JP3781762B2 - 3D coordinate calibration system - Google Patents

Description

  The present invention relates to a method for matching a coordinate system composed of an origin and a coordinate axis of each measuring device when measuring an object to be measured using a plurality of three-dimensional shape measuring devices.

  As a method for measuring a three-dimensional shape in a non-contact manner, a projection method using fringe scanning is known. This method is generally performed as follows. A light pattern having a sinusoidal luminance distribution is projected from a light source to an object through a grid in which light and shade values are printed in a sinusoidal form. Then, the fringe image on the object is photographed by a camera installed at a place different from the light source. The image is taken while shifting the grating N times by 1 / N of the wavelength in the direction perpendicular to the stripe while the object is stationary. The photographed image appears as if the sine wave light pattern projected on the object travels by 2π / N radians. The luminance value at the measurement point is measured from the projection direction, and the phase value of the lattice pattern is calculated from each luminance value. Since the phase of the grating pattern is modulated according to the height displacement of the measurement point, the amount of modulation of this phase is calculated and substituted into the geometric relational expression of the optical device to calculate the height displacement of the object. Find the original shape.

Japanese Patent Laid-Open No. 1-1119708

  However, the above measurement 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 measure with a single three-dimensional shape measuring apparatus. In such a case, measurement is performed by arranging a plurality of three-dimensional shape measuring devices on the front, back, top, bottom, left and right. Here, since each 3D shape measurement device measures with its own origin and coordinate axes, the measurement data of each device cannot be simply connected, and the coordinate system consisting of the origin and coordinate axes of each measurement device Need to match.

  Therefore, the present invention matches the coordinate systems such as the origin and coordinate axes of a plurality of three-dimensional shape measurements, integrates the measurement values of a plurality of three-dimensional shape measurement devices, measures the back side of the object to be measured, It is an object to provide a method capable of measuring a three-dimensional shape even when an object is large.

In order to achieve the above-mentioned object, in the present invention, two surfaces which are arranged at positions that can be measured from a plurality of three-dimensional measuring apparatuses each having a coordinate system having a unique origin and coordinate axes are used as the measured surface. A three-dimensional calibration object having a flat plate shape and a plurality of three-dimensional measurement devices, each of the three-dimensional measurement devices; A plane equation calculating means for measuring by a coordinate system unique to the original measuring device and calculating each plane equation of each surface to be measured from three or more three-dimensional coordinate values for each coordinate system unique to each of the three-dimensional measuring devices; The rotation matrix used to match the coordinate systems of the three-dimensional measuring devices facing each other across the calibration three-dimensional object from the plane equations of the two measured surfaces that are the front and back pairs of the calibration three-dimensional object Rotation matrix calculating means for calculating The three-dimensional coordinate values of two measurement points located symmetrically on the measurement surface of each three-dimensional measurement device facing each other across the calibration three-dimensional object among the three-dimensional measurement devices of , Each three-dimensional measurement device is measured by its own coordinate system, each measurement vector value from each three-dimensional measurement device to each measurement point is calculated, and each three-dimensional measurement device based on each measurement vector value And parallel vector calculation means for calculating a parallel vector for matching the unique coordinate system.

  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 three-dimensional shape can be obtained even when the object to be measured is large. It becomes possible to measure.

  Next, a specific example of an embodiment of a method for matching 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 an appearance of a three-dimensional shape measuring apparatus. The three-dimensional shape measuring apparatus includes two cameras 100 and two projectors 101.

  Then, a three-dimensional measurement of the three-dimensional object is performed by irradiating a target three-dimensional object with a sinusoidal stripe image from these projectors 101 and photographing the three-dimensional object with two cameras 100. At that time, the shape of the object to be measured is shown using the coordinate system 102 composed of the origin (O) of the spatial position of the object and the coordinate axes X, Y, and Z.

  A plurality of three-dimensional shape measuring apparatuses having such a configuration are arranged to perform three-dimensional measurement of a measurement object. FIG. 2 is a perspective view showing an appearance of a measuring device using four three-dimensional shape measuring devices 103, 104, 105, and 106. FIG. In this apparatus, one three-dimensional shape measuring apparatus shown in FIG. Each three-dimensional shape measuring device is fixed to a rigid frame.

