과 같이 변환되며,

상기 제7 단계에서 상기 영상처리단말은 각 홀에 대해 하기의 수학식 결과값이 최소가 될때의 변수값을 산출하는 것을 특징으로 하는 입체형 캘리브레이터를 이용한 3차원 정렬 오차 산출방법이 제공된다.

여기서, i 는 홀의 수에 대응되는 수로 설정되고, 상기 γ11,γ12, ...γ33 은 3×3 형태의 행렬로 표현되는 회전 관련 행렬에 대응되는 성분값이며, t1,t2,t3 는 3×1 형태의 벡터로 표현되는 이동벡터 관련 벡터에 대응되는 성분값임.When the vector component for any point in the 3D coordinate system is (X, Y, Z, 1) and the vector component for any point in the W coordinate system is (x, y, z, 1), the 3D error matrix (X _3D ) is transformed into a matrix form as shown in the following equation,

The coordinate values [X, Y, Z, 1} in the 3D coordinate system are transformed as shown in the following equation,

In the seventh step, the image processing terminal calculates a variable value when a result of the following equation is minimized for each hole, and a three-dimensional alignment error calculating method using the stereoscopic calibrator is provided.

Here, i is set to a number corresponding to the number of holes, and 粒 11, 粒 12, ..., 粒 33 are component values corresponding to a rotation-related matrix expressed by a 3x3 matrix, and t1, t2, A component value corresponding to a motion vector-related vector represented by a vector of one form.

According to the present invention, it is possible to quickly and easily calculate a three-dimensional alignment error value using the three-dimensional minutiae coordinate values obtained from the photographed image of the three-dimensional calibrator.

Therefore, it is possible to acquire the three-dimensional data of the object to be scanned having the three-dimensional shape more quickly and accurately in the three-dimensional scanner.

BRIEF DESCRIPTION OF THE DRAWINGS Fig. 1 is a schematic view of a three-dimensional alignment error calibration apparatus using a three-dimensional calibrator to which the present invention is applied; Fig.
Figure 2 illustrates the structure of the stereoscopic calibrator 100 shown in Figure 1;
3 is a flowchart illustrating a three-dimensional alignment error calculation method using the stereoscopic calibrator according to the present invention.
FIG. 4 is a diagram for explaining a reference coordinate system setting method in FIG. 3; FIG.
FIG. 5 is a diagram for explaining a method of setting a rotation matrix R in FIG. 3; FIG.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS The present invention will now be described in detail with reference to the accompanying drawings. It is to be noted that like elements in the drawings are denoted by the same reference numerals whenever possible. It should be understood, however, that the terminology or words of the present specification and claims should not be construed in an ordinary sense or in a dictionary, and that the inventors shall not be limited to the concept of a term It should be construed in accordance with the meaning and concept consistent with the technical idea of the present invention based on the principle that it can be properly defined. Therefore, the embodiments described in the present specification and the configurations shown in the drawings are merely the most preferred embodiments of the present invention, and not all of the technical ideas of the present invention are described. Therefore, It is to be understood that equivalents and modifications are possible.

FIG. 1 is a diagram showing a schematic configuration of a three-dimensional alignment error calibration apparatus using a three-dimensional calibrator to which the present invention is applied.

As shown in FIG. 1, the apparatus for calibrating a three-dimensional alignment error using a three-dimensional calibrator according to the present invention includes a three-dimensional calibrator 100 and an image processing terminal 200. At this time, the image processing terminal 200 may be various types of terminals for acquiring three-dimensional image information, and may be a three-dimensional scanner or the like.

The three-dimensional calibrator 100 has a plurality of holes formed on a plate having a multi-layered cross-section.

FIG. 2 is a plan view of the three-dimensional calibrator 100, FIG. 2 (B) is a perspective view of the three-dimensional calibrator 100, FIG.

As shown in FIG. 2, the three-dimensional calibrator 100 is constructed by arranging a plurality of holes 120 on a multi-layered solid plate having a different thickness in cross section, more specifically, a circular plate 110. The circular plate 110 has a first circular plate 111 having a first diameter and a second circular plate 112 having a second diameter smaller than the first circular plate 111 at a central portion of the upper surface of the first circular plate 111 ) Are integrally combined.

