JPH0953914A - Three-dimensional coordinate measuring instrument - Google Patents

Abstract

PROBLEM TO BE SOLVED: To easily find the three-dimensional coordinates of an objective point from picture data at a high speed without using the optical characteristics of a light source and a camera nor the positional information of the camera. SOLUTION: The three-dimensional coordinates of a measuring point Q are found by observing the positional relations between the point Q and six or more reference points P1-Pm in different planes by means of an image picking-up section 1 and fetching the positional relations by means of a two-dimensional coordinate acquiring section 2 composed of a plurality of two-dimensional coordinate acquiring means G1-Gn, and then, combining the positional relations.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a three-dimensional coordinate measuring device for measuring the three-dimensional coordinate of an object.

[0002]

2. Description of the Related Art Conventionally, various methods have been proposed as methods for measuring the three-dimensional coordinates of an object. For example,
A conventional binocular vision method that applies photogrammetry, a method that irradiates an object with slit light and receives reflected light, and
The unit subspace division method and the like described in "Method and apparatus for measuring three-dimensional coordinate position" described in Japanese Patent Laid-Open No. 5-79819 by Koichi Egawa et al.

The above-mentioned conventional binocular vision system to which photogrammetry is applied is a system in which the three-dimensional coordinates of an object are measured by the principle of triangulation using the position information of a plurality of image pickup devices. The method of irradiating the object with slit light and receiving the reflected light is a method of measuring the three-dimensional coordinates of the object by triangulation using the position information of the light source position and the camera.

Then, in the unit subspace division method, the three-dimensional coordinates of the object are measured as follows. First,
The measurement target space is divided into unit subspaces (voxels) of a hexahedron, and a correspondence table is created in which the three-dimensional coordinate positions of the vertices are associated with the two-dimensional coordinate values on the imaging screen. By using this correspondence table, the voxel vertex closest to the measurement point on the imaging screen is calculated, and the voxel including the measurement point is extracted.

Next, considering the projection of each surface of the voxel or the surface on the extension thereof onto the image pickup screen, a plurality of surfaces in which the projection points of the measurement points are included are calculated. Next, using the above correspondence table, the three-dimensional coordinates of the projection point of the measurement point on the surface are obtained for each surface, and a straight line passing through the projection points obtained on the plurality of surfaces is calculated. Then, the intersection of the straight lines calculated for each of the image data obtained by the plurality of imaging devices is calculated, and the coordinates of the intersection are set as the three-dimensional coordinates of the object.

[0006]

However, there have conventionally been the following problems. First, in the conventional binocular vision method applying photogrammetry, the optical characteristics of the cameras and the position information of the cameras are required, and the focal length of each camera, the positional relationship of the two cameras, the optical axes of the two cameras, and so on. I was measuring the angle difference in advance. Precise measurement of the optical characteristics of the camera and the position of the optical axis of the camera requires great effort. Further, in the method in which the slit light is applied to the object and the reflected light is received by the camera, there is a problem that the illumination condition is limited, such that the effect of external light must be taken into consideration because the light is applied.

Further, the unit subspace division method enables three-dimensional coordinate measurement which does not require optical characteristics of the light source or the camera, camera position information and the like. However, since the measurement target space is divided into many voxels, it is necessary to measure the three-dimensional coordinates of many points in the measurement target space in advance, which may be impossible in practice. Further, since the nearest voxel vertex of the measurement point is searched, the voxel inside the measurement point is searched, and the surface for defining a straight line is searched, there is a problem that the calculation time becomes huge.

The present invention has been made in order to solve the above problems, and does not use the optical characteristics of the light source or the camera and the position information of the camera, but the three-dimensional coordinates of the target point from the image data. The purpose is to seek easily and quickly.

[0009]

A three-dimensional coordinate measuring apparatus according to the present invention comprises a plurality of image pickup means and six or more points that are not on the same plane, and a relative point of each relative position is known. First two-dimensional coordinate acquisition means for acquiring two-dimensional coordinates on the captured image obtained by the imaging means, and coordinate calculation parameters for calculating coordinate calculation parameters using the two-dimensional coordinates of the reference point and the relative positional relationship. The calculation means, the second two-dimensional coordinate acquisition means for acquiring the two-dimensional coordinates of the measurement point on each captured image captured by the imaging means, the measurement using the coordinate calculation parameter and the two-dimensional coordinates of the measurement point Coordinate calculating means for calculating the three-dimensional coordinates of the point. As a result, the three-dimensional coordinates of the measuring point can be obtained without the position information of the measuring means. Also, the vertex of the cube is used as a reference point. Therefore, the obtained three-dimensional coordinates are normalized.

