JP2003294433A - Method for synchronizing coordinate systems of plural three dimensional shape measuring devices - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a method for synchronizing origins and axes of two or more three-dimensional shape measuring devices when each of those measuring devices is used for shape measurement. <P>SOLUTION: In the method, a known-shaped solid body for calibration 120 (a plane board with a black line marked on its surface) is measured by using a plurality of three-dimensional shape measuring devices 103, 104, 105, 106 to obtain a fitting plane equation for each three-dimensional shape measuring device. Then both a rotational matrix R113 and a parallel vector T112 for providing coordinate conversion to the origins/coordinate axes of each fitting plane equation are obtained to synchronize coordinate systems 110, 111 comprising a plurality of origins/coordinate axes of three-dimensional shape measuring devices with one coordinate system of a three-dimensional shape measuring device. <P>COPYRIGHT: (C)2004,JPO

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method of aligning a coordinate system composed of an origin of each measuring device and a coordinate axis when measuring an object to be measured using a plurality of three-dimensional shape measuring devices.

[0002]

2. Description of the Related Art A projection method using fringe scanning is known as a method for measuring a three-dimensional shape in a non-contact manner. This method is generally performed as follows. A light pattern having a sinusoidal luminance distribution is projected from a light source onto an object through a grid in which grayscale values are printed in a sinusoidal shape. Then, a striped image on the object is photographed by a camera installed in a place different from the above light source. With the object still, the image is taken while shifting the grating in the direction perpendicular to the stripes N times by 1 / N of the wavelength. In the captured image, the sine wave light pattern projected on the object appears to advance by 2π / N radians. The brightness value at the measurement point is measured from the projection direction, and the phase value of the lattice pattern is calculated from each brightness value. Since the phase of the grating pattern is modulated according to the height displacement of the measurement point, calculate the phase modulation amount and substitute it into the geometrical relational expression of the optical device to calculate the height displacement amount of the object. Find the original shape.

[0003]

However, the above measuring method cannot measure the back side of the object to be measured. In addition, when the object to be measured is large, it may not be possible to perform measurement with one three-dimensional shape measuring device. In such a case, a plurality of three-dimensional shape measuring devices are arranged on the front and back sides, and vertically and horizontally to measure. Here, each three-dimensional shape measuring device measures with its own origin and coordinate axis, so it is not possible to simply connect the measurement data of each device,
It is necessary to match the coordinate system consisting of the origin of each measuring device and the coordinate axis.

Therefore, according to the present invention, the coordinate systems such as the origins and coordinate axes of a plurality of three-dimensional shape measuring devices are made to coincide with each other, and the measurement values of a plurality of three-dimensional shape measuring devices are integrated to measure the back side of the object to be measured. An object of the present invention is to provide a method capable of measuring a three-dimensional shape even when the object to be measured is large.

[0005]

In order to achieve the above object, the invention according to claim 1 is a method of matching the coordinate systems of a plurality of three-dimensional shape measuring apparatuses, each of which has its own origin and coordinate axis. A three-dimensional shape for calibration is arranged at a position that can be measured by a plurality of three-dimensional shape measuring devices each having a coordinate system such that one surface to be measured or two or more surfaces to be measured whose relative positions are known is calibrated. The measuring device measures three or more different points on the surface to be measured to obtain the three-dimensional position of each point, calculates the fitting surface equation of the surface to be measured from the measured values, and determines the target surface of each fitting surface. It is characterized in that the coordinate system of one fitting surface equation is used to perform coordinate conversion of another fitting surface equation from the positional relationship between the measurement surfaces.

According to the invention of claim 1, 1
When measuring a large object that cannot be measured with a three-dimensional shape measuring device on a stand or the shape of the back side of the measuring object with multiple three-dimensional shape measuring devices, all origins and coordinate systems can be matched, It becomes possible to measure a three-dimensional shape at high speed. In addition, by measuring the complicated portion of the shape that is difficult to measure with high accuracy with one 3D shape measuring device with multiple 3D shape measuring devices, the shape data of the object can be obtained with higher accuracy. It becomes possible.

According to a second aspect of the present invention, in the method of matching the coordinate systems of the plurality of three-dimensional shape measuring apparatus according to the first aspect, the fitting surface equation is used to calculate a measurement error for the measurement data of the three or more points. It is characterized by being obtained by minimizing it.