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

  In the measurement operation, first, measurement is started from the three-dimensional shape measurement apparatus 103, and the lower left portion of the measurement object 107 to be measured is measured. Sequentially, the same measurement is performed by the other three-dimensional shape measuring apparatuses 104, 105, and 106, and the measurement data measured by each apparatus is output to four personal computers (not shown).

  However, each three-dimensional shape measuring apparatus 103, 104, 105, 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 the origin and coordinate axes are different for different measuring devices. For this reason, the measurement data of each of the four three-dimensional shape measurement apparatuses cannot be integrated. Therefore, it is necessary to perform coordinate conversion on the origin and coordinate axes of each three-dimensional shape measurement apparatus so that the origin and coordinate axes of each three-dimensional shape measurement apparatus coincide.

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

上記の式（１）から、座標系１１１を座標系１１０に一致させるには、座標軸を回転させる３×３の行列Ｒ１１３と、原点を移動させる平行ベクトルＴ１１２を求めることに帰着する。

From the above equation (1), in order to make the coordinate system 111 coincide with the coordinate system 110, the result is to obtain a 3 × 3 matrix R113 for rotating the coordinate axis and a parallel vector T112 for moving the origin.

  In order to obtain the rotation matrix R113 and the parallel vector T112, the flat plate 120 as the calibration three-dimensional object shown in FIG. 4 is installed at the position shown in FIG. 5, and the flat plate 120 is provided with four three-dimensional shape measuring devices 103 to 103. Each measurement is performed at 106.

  The flat plate 120 shown in FIG. 4 is obtained by applying a flesh-colored paint to the base 122 and applying black grid-like lines 121 thereon, and the same plate is applied on both surfaces of the flat plate 120. The position of the line 121 is also matched on the front and back.

  First, the operation for obtaining the rotation matrix R113 will be described. With the three-dimensional shape measuring apparatus 104, one surface of the flat plate 120 shown in FIG. The measurement data is obtained as coordinate values such as a first point (x1, y1, z1), a second point (x2, y2, z2), and a third point (x3, y3, z3). These three points are selected so as not to line up on the same straight line. If the coordinates of the three points are obtained, the plane is determined, so that 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)

と表すことができる。この式（２）に、計測した被測定面の上記３点の座標、第１点（ｘ１、ｙ１、ｚ１）、第２点（ｘ２、ｙ２、ｚ２）、第３点（ｘ３、ｙ３、ｚ３）を代入すれば、３つの式（２）ができ、これらからα、β、ｄの値を求めることができる。

It can be expressed as. In this equation (2), the coordinates of the three points of the measured surface to be measured, the first point (x1, y1, z1), the second point (x2, y2, z2), the third point (x3, y3, z3) ) Can be substituted to obtain three equations (2), from which the values of α, β, and d can be obtained.

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

  The sum of squared error E is

となる。そして、誤差が最も小さくなるときにこの関数が極値を持つ条件から、最終的に当てはめ平面の平面方程式の未知数α、β、ｄは以下の行列を解くことにより求められる。

It becomes. Then, from the condition that this function has an extreme value when the error becomes the smallest, the unknowns α, β, d of the plane equation of the fitted plane are finally obtained by solving the following matrix.

この１次元連立方程式の数値解析を行い、未知数α、β、ｄを決定し、これにより、当てはめ平面の方程式を決定する。

Numerical analysis of the one-dimensional simultaneous equations is performed to determine the unknowns α, β, and d, thereby determining the equation of the fitting plane.

  FIGS. 6A and 6B are diagrams showing a state in which the two-dimensional shape measuring devices 104 and 106 measure the flat plate 120 with the front and back surfaces being measured surfaces, where FIG. 6A is a perspective view and FIG. 6B is a three-dimensional shape. FIG. 4C is a drawing of a fitting plane of the measuring device 104, and FIG. 5C is a drawing of a fitting plane of the three-dimensional shape measuring device 106. As described above, the equation of the fitting plane 130 measured from the apparatus 104 and the equation of the fitting plane 131 measured from the apparatus 106 can be obtained.