[0010]

DETAILED DESCRIPTION OF THE INVENTION An embodiment of the present invention will be described below with reference to the drawings. First, the operating principle of the present invention will be described. For simplification, the operation principle of the three-dimensional coordinate measuring apparatus of the present invention will be described using the binocular geometric model of FIG. P ₁ , P ₂ , P ₃ , P ₄ , and P _{5 in} FIG. 1 are reference points whose relative positional relationship is known. This may be P _i (i = 0, 1, ...) Of 6 points or more whose relative positions are known. Further, for the cameras 11 and 12 whose focal lengths are positions f and f ′, coordinate systems (a, b, c),
(A ', b', c ') are set. The origin O,
O'is the centers 11a and 12a of the lenses of the camera 11 and the camera 12, respectively, and its z axis and z'axis are set so that the photographing direction of the camera is positive and coincide with the respective optical axes. We will call it the 12th series.

Reference points P _i (i = 0, 1, ..., 5),
Camera 11 system position vector of each vector p _i of the camera 12 based vector _{p 'i (i = 0,1,} ··
・, 5). Further, the position vectors of the measurement point Q in the camera 11 system and the camera 12 system are vector q and vector q ', respectively. The reference point P _{i is set} to the two cameras 11, 12
Camera 11 when projected onto the image pickup surfaces 11b and 12b of
The coordinates in the system and the camera 12 system are (u _i , v _i ,
f) and (u ′ _i , v ′ _i , f ′) (i = 0, 1, ...
・ ・ 5)

Further, by using four reference points P ₀ , P ₁ , P ₂ and P ₃ whose coordinate system (x, y, z) is not on the same plane,
P ₀ is the origin, P ₀ -P ₁ is the x-axis, P ₀ -P ₂ is the y-axis, P
_{The 0-} P ₃ is defined as the z-axis, and this will be referred to as the measurement system. The coordinates of the measurement system of the reference point P _i are (x _i ,
y _i , z _i ), (i = 0, 1, ..., 5), and the coordinates of the measurement system of the measurement point Q are (α, β, γ).

Here, the determination of the coordinate calculation parameter will be described. Coordinate display of the projection point of the reference point P _i in the camera 11 system (u _i , v _i , f) (i = 0, 1, ...,
5) is a linear transformation T represented by the following equation 1 and a point [X on the four-dimensional projective space represented by the vector p _i of the following equation 2
_i , Y _i , Z _i , W _i ] ^t (however,
λ _i is an unknown constant).

[0014]

[Equation 1]

[0015]

[Equation 2]

The coordinates in the four-dimensional projective space considered here mean that P ₀ , P ₁ , P ₂ and P ₃ are vectors e ₀ =
[1,0,0,0] ^t , vector e ₁ = [0,1,0,
0] ^t , vector e ₂ = [0,0,1,0] ^t , and vector e ₃ = [0,0,0,1] ^t . Then, T shown in the above-mentioned expression 1 becomes the following expression 3.

[0017]

(Equation 3)

However, the equation 2 includes the unknown constant λ _i and has one degree of freedom, and therefore t3 = 1.
Then, the above equation 2 becomes the following equation 4.

[0019]

(Equation 4)

Similarly, the following equation 5 is obtained from the camera 12 system.

[0021]

(Equation 5)

Hereinafter, t _i , t ′ _i (i = 0, 1, 2), u
_{Let j} , v _j , u ′ _j , v ′ _j , (j = 0, 1, 2, 3) be the coordinate calculation parameters. Here, let us consider the determination of the coordinate calculation parameters t _i , t ′ _i (i = 0, 1, 2). Since the positional relationship of the reference points P _i (i = 0, 1, ...) Is known, the coordinates (x _i , y _i , z _i ) (i = 4) in the measurement system (x, y, z). 5, ...) are also known. Therefore, the vector p _i (i = 4,5, ...)
Can be expressed by Equation 6 below.