According to the second aspect of the present invention, since the fitting surface equation is obtained by minimizing the measurement error for the measurement data of three or more points, a plurality of three-dimensional shape measuring devices can achieve higher accuracy. It becomes possible to obtain the shape data of the object.

According to a third aspect of the present invention, as a preferred form of the method for matching the coordinate systems of the plurality of three-dimensional shape measuring apparatuses according to the second aspect, the cubic of each point measured by each of the three-dimensional shape measuring apparatuses is used. With respect to the measured value at the original position, the fitting surface equation is obtained from the extreme value of the sum of squared errors.

According to a fourth aspect of the present invention, in the method for matching the coordinate systems of the plurality of three-dimensional shape measuring apparatus according to the first, second or third aspect, the measured surface is a plane and the fitting surface is a fitting plane. It is characterized by

According to the fourth aspect of the invention, since the surface to be measured is a flat surface, it suffices to measure parallel front and back flat surfaces.
Further, since the flatness can be produced with high precision by the machine tool, the origin and coordinate axes of each three-dimensional shape measuring device can be aligned with high precision. In addition, it is easy and inexpensive to make a three-dimensional object for calibration.

According to a fifth aspect of the present invention, as a preferred form of the method for matching the coordinate systems of the plurality of three-dimensional shape measuring apparatuses according to any one of the first to fourth aspects, the coordinate transformation is performed by using a rotation matrix. It is characterized by performing the parallel vector.

[0013]

BEST MODE FOR CARRYING OUT THE INVENTION Next, specific examples of embodiments of a method for matching the coordinate systems of a plurality of three-dimensional shape measuring apparatuses according to the present invention will be described in detail with reference to the drawings.

FIG. 1 is a perspective view showing the appearance of a three-dimensional shape measuring apparatus. The three-dimensional shape measuring device has two cameras 1.
00 and two projectors 101.

Then, the three-dimensional measurement of the three-dimensional object is performed by irradiating the three-dimensional object as a target with the sinusoidal striped image from these projectors 101 and photographing the three-dimensional object with the two cameras 100. At that time, a coordinate system 1 including the origin (O) of the spatial position of the object and the coordinate axes X, Y, and Z.
02 will be used to indicate the shape of the measured object.

A plurality of three-dimensional shape measuring devices having such a configuration are arranged to perform three-dimensional measurement of the measuring object. Figure 2
Are four three-dimensional shape measuring devices 103, 104, 10
It is a perspective view which shows the external appearance of the measuring device using 5,106. In this apparatus, the three-dimensional shape measuring apparatus shown in FIG. 1 is installed one each in the vertical and horizontal directions. Each three-dimensional shape measuring device is fixed to a frame having high rigidity.

As shown in FIG. 2, the measuring object 107 is located substantially at the center of each device, and the three-dimensional shape measuring device 104 at the upper left portion measures the upper left portion of the measuring object 107. The lower left three-dimensional shape measuring apparatus 103 measures the lower left portion of the measurement object 107. Similarly, the three-dimensional shape measuring device 106 measures the upper right part of the measuring object 107, and the three-dimensional shape measuring device 105 measures the lower right part of the measuring object 107. Accordingly, the four three-dimensional shape measuring devices can measure almost the entire circumference of the measuring object 107.

The measuring operation is as follows. First, the three-dimensional shape measuring apparatus 1
The measurement object 107 to be measured is started from 03.
Measure the lower left part of. In order, another three-dimensional shape measuring device 1
The same measurement is performed at 04, 105, and 106, and the measurement data measured by each device is output to a personal computer (not shown) for four units.

However, each three-dimensional shape measuring device 103, 1
Each of 04, 105, and 106 has a coordinate system including an origin and coordinate axes for performing three-dimensional measurement of the measurement object 107. These origins and coordinate axes are unique to each measuring device, and different measuring devices have different origins and coordinate axes. Therefore, the measurement data of each of the four three-dimensional shape measuring devices cannot be integrated. Therefore, it is necessary to perform coordinate conversion on the origin / coordinate axes of each three-dimensional shape measuring device so that the origin / coordinate axes of each three-dimensional shape measuring device match.