  When each unit normal vector is n1 and n2, the rotation matrix R is given by

から求まる。

Obtained from

  Next, how to obtain the parallel vector T will be described. 7A and 7B are diagrams showing a state in which corresponding points on the front and back of the flat plate 120 are measured by the two three-dimensional shape measuring devices 104 and 106, where FIG. 7A is a perspective view and FIG. 7B is a calculation of a parallel vector T. FIG. A black line 121 is 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 there are a plurality of intersections. Therefore, as shown in FIG. 7, an intersection point is P, and an intersection point corresponding to the back surface of the intersection point is P ′.

  Here, T1 is a vector from the origin 132 of the three-dimensional shape measurement apparatus 104 to the intersection P, T3 is a vector from the origin 133 to the intersection P ′ of the three-dimensional shape measurement apparatus 106, and T2 is an intersection P ′ from the intersection P. The desired parallel vector T (from the origin of the device 106 to the origin of the device 104) is

となる。

It becomes.

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

  Accordingly, T1 and T3 can be obtained from the point Pa and the point Pa ′ in the analysis. By the way, the direction of the vector T2 can be obtained from the normal vector of the fitting plane equation shown in FIG. 6 from the plate thickness of the flat plate, and the vector T2 can be obtained. Therefore, from these, vectors T1, T2, and T3 are obtained, and vector T is obtained from Equation (6).

  As described above, the coordinate transformation of the three-dimensional shape measuring device 106 to the coordinate system of the three-dimensional shape measuring device 104 can be performed. Similarly, the coordinate transformation of the three-dimensional shape measurement device 105 to the coordinate system of the three-dimensional shape measurement device 104 is performed, and the coordinate transformation of the three-dimensional shape measurement device 103 to the coordinate system of the three-dimensional shape measurement device 104 is performed. Can be matched with the coordinates of the three-dimensional shape measuring apparatus 104.

  In the above embodiment, a flat plate 140 as shown in FIG. 8 can be used as a three-dimensional object for calibration instead of the flat plate 120 shown in FIG. In this embodiment, a groove 141 is cut instead of the black line 121 of FIG. In the same manner as in the embodiment of FIG. 4, the uncut surface 142 is used as a surface to be measured, and a fitting plane equation of the plane plate 140 is obtained therefrom, and their rotation matrix R is obtained. Further, the parallel vector T can be obtained from the intersection point P of the groove 141 and the corresponding intersection point (not shown) on the back surface thereof.

  Further, instead of the flat plate 120 shown in FIG. 4, a triangular prism 150 as shown in FIG. 9 can be used as a three-dimensional object for calibration. This is used when the three-dimensional shape measuring apparatuses 201, 202, and 203 are arranged every 120 degrees. The three-dimensional shape measuring apparatus 201 obtains a fitting plane equation of the measured surface 151 of the triangular prism 150, the three-dimensional shape measuring apparatus 202 calculates the fitting plane equation of the measured surface 152, and the three-dimensional shape measuring apparatus 203 is measured. A fitting plane equation of 153 is obtained. Thereafter, the rotation matrix R is obtained in the same manner from the angles at which the measured surfaces 151, 152, 153 intersect. Further, a measuring point is determined by providing a raised shape or a line by painting on the measured surfaces 151, 152, 153 of the three-dimensional object 150 for calibration, and a parallel vector T is obtained from the mutual positional relationship of these measuring points.

  Instead of the flat plate 120 shown in FIG. 4, a hexahedron 160 as shown in FIG. 10 can be used as a three-dimensional object for calibration. Nothing is processed on the surface of the hexahedron 160. An equation of a fitting plane is obtained by using each surface of the hexahedron 160 as a surface to be measured, and a rotation matrix R is obtained in the same manner as in the above embodiment. A parallel vector T is obtained from the edge point P of the hexahedron 160.

  In the above embodiments, the surface to be measured of the calibration three-dimensional object 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 solid object. In addition, it is only necessary that the surface shape of the surface to be measured is known, and when there are a plurality of surfaces to be measured, it is only necessary that the mutual positional relationship is known. Since a surface other than a plane may be used in this way, the fitting plane in the above embodiment is a subordinate concept of the fitting surface. The measuring method of the three-dimensional shape measuring apparatus can be applied to various types such as those using a laser, and is not limited to a specific one.