[0023]

(Equation 6)

[Mathematical formula-see original document] This equation 6 is represented by T and the four-dimensional coordinate system
₀ , vector e ₁ , vector e ₂ , vector e ₃ ], the following Expression 7 is obtained.

[0025]

(Equation 7)

By comparing this equation 7 with the above equation 4,
[X _i , Y _i , Z _i , W _i ] (i = 4,5, ...) Is known. Then, if λ _i is deleted from Equation 4, each P _i , (i
= 4, 5, ...), two sets of linear equations of the following equations 8 and 9 in which t ₀ , t ₁ , and t ₂ are variables are obtained.

[0027]

(Equation 8)

[0028]

[Equation 9]

Therefore, further two or more reference points P _i
If Equations 8 and 9 are obtained for (i = 4,5, ...), four or more linear equations are obtained for three variables of t ₀ , t ₁ , and t ₂ , so that the minimum By the method of squares, t ₀ , t ₁ ,
t ₂ is obtained. _{Similarly, t '0, t' 1} , t '2 also determined.

Next, as a method of determining the three-dimensional coordinates of a certain measuring point, the measuring system coordinates (α, β, γ) of the measuring point Q are determined.
Think about how to ask. The camera 11 system and the camera 12 when the measurement point Q is projected onto the imaging surfaces of the two cameras
The coordinates in the system are (u, v, f), (u ',
v ', f'). The position vector q of the measurement point Q in the camera 11 system is represented by the following Expression 10.

[0031]

(Equation 10)

When this equation 10 is represented by T and the four-dimensional coordinate system [vector e ₀ , vector e ₁ , vector e ₂ , vector e ₃ ], the following equations 11 and 12 are obtained.

[0033]

[Equation 11]

[0034]

(Equation 12)

That is, the following expression 13 is obtained (λ is an unknown constant).

[0036]

(Equation 13)

Therefore, if λ of this equation 13 is eliminated, the following equation 14 and equation 1 with α, β and γ as variables are shown.
Two sets of linear equations of 5 are obtained.

[0038]

[Equation 14]

[0039]

(Equation 15)

However, as it is, it cannot be solved because the number of expressions is smaller than the number of variables. Therefore, since both the camera 11 system and the camera 12 system are orthonormal systems, it is used that the display on the camera 11 system and the display on the camera 12 system are congruent. That is, S is a certain rotation matrix, and vector h is a certain constant vector representing translation, vector q = S vector q ′ + vector h, vector p _i = S vector p ′ _i + vector h (i = 0, 1, 2 and 3) are established, these are substituted into the above equation 11 to obtain the following equation 16.

[0041]

(Equation 16)

By multiplying S ^t from the left side of both sides of this ^equation 16, the following ^equation 17 is obtained.

[0043]

[Equation 17]

Then, in the same manner as described above, α,
Two more linear equations with β and γ as variables, Equation 1
8 and the number 19 are obtained.

[0045]

(Equation 18)

[0046]

[Equation 19]

Therefore, four sets of linear equations having α, β, γ as variables, Formulas 14, 15, 18, and 19 are obtained, and the three-dimensional coordinates (α, β, γ) can be obtained.

An embodiment of the present invention will be described below. FIG. 2 is a configuration diagram showing a configuration of the three-dimensional coordinate measuring device according to the embodiment of the present invention. This figure is roughly divided into reference points P _i (i = 1, ..., m) (m ≧
6), the image pickup unit 1, the two-dimensional coordinate acquisition unit 2, the coordinate calculation parameter calculation unit 3, and the three-dimensional coordinate calculation unit 4. The imaging unit 1 includes a plurality of cameras Ci (i = 1, 2, ..., N).
It is composed of It is not necessary to clarify in advance the positional relationship between the cameras Ci and their optical characteristics. The two-dimensional coordinate acquisition unit 2 is composed of a plurality of two-dimensional coordinate acquisition means Gi (i = 1, 2, ..., N).