2, a plurality of holes 120 are disposed at a predetermined distance from a center point O of the first and second circular plates 111 and 112 to have a predetermined radius to form a circular hole band, The hole bands are configured to form a plurality of, e.g., first through third hole bands having different radii from the center point O. At this time, the number of the holes 120 forming the first to third hole bands is set to be the same. In FIG. 2, one hole band is shown to be composed of eight holes 120, but each hole band can be formed of at least four holes 120, and as the number of holes 120 increases, It is preferable that the error measurement is appropriately set in consideration of the processing environment depending on the size of the circular plate 110 and the interval between the holes.

In addition, the holes 120 arranged in the plurality of hole bands are sequentially formed so as to be positioned on a straight line extending from the center point O of the circular plate 110.

1, the image processing terminal 200 basically comprises a camera 210 and an image processing unit 220. That is, the image processing terminal 200 captures an image of the stereoscopic calibrator 100 through the camera 210, and the image processing unit 220 analyzes the stereoscopic calibrator image, The 3D alignment error is calculated. At this time, the camera 210 may be a 3D camera. The 3D camera alignment error calculation process performed by the image processing unit 220 will be described in more detail in the following description of the operation.

FIG. 3 is a flowchart illustrating a method of calculating a three-dimensional alignment error using the stereoscopic type calibrator according to the present invention.

First, a stereoscopic calibrator 100 having a structure as shown in FIG. 2 is mounted on a rotation stage (not shown), and the image processing terminal 200 is disposed at a position spaced apart from the stereoscopic calibrator 100 by a predetermined distance .

 In the above-described state, the rotary stage equipped with the three-dimensional calibrator 100 is rotationally driven, and the image processing terminal 200 photographs the three-dimensional calibrator 100 through the camera 210, (ST10).

Next, the image processing terminal 200 sets a reference coordinate system for alignment error correction for the camera 210 provided therein (ST20). 4, the image processing terminal 200 includes a 3D coordinate system (hereinafter referred to as a 3D coordinate system), a stereoscopic calibrator coordinate system (hereinafter referred to as a W coordinate system), a rotation axis initial state coordinate system (Hereinafter referred to as "S ₀ coordinate system") and a rotation axis coordinate system (hereinafter referred to as S coordinate system). Here, the 3D coordinate system is a space-based coordinate system corresponding to the position of the camera 210 provided in the image processing terminal 200, and the S ₀ coordinate system is fixedly set in advance as a rotation axis initial coordinate system of the rotation stage.

)을 수학식 1과 같이 정의하고, 이동벡터(

)는 수학식2와 같이 정의하였다.The image processing terminal 200 sets a rotation matrix R and a motion vector t to be applied to the stereoscopic calibrator 100 based on the coordinate system defined as described above (ST30). For 3D alignment error correction, the rotation matrix (R) and motion vector (t) should be calculated. 5 (X), the inventors of the present invention calculate the rotation matrix of the posture in the B coordinate system on the basis of the arbitrary A coordinate system

) Is defined as Equation (1), and a motion vector

) Is defined as Equation (2).

Where l is the x-axis vector in the B-coordinate system described on the A-coordinate system basis, m is the y-axis vector in the B-coordinate system described on the A-coordinate system basis, and n is the y- It is a vector. The positions of subscripts related to the rotation matrix R and the motion vector t described in the present specification are set as described above.

)는 A 좌표계 기준으로 A 좌표계 원점에서 B 좌표계 원점으로의 벡터이다.Here, the motion vector (

) Is a vector from the origin of the A coordinate system to the origin of the B coordinate system based on the A coordinate system.

)은 오일러 각(α,β,γ)으로 생성된 회전행렬(R)로 표현하면 수학식 3과 같이 나타낼 수 있다. 이때, 상기 α,β,γ는 각각 x,y,z축의 회전각을 나타낸다.Further, the rotation matrix (

) Can be represented by a rotation matrix R generated by Euler angles (?,?,?) As shown in Equation (3). Here,?,?, And? Represent the rotation angles of the x, y, and z axes, respectively.

As described above, in a state where the rotation matrix R and the motion vector t are defined as in Equations (1) to (3), the image processing terminal 200, as shown in (Y) , The point on the rotation axis of the rotary plate stage on which the three-dimensional calibrator located at the shortest distance from the origin of the 3D coordinate system is disposed is set as the origin of the S-coordinate system (ST40). At this time, an arbitrary point (x _3D ) defined on the basis of the 3D coordinate system is converted to the point (x _S ) as shown in Equation (4).