FIG. 3 is a diagram showing the principle of coordinate conversion from the coordinate system 110 to the coordinate system 111. In two three-dimensional shape measuring devices, a point P (X1, Y1, Z1) on the coordinate system 110 of one three-dimensional shape measuring device is (X2, Y2, Z
2). If these are displayed as vectors, vectors r1 = (X1, Y1, Z1), r2 = (X2, Y
2, Z2). T112 in the figure indicates a parallel vector, and R113 indicates a rotation matrix. From FIG. 3, the following equation holds.

[0021]

[Equation 1] From the above equation (1), in order to match the coordinate system 111 with the coordinate system 110, a 3 × 3 matrix R11 that rotates the coordinate axes is used.
3 and the parallel vector T112 for moving the origin.

This rotation matrix R113 and parallel vector T1
In order to obtain 12, the flat plate 120 as the three-dimensional object for calibration shown in FIG. 4 is installed at the position shown in FIG.
0 is measured by each of the four three-dimensional shape measuring devices 103 to 106.

The flat plate 120 shown in FIG.
A flesh-colored paint is applied on the surface of the flat plate 120, and a black grid line 121 is applied on it.
Both sides are painted. The positions of the lines 121 are also matched on the front and back.

First, the operation for obtaining the rotation matrix R113 will be described. The three-dimensional shape measuring device 104 measures one surface of the plane plate 120 shown in FIG. 4 as a surface to be measured, and measures three points on this surface. The measurement data is the first point (x1, y
1, z1), second point (x2, y2, z2), third point (x
3, y3, z3) as coordinate values.
These three points are chosen so that they do not line up on the same straight line. If the coordinates of three points are obtained, the plane is determined.
The fitting plane equation of the plane plate being measured can be obtained.

Here, the fitting plane equation is obtained as follows. When the normal vector of the plane equation is (α, β, -1)

[0026]

[Equation 2] It can be expressed as. In this equation (2), the coordinates of the above-mentioned three points on the measured surface, the first point (x1, y1, z1), the second point (x2, y2, z2), and the third point (x3, y3, z).
By substituting 3), three equations (2) can be created, and the values of α, β, and d can be obtained from these.

However, since the measured coordinate values include a measurement error, the calculated values of α, β and d are not accurate. Therefore, the square sum E of the measurement error is obtained.

The sum of squared errors E is

[0029]

[Equation 3] Becomes Then, from the condition that this function has an extreme value when the error becomes the smallest, the unknowns α, β, and d of the plane equation of the fitting plane are finally obtained by solving the following matrix.

[0030]

[Equation 4] Numerical analysis of this one-dimensional simultaneous equation
Determine β, d, and thereby the equation of the fitting plane.

FIG. 6 shows two three-dimensional shape measuring devices 104.
6A and 6B are views showing a state in which the flat plate 120 is measured with both front and back surfaces as the surfaces to be measured. FIG. 6A is a perspective view, FIG. 6B is a view of a fitting plane of the three-dimensional shape measuring apparatus 104, and FIG. It is a figure of the fitting plane of the three-dimensional shape measuring device 106.
The equation of the fitting plane 130 measured from the device 104 and the equation of the fitting plane 131 measured from the device 106 can be determined as described above.

When the unit normal vectors are n1 and n2, the rotation matrix R is

[0033]

[Equation 5] Can be obtained from

Next, how to obtain the parallel vector T will be described. FIG. 7 shows two three-dimensional shape measuring devices 104 and 10.
6A and 6B are views showing a state in which corresponding points on the front and back of the plane plate 120 are measured by 6 and 6, in which FIG. 6A is a perspective view and FIG. Black lines 121 are painted on the front and back of the flat plate 120 shown in FIG. This black line has a vertical line and a horizontal line, and has a plurality of intersections. Therefore, as shown in FIG. 7, an intersection is defined as P, and an intersection corresponding to the back surface of the intersection is defined as P ′.