The three-dimensional coordinate measuring device of this embodiment will be described below with reference to FIG. The reference point P _i is shown in FIG.
, P ₀ , ..., P _m , which are the vertices of the solid 11, are 6 or more points that are not on the same plane and have a known positional relationship with each other. Here, the six vertices R of the cube 12 shown in FIG.
By using ₀ , ..., R _m , the coordinates of the measurement point in the orthonormal coordinate system can be easily obtained.

First, the camera Ci of the image pickup unit 1 (i = 1,
2, ..., N), 6 or more reference points P ₀ , ..., P _m
Is imaged. The n images obtained by the cameras Ci (i = 1, 2, ..., N) are image i (i = 1, 2, ...
,, n). Image i (i = 1, 2, ..., N)
Are sent to the two-dimensional coordinate acquisition means Gi (i = 1, 2, ..., N) of the two-dimensional coordinate acquisition unit 2 through the image passing lines 10i (i = 1, 2, ..., N). .

The two-dimensional coordinate acquisition unit 2 is composed of a plurality of two-dimensional coordinate acquisition means Gi (i = 1, 2, ..., N). Each two-dimensional coordinate acquisition unit Gi includes an image memory (not shown), and has a function of detecting a reference point and outputting the two-dimensional coordinate thereof. This may be designated by the operator while looking at the display unit 13 shown in FIG. 5, or may be automatically detected by using a pattern recognition technique.

The two-dimensional coordinates of the reference point on the image i are acquired by the two-dimensional coordinate acquisition means Gi (i = 1, 2, ..., N), and then the numerical passage line 20i (i = 1, 1). 2, ...
, N) and is sent to the coordinate calculation parameter calculation unit 3. Reference point P _j on image i (j = 0, 1, ...,
m) the two-dimensional coordinates (u ⁱ _j , v ⁱ _j ), and a data signal 300 that is the positional relationship information of P _j (j = 4,5, ..., M) of the reference point stored in advance. (X _j , y _j , z
_j ), the coordinate calculation parameter calculation unit 3 calculates the formula shown below.

[0053] _{^{xu i j = (1-x}} j -y j -z j) (u i j -
u ⁱ ₀ ), yu ⁱ _j = x _j (u ⁱ _j −u ⁱ ₁ ), zu ⁱ _j = y _j (u
ⁱ _j −u ⁱ ₂ ), wu ⁱ _j = z _j (u ⁱ ₃ −u ⁱ _j ), xv ⁱ _j =
_{(1-x j -y j -z} j) (v i j -v i 0), yv i j = x
^{_{j (v i j -v i 1}} ), zv i j = y j (v i j -v i 2), wv i j
^{_{= Z j (v i 3 -v}} i j). Then, the coordinate calculation parameter calculation unit 3 calculates
The least squares method is applied to the equation shown by 0 (where m is 5 or more), and t ⁱ ₀ , t ⁱ ₁ , t ⁱ ₂ for each image i (i = 1, 2, ..., N). Ask for.

[0054]

(Equation 20)

These t ⁱ ₀ , t ⁱ ₁ , t ⁱ ₂ and u ⁱ _j , v ⁱ _j (j
= 0, 1, 2, 3) is called a coordinate conversion parameter. This coordinate conversion parameter is sent to the three-dimensional coordinate calculation unit 4 via the numerical pass line 500. Next, the measurement point Q is imaged by the camera Ci (i = 1, 2, ..., N) of the imaging unit 1. The n images obtained by the camera Ci (i = 1, 2, ..., N) are image i ′ (i = 1, 2, ..., N), respectively.
Call. Each image i ′ is an image passing line 10i (i =
1, 2, ..., N), and is sent to the two-dimensional coordinate acquisition means Gi (i = 1, 2, ..., N) of the two-dimensional coordinate acquisition unit 2.

Two-dimensional coordinates (u ⁱ ,
v ⁱ ) (i = 1, 2, ..., N) is acquired by each two-dimensional coordinate acquisition means Gi in the same manner as the case of the reference point, and the numerical value passing line 40i (i = 1, 2, ... , N), and is sent to the three-dimensional coordinate calculation unit 4. The three-dimensional coordinate calculation unit 4 uses the three-dimensional conversion parameters t ⁱ ₀ , t ⁱ ₁ , t ⁱ ₂ , and u.
_{^{i j, v i j (i}} = 1,2, ···, n) (j = 0,1,
2, 3), the two-dimensional coordinates (u ⁱ , v ⁱ ) of the measurement point (i = 1,
2, ..., N) is used to calculate the following equation.

