JPS60102504A - Position measuring method of three-dimensional body - Google Patents

Abstract

PURPOSE:To facilitate the measurement of the position of a three-dimensional body, by placing one or a plurality of mirrors around the side or the like of the three-dimensional body, displaying the body and the image on the mirror on one screen at the same time, and analyzing the body and the image. CONSTITUTION:For example, one mirror 3 is appropriately positioned with respect to a body 2 on an experiment table 1. A mirror image 4 of the body and the body 2 are photographed by a camera (not shown) and the like as a picture on one screen. The picture is analyzed manually or by an electronic computer, and the positions of the characteristic points of the vortex and the like of the body 2.

Description

[Detailed description of the invention] In order to visually know the spatial position of a feature point on an object from its image, a screen from one viewpoint is insufficient, and multiple screens from different viewpoints are necessary. It is. So-called stereoscopic vision is also an effective method for this purpose. However, since these methods handle one screen of the object for one viewpoint, they handle multiple screens as a whole, and the amount of information to be handled is large.

If we were to place a mirror somewhere around an object and obtain its mirror image, that mirror image would give us the same information as if we were viewing the object from a different perspective. Taking advantage of this, one or more mirrors are placed around an object, such as on the side, behind, above, or below the object, and the object and its mirror images are simultaneously displayed on a single screen. If you copy it, it will become 1 image.
It is possible to obtain images from multiple viewpoints. Inversion by mirror image can be achieved by performing corresponding calculation processing.

For example, the setup when using one mirror is shown in Figure 1 (
It seems like a). Assume that we want to know the positions of feature points (for example, each vertex) of an object 2 on an experimental table 1. A mirror 3 is placed at an appropriate position so that the mirror image 4 of the object 2 is reflected at an appropriate position. The field of view indicated by the broken line in FIG. 1(a) is photographed using a camera or a TV camera as a single screen image as shown in FIG. 1(b). By analyzing this image manually or using an electronic computer, it is possible to calculate at least the coordinates of the vertices that are reflected in both the object image and the mirror image.

The principle is as follows. In Figure 2, if Xθ is a point on the object, Xm is its mirror image, and α is the normal vector of the mirror, then the target point Xθ on the object is converted by the mirror to the mirror image point Xm as follows: Xm =(I3×3-2/|α|2
・ααT)
2) Here, ...(3) becomes.

The coordinate system and imaging parameters are set as shown in FIG. 3. Here, X, Y, Z: World coordinate system, Xc, Yc, Zc: Camera coordinate system, XI, YI: Image coordinate system, θ: Turning angle, ■:
Tilt angle, t: camera distance, f: focal length, Pf: focal point,
It is. As a result, the transformation matrix Tcw from the world coordinate system to the camera coordinate system is Tcw = sin ■ sin θ sin ■ cos θ − co
s■ 0-cosθ sinθ 0 0 -cos■sinθ -cos■cosθ -sin■
t0 0 0 1...(4) The perspective transformation matrix Tp is Tp=1...(5) 1 1 r 1 Here,.

The procedure for position calculation is as follows.

(1) Express the object point Xθ and the mirror image point Xm with respect to the camera coordinate system, and let them be Xcθ and Xcm, respectively.

Xcθ=TcwXθ, Xcm=TcwTmθXθ…(6
)(2) Perform perspective transformation and set Xiθ,Xim.

Xiθ=TpTcwXθ, Xim=TpTcwTmθX
θ(3) Let the fourth elements of Xio and Xim in the above equation (7) be w1 and w2, respectively.

…(8) however, It is.

(4) Combine the coordinate values of the target point and mirror image point in the image
=(xiθ, yiθ, xim, yim)T.

Projecting Xiθ and Xim in equation (7)...(9) Here, (5) From equation (7) and equation (9), WXi=I2×4Tcw Xθ I2×4TcsTmθ...(10) (6) Extracting the unknowns included in the left side (w1, w2) of equation (10), WXi=A2Xθ...(11) Here, (7) From equation (10) and equation (11), (A1-A2)Xθ= 0...(12), and when divided accordingly, equation (12) becomes AXθ=-b, and from this, the target point on the object is set as Xθ=-A-1b.

By the above method, for example, as shown in Fig. 4, a plurality of mirrors (
Here, by using three images (1, 2, and 3), it is possible to measure the position of the feature point of the object in more detail. 4 is a transparent plate that supports the object.

[Brief explanation of the drawing]

Figure 1 shows an example of a setup using one mirror and the image obtained from it, Figure 2 explains the mirror image, Figure 3 explains the imaging system, and Figure 4 shows an example of the setup using three mirrors. It shows. Patent applicant Tsunego Honda

Claims (1)

[Claims] One or more mirrors are placed around the three-dimensional object, such as behind, to the sides, above, or below the object, and the object and the mirror images reflected in those mirrors are simultaneously projected as a single screen image. A method for measuring the position of a three-dimensional object, characterized in that the position of each feature point existing on the object can be calculated by analyzing.