Here, the vector from the origin 132 of the three-dimensional shape measuring device 104 to the intersection point P is T1, and the vector from the origin 133 of the three-dimensional shape measuring device 106 to the intersection point P'is T.
3. If the intersection point P to the intersection point P ′ is T2, the parallel vector T to be obtained (from the origin of the device 106 to the origin of the device 104)
Is

[0036]

[Equation 6] Becomes

Further, T1 and T3 can be obtained because the three-dimensional coordinates of the intersection P and the intersection P'are known from the measurement data. However, in order to reduce the measurement error, the three-dimensional coordinates of the intersection P and the intersection P ′ pass the measurement data, and
A straight line having the same direction as the normal vector of the fitting plane equation shown in is obtained, and the intersection of the straight line and the fitting plane is obtained as the three-dimensional coordinates of points Pa and Pa ′ in the analysis.

Therefore, from the analytical point Pa and the point Pa 'to T
1, T3 can be obtained. By the way, the vector T
The direction of 2 is obtained from the normal vector of the fitted plane equation shown in FIG. 6, and the size is obtained from the thickness of the plane plate, and the vector T2 can be obtained. Therefore, the vectors T1, T2, and T3 are obtained from these, and the vector T is obtained from the equation (6).

As described above, the three-dimensional shape measuring device 106
Can be coordinate-converted into the coordinate system of the three-dimensional shape measuring device 104. Similarly, the three-dimensional shape measuring apparatus 10
5 is converted into the coordinate system of the three-dimensional shape measuring device 104, the coordinate conversion of the three-dimensional shape measuring device 103 is converted into the coordinate system of the three-dimensional shape measuring device 104, and all four coordinate systems are coordinated by the three-dimensional shape measuring device 104. It becomes possible to match with.

In the above embodiment, instead of the flat plate 120 shown in FIG. 4, a flat plate 140 as shown in FIG.
Can be used as a three-dimensional object for calibration. In this embodiment, instead of the black line 121 of FIG.
Has been cut. Similar to the embodiment of FIG. 4, the uncut surface 142 is used as the surface to be measured, and the flat plate 140
Then, the fitted plane equation is calculated and the rotation matrix R is calculated. Further, the parallel vector T can be obtained from the intersection P of the groove 141 and the corresponding intersection not shown on the back surface thereof.

Instead of the plane plate 120 shown in FIG. 4, a triangular prism 150 as shown in FIG. 9 can be used as a calibration solid. This is used when the three-dimensional shape measuring devices 201, 202, 203 are arranged every 120 degrees. The three-dimensional shape measuring device 201 is a triangular prism 15.
The fitting plane equation of the measured surface 151 of 0 is obtained, the three-dimensional shape measuring apparatus 202 finds the fitting plane equation of the measured surface 152, and the three-dimensional shape measuring apparatus 203 finds the fitting plane equation of the measured surface 153. After that, the rotation matrix R is similarly obtained from the angle at which the measured surfaces 151, 152, 153 intersect. Further, a ridge shape or a line by painting is provided on each measured surface 151, 152, 153 of the calibration three-dimensional object 150 to determine a measurement point, and the parallel vector T is obtained from the mutual positional relationship of these measurement points.

Instead of the plane plate 120 shown in FIG.
A hexahedron 160 as shown in 0 can also be used as a calibration solid. Nothing is processed on the surface of the hexahedron 160. Each surface of the hexahedron 160 is used as a surface to be measured to find a fitting plane equation, and the rotation matrix R is found in the same manner as in the above embodiment. Edge point P of hexahedron 160
The parallel vector T is obtained.

In the above embodiments, the surface to be measured of the calibration solid is a flat surface, but the present invention is not limited to a flat surface. For example, it is possible to use a sphere as the calibration three-dimensional object. In addition, it suffices that the surface shape of the surface to be measured is known, and if there are a plurality of surfaces to be measured, the positional relationship between them may be known. Since a plane other than a plane may be used as described above, the fitting plane in the above embodiment is a subordinate concept of the fitting plane. The measuring method of the three-dimensional shape measuring apparatus can be applied to various things such as those using a laser, and is not limited to a particular one.

[0044]

As described above, according to the method of the present invention, the measurement values of a plurality of three-dimensional shape measuring devices are integrated to measure the back side of the object to be measured or the object to be measured is large. However, it becomes possible to measure a three-dimensional shape.

[Brief description of drawings]

FIG. 1 is a perspective view showing an appearance of a three-dimensional shape measuring apparatus.