It is a perspective view which shows the external appearance of a three-dimensional shape measuring apparatus. It is a perspective view which shows the external appearance of the measuring device using four three-dimensional shape measuring devices. It is a figure which shows the principle which performs coordinate conversion from one coordinate system to another coordinate system. It is a figure which shows the plane board as a three-dimensional object for calibration, Comprising: (a) is a front view, (b) is a top view, (c) is a side view, (d) is a perspective view. It is a figure which shows arrangement | positioning of four 3D shape measuring apparatuses and a plane board, Comprising: (a) is a front view, (b) is a top view, (c) is a side view. It is a figure which shows the state which measures a plane board with two 3D shape measuring devices, Comprising: (a) is a perspective view, (b), (c) is a figure of a fitting plane. It is a figure which shows the state which measures the corresponding point of the front and back of a plane plate with two 3D shape measuring apparatuses, Comprising: (a) is a perspective view, (b) is a figure which shows the calculation method of a parallel vector. It is a perspective view which shows the top view with a groove | channel as a three-dimensional object for calibration. It is a figure which shows the state which used the triangular prism as the three-dimensional object for calibration. It is a figure which shows the state which used the hexahedron as a three-dimensional object for calibration.

Explanation of symbols

DESCRIPTION OF SYMBOLS 100 Camera 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 111 of one three-dimensional shape measuring device Other The origin and coordinate axis 112 of the 3D shape measuring device Parallel vector T
113 Rotation matrix R
120 Three-dimensional object for calibration (flat plate)
121 Line 122 Base 130 Fitting (flat) surface 131 of one three-dimensional shape measuring device 131 Fitting (flat) surface 140 of another three-dimensional shape measuring device 140 Solid object for calibration (flat plate)
141 groove 142 surface 150 triangular prism 151 measured surface 152 measured surface 153 measured surface 160 hexahedron 201 three-dimensional shape measuring device 202 three-dimensional shape measuring device 203 three-dimensional shape measuring device

Claims (5)

A three-dimensional calibration object in the form of a flat plate, which is arranged at a position that can be measured from a plurality of three-dimensional measuring devices each having a coordinate system composed of an original origin and coordinate axes, and has two surfaces that are front and back pairs as a surface to be measured;
The plurality of three-dimensional measuring devices measure three-dimensional coordinate values of three or more points on each measurement target surface to be measured for each three-dimensional measuring device by using a coordinate system unique to each three-dimensional measuring device, A plane equation calculation means for calculating each plane equation of each surface to be measured from three or more three-dimensional coordinate values for each coordinate system unique to each of the three-dimensional measurement devices;
A rotation matrix used for matching the coordinate systems of the three-dimensional measuring devices facing each other across the calibration three-dimensional object from the plane equations of the two measured surfaces that are the front and back pairs of the calibration three-dimensional object. A rotation matrix calculating means for calculating;
Each three-dimensional coordinate of each of the two measurement points located symmetrically on each measured surface of each three-dimensional measurement device facing each other across the calibration three-dimensional object among the plurality of three-dimensional measurement devices The value is measured by the coordinate system unique to each three-dimensional measurement device, each measurement vector value from each three-dimensional measurement device to each measurement point is calculated, and each three-dimensional value is calculated based on each measurement vector value. A tertiary coordinate calibration system, comprising: parallel vector calculation means for calculating a parallel vector for matching a coordinate system unique to the measurement apparatus. The rotation matrix calculation means includes means for calculating a rotation matrix based on two normal vectors obtained from the respective plane equations of the two measured surfaces to be front and back. 3D coordinate calibration system. The plane equation calculating means includes means for calculating a square sum of errors from three or more three-dimensional coordinate values, and means for calculating each plane equation from the extreme value of the square sum. The tertiary coordinate calibration system according to any one of claims 1 and 2. The three-dimensional coordinate calibration system according to any one of claims 1 to 3 , wherein the parallel vector calculation means includes means for calculating from each measurement vector value and a vector value between the measurement points. A plurality of wires by painting or groove in the respective surface to be measured of the calibration three-dimensional object, any one of claims 1 to 4 an intersection of the plurality of lines, characterized in that said measurement points Or 3D coordinate calibration system.

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