Au ⁱ = t ⁱ ₀ (u ⁱ ₀ −u ⁱ ), bu ⁱ = t ⁱ ₁
(U ⁱ −u ⁱ ₁ ) + au _i , cu ⁱ = t ⁱ ₂ (u ⁱ −u ⁱ ₂ ) + a
u _i , du ⁱ = t ⁱ ₂ (u ⁱ −u ⁱ ₃ ) + au _i , av ⁱ = t ⁱ ₀
(V ⁱ ₀ −v ⁱ ), bv ⁱ = t ⁱ ₁ (v ⁱ −v ⁱ ₁ ) + av _i , c
v ⁱ = t ⁱ ₂ (v ⁱ −v ⁱ ₂ ) + av _i , d v ⁱ = t ⁱ ₂ (v ⁱ −
v ⁱ ₃ ) + av _i . Then, the three-dimensional coordinate calculation unit 4 applies the least squares method to the equation (where n is 2 or more) represented by the following equation 21 to obtain the data signal 600 that is the three-dimensional coordinate of the measurement point Q.
Obtain (α, β, γ).

[0058]

(Equation 21)

If six vertices of a cube as shown in FIG. 4 are used as the reference points, three-dimensional coordinates in the orthonormal coordinate system can be easily obtained.

[0060]

As described above, according to the present invention, the positional relationship of the measurement point with respect to the reference point, which is composed of six or more points that are not on the same plane and whose relative position is known, is determined by a plurality of points. The three-dimensional coordinates of the measurement point were obtained by observing from the position and importing them as two-dimensional coordinates and combining them. That is, instead of the optical characteristics of the camera or the position information of the camera, which is difficult to measure precisely, the three-dimensional position of the measurement point is measured using the positional relationship of 6 points that are not on the same plane and can be easily measured. I chose

Therefore, the three-dimensional coordinates of the target point can be easily and quickly obtained from the image data without using the light source, the optical characteristics of the camera, and the position information of the camera. Further, by using the vertex of the cube as the reference point, the three-dimensional position in the orthonormal coordinate system can be easily measured without using the optical characteristics of the camera or the position information of the camera.

[Brief description of drawings]

FIG. 1 is a perspective view showing a binocular geometric model for explaining the operation principle of the three-dimensional coordinate measuring apparatus of the present invention.

FIG. 2 is a configuration diagram showing a configuration of a three-dimensional coordinate measuring device according to an embodiment of the present invention.

FIG. 3 is an explanatory diagram showing a relationship between reference points in the present invention.

FIG. 4 is an explanatory diagram showing a relationship between reference points in the present invention.

5 is a screen diagram showing an output example of the three-dimensional coordinate measuring apparatus of FIG.

[Explanation of symbols]

DESCRIPTION OF SYMBOLS 1 ... Imaging part, 2 ... Two-dimensional coordinate acquisition part, 3 ... Coordinate detection parameter calculation device, 4 ... Three-dimensional coordinate calculation device 101-1
0n ... image passing lines, 201 to 20n, 401 to 40n,
500 ... Numerical value passing line, 300, 600 ... Data signal, C
1-Cn ... Camera, Gn ... Two-dimensional coordinate acquisition means, P0
P5, Pm ... Reference point, Q ... Measurement point.

Claims (2)

[Claims] 1. A two-dimensional image on an imaged image obtained by said imager with respect to a reference point which is composed of a plurality of imager and six or more points that are not on the same plane and whose relative positions are known. First two-dimensional coordinate acquisition means for acquiring coordinates, coordinate calculation parameter calculation means for calculating coordinate calculation parameters using the two-dimensional coordinates of the reference point and the relative positional relationship, and each imaged by the imaging means. Second two-dimensional coordinate acquisition means for acquiring the two-dimensional coordinates of the measurement point on the captured image, and coordinates for calculating the three-dimensional coordinates of the measurement point using the coordinate calculation parameter and the two-dimensional coordinates of the measurement point. A three-dimensional coordinate measuring device comprising a calculating means. 2. The three-dimensional coordinate measuring device according to claim 1, wherein the reference point is a vertex of a cube.