Also, x _s0 can be expressed by Equation (5).

)는 S 좌표계 기준으로 S 좌표계 원점에서 3D 좌표계 원점까지의 벡터이며, 수학식6과 같이 정의될 수 있다.Then, the image processing terminal 200 sets the origin of the 3D coordinate system to be positioned on the X-axis of the S-coordinate system (ST50). That is,

) Is a vector from the S-coordinate system origin to the 3D coordinate system origin based on the S-coordinate system, and can be defined as shown in Equation (6).

The image processing terminal 200 calculates a 3D error matrix for transforming the coordinates of the hole 120 defined on the basis of the stereoscopic calibrator 100 on the basis of the 3D coordinate system (ST60). That is, the relational expression for transforming from Equations (4) and (5) is defined as Equation (7).

는 S 좌표계를 기준으로 3D 좌표계에서의 회전 행렬이고,

는 S_O좌표계(회전축 초기상태 좌표계)를 기준으로 W 좌표계에서의 회전 행렬이며, t는 이동벡터 성분으로

는 S 좌표계 원점에서 3D 좌표계의 원점까지의 이동행렬이고,

는 S₀ 좌표계 원점에서 W좌표계 원점까지의 이동행렬이다.Here, R denotes a rotation-related matrix,

Is a rotation matrix in the 3D coordinate system with respect to the S coordinate system,

Is a rotation matrix in the W coordinate system based on the S _O coordinate system (initial state coordinate system of the rotation axis), t is a motion vector component

Is the movement matrix from the origin of the S-coordinate system to the origin of the 3D coordinate system,

Is a movement matrix from the origin of the S ₀ coordinate system to the origin of the W coordinate system.

, R,

)은 3×3 행렬 형태로 표현되고, 이동벡터 관련 행렬(

,

)은 3×1 벡터 형태로 표현된다. 여기서, "T"는 전치행렬(transpose)을 의미한다. In this case, the rotation related matrix (

, R,

) Are expressed in the form of a 3x3 matrix, and a motion vector-related matrix (

,

) Is expressed in the form of a 3x1 vector. Here, "T" means transpose.

Therefore, the relational expression for converting the minutiae calibrator 100 minutiae coordinate values on the basis of the 3D coordinate system can be expressed by Equation (8). At this time, the transforming relation has coordinate values of (X, Y, Z, 1) on the basis of the 3D coordinate system with respect to the minutiae of each hole 120 and minutia coordinate values based on the stereoscopic calibrator 100 coordinate system (Xw) (x, y, z, 1), and can be expressed as a 4 × 4 3D error matrix as shown in Equation (8).

Here,? 11,? 12, ...,? 33 are component values corresponding to a rotation-related matrix expressed by a 3x3 matrix, and t1, t2, and t3 correspond to movement related vectors expressed by a 3x1 vector Lt; / RTI >

Then, the image processing terminal 200 acquires a minutiae image from the rotated image of the stereoscopic calibrator 100 photographed through the camera 210 in step ST10 (ST70). At this time, the minutiae point is set to a point where the vertical center line of the center of the hole 120 of the stereoscopic calibrator 100 meets the upper surface horizontal line of the circular plate, and the minutiae point image is the image in which the minutiae point is located in the xz plane of the 3D coordinate system. Accordingly, the coordinate values (X, Y, Z, 1) on the basis of the 3D coordinate system for the minutiae image can be expressed by Equation (9) from Equation (8).

Then, the image processing terminal 200 obtains the X-axis and Z-axis coordinate values and the rotation angle with respect to the center of each hole 120 in the minutiae image (ST80). At this time, the Y axis coordinate value corresponding to the acquired X axis and Z axis coordinate values becomes "0 ".

Then, the image processing terminal 200 acquires the coordinate values of the X-axis and Z-axis based on the 3D coordinate system for each hole 120 obtained in step ST80, the rotation angle, and the H-coordinate system based on the W- To calculate a final 3D error matrix corresponding to the actual measurement value of the stereoscopic calibrator (ST90). At this time, the image processing terminal 200 calculates a final 3D error matrix satisfying a minimum value, for example, a value of "0 "

Here, i is an index number of the hole 120, and is set to correspond to the number in the hole 120. [

That is, the image processing terminal 200 uses the nonlinear least squares method to convert the variable values when the Equation 10 is minimized into the final 3D error matrixes? 11,? 12, ...,? 33, t1, t2, t3 Setting.