FIG. 2 is a perspective view showing the appearance of a measuring device using four three-dimensional shape measuring devices.

FIG. 3 is a diagram showing a principle of coordinate conversion from one coordinate system to another coordinate system.

4A and 4B are views showing a plane plate as a calibration solid, wherein FIG. 4A is a front view, FIG. 4B is a plan view, FIG. 4C is a side view, and FIG.

5A and 5B are views showing the arrangement of four three-dimensional shape measuring devices and a plane plate, where FIG. 5A is a front view and FIG. 5B is a top view.
(C) is a side view.

FIG. 6 is a diagram showing a state in which a flat plate is measured by two three-dimensional shape measuring devices, in which (a) is a perspective view and (b) is
(C) is a view of a fitting plane.

7A and 7B are diagrams showing a state in which corresponding points on the front and back of a plane plate are measured by two three-dimensional shape measuring devices, FIG. 7A is a perspective view, and FIG. 7B is a diagram showing how to obtain a parallel vector. Is.

FIG. 8 is a perspective view showing a plan view having a groove as a calibration three-dimensional object.

FIG. 9 is a diagram showing a state in which a triangular prism is used as a calibration solid.

FIG. 10 is a diagram showing a state in which a hexahedron is used as a calibration three-dimensional object.

[Explanation of symbols]

100 cameras 101 projector 102 coordinate system 103 three-dimensional shape measuring device 104 three-dimensional shape measuring device 105 three-dimensional shape measuring device 106 three-dimensional shape measuring device 107 measurement object 110 Origin and coordinate axis of one three-dimensional shape measuring device 111 Origin and coordinate axes of other three-dimensional shape measuring devices 112 Parallel vector T 113 rotation matrix R 120 Three-dimensional object for calibration (flat plate) 121 lines 122 base 130 Fitting (flat) surface of one three-dimensional shape measuring device 131 Fitting (flat) surface of another three-dimensional shape measuring device 140 Three-dimensional object for calibration (flat plate) 141 groove 142 sides 150 triangular prism 151 surface to be measured 152 surface to be measured 153 Measured surface 160 hexahedron 201 Three-dimensional shape measuring device 202 Three-dimensional shape measuring device 203 three-dimensional shape measuring device

   ─────────────────────────────────────────────────── ─── Continued front page    F term (reference) 2F065 AA04 AA53 BB05 DD19 EE00                       FF06 FF61 HH06 JJ03 JJ05                       LL41 PP01 QQ00 QQ17 QQ18                 2F069 AA04 AA61 DD22 FF01 FF07                       GG04 GG07 GG13 MM04 NN00                       NN15 NN17

Claims (5)

[Claims] 1. One measurement surface or two or more measurement surfaces whose relative positions are known are located at positions that can be measured by a plurality of three-dimensional shape measuring devices each having a coordinate system having its own origin and coordinate axes. The three-dimensional shape measuring device is arranged, three or more different points on the measured surface are measured by each three-dimensional shape measuring device to obtain the three-dimensional position of each point, and the fitting surface equation of the measured surface is obtained from the measured values. And a plurality of three-dimensional shapes characterized in that the coordinate system of one fitting surface equation is used to perform coordinate transformation of another fitting surface equation from the positional relationship between the measured surfaces that are the objects of each fitting surface. A method of matching the coordinate systems of measuring devices. 2. The coordinate system of a plurality of three-dimensional shape measuring apparatuses according to claim 1, wherein the fitting surface equation is obtained by minimizing measurement error for measurement data of the three or more points. How to match. 3. The fitting surface equation is obtained from the extreme value of the sum of squares of the error for the measurement value of the three-dimensional position of each point measured by each of the three-dimensional shape measuring devices. A method of matching the coordinate systems of a plurality of three-dimensional shape measuring devices. 4. The method for matching coordinate systems of a plurality of three-dimensional shape measuring apparatuses according to claim 1, 2 or 3, wherein the surface to be measured is a flat surface and the fitting surface is a fitting plane. 5. The method for matching the coordinate systems of a plurality of three-dimensional shape measuring devices according to claim 1, wherein the coordinate conversion is performed by obtaining a rotation matrix and a parallel vector. .