)과 이동벡터(

)를 포함하는 3D 정렬오차값을 산출한다(ST100). Then, the image processing terminal 200 uses the final 3D error matrix calculated in step ST90,

) And the motion vector (

) (Step ST100).

100: cubic calibrator, 110: circular plate,
120: Hall,
200: image processing terminal, 210: camera,
220: image processing unit.

Claims (7)

A plurality of holes are formed on a three-dimensional plate having a multi-layered cross-section,
Wherein the stereolithography plate is formed by integrally joining a second circular plate having a second diameter smaller than the first diameter on a first circular plate having a first diameter,
And a plurality of hole bands spaced apart from the center point of the three-dimensional plate by a predetermined distance and spaced apart from each other by a predetermined number of holes are formed on the three-dimensional plate so as to have different distances from the center point. Dimensional calibrator.
The method according to claim 1,
Wherein the first to third hole bands are formed on the three-dimensional plate,
And at least one of the first to third hole bands is formed in each layer of the three-dimensional plate.
3. The method according to claim 1 or 2,
Wherein the holes of the different holes are arranged on straight extension lines with respect to the center point of the three-dimensional plate.
And a stereoscopic calibrator constituted by a plurality of holes formed in the respective layers while having a cross section formed in a multilayer structure. The stereoscopic calibrator includes a stereoscopic calibrator having a 3D A three-dimensional alignment error calculating method using a three-dimensional calibrator for calculating an alignment error,
A first step of acquiring a three-dimensional rotation image of the three-dimensional calibrator through a camera provided in the image processing terminal,
A second step of setting a point on a rotation axis of a rotary plate stage on which a three-dimensional calibrator is located at a shortest distance from an origin of a 3D coordinate system based on a camera position in an image processing terminal as an origin of an S-
A third step of setting the origin of the 3D coordinate system on the X-axis of the S-coordinate system in the image processing terminal,
A fourth step of calculating a 3D error matrix for converting the coordinates of the hole based on the stereoscopic calibrator to the 3D coordinate system in the image processing terminal,
A fifth step of obtaining X-axis and Z-axis coordinate values and a rotation angle with respect to each hole center of the stereoscopic calibrator from the rotation image acquired in the first step at the image processing terminal,
The image processing terminal calculates the final 3D error matrix based on the coordinate values of the X and Z axes based on the 3D coordinate system for each hole obtained from the fifth step, the rotation angle, and the hole coordinate values based on the W coordinate system corresponding thereto A sixth step of,
And calculating a 3D alignment error value based on the final 3D error matrix at the image processing terminal. [5] The method according to claim 1, wherein the three-dimensional alignment error is calculated using a three-dimensional calibrator.
5. The method of claim 4,
Wherein the coordinate value of the hole is set to a specific point coordinate value at which the center vertical center line of the hole meets the upper surface horizontal line of the stereolithography plate.
5. The method of claim 4,
Wherein the 3D error matrix is composed of a rotation-related matrix R and a motion vector component t, and is set according to the following equation: " (3) "
Equation

Here, R denotes a rotation-related matrix,

Is a rotation matrix in the 3D coordinate system with respect to the S coordinate system,

Is a rotation matrix in the W coordinate system based on the S _O coordinate system (initial state coordinate system of the rotation axis), t is a motion vector component

Is the movement matrix from the origin of the S-coordinate system to the origin of the 3D coordinate system,

Is a movement matrix from the origin of the S ₀ coordinate system to the origin of the W coordinate system.
The method according to claim 6,
If the vector component for any point in the 3D coordinate system is (X, Y, Z, 1) and the vector component for any point in the W coordinate system is (x, y, z, 1) Is transformed into a matrix form such as a mathematical expression of < RTI ID = 0.0 &

The coordinate values [X, Y, Z, 1} in the 3D coordinate system are transformed as shown in the following equation,

Wherein in the seventh step, the image processing terminal calculates a variable value when a result of the following equation is minimized for each hole.

Here, i is set to a number corresponding to the number of holes, and 粒 11, 粒 12, ..., 粒 33 are component values corresponding to a rotation-related matrix expressed by a 3x3 matrix, and t1, t2, A component value corresponding to a motion vector-related vector represented by a vector of one form.

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