KR100457080B1 - Method for surveying the characteristics of joint on rock slope using image - Google Patents

Abstract

The present invention relates to a method for investigating the geometric characteristics of joints of rock slopes, which is essential for the design and stability analysis of exposed rock slopes. In addition to obtaining survey data, the survey data are accurate and accordingly provide high reliability in the results of statistical processing of joint data. will be.

The present invention comprises the steps of establishing a shooting plan according to the analysis target and site conditions; Installing a digital camera at a predetermined position according to the shooting plan; Installing a spatial coordinate measuring device at the survey origin for coordinate measurement: setting three control points on a rock slope to be analyzed; Measuring the spatial coordinates of the control point using a spatial coordinate measuring device installed at the surveying point: Taking a photograph of the subject: The camera controller is adjusted so that any control point coincides with the center of the image in the photographed image Photographing a photographing surface by adjusting a photographing direction of the camera using the photographing method; Installing a ground assist point device such that a ground assist point is located on a collinear line connecting the control point of the image pit and the rock slope; Measuring spatial coordinates of the ground auxiliary point using a spatial coordinate measuring device installed at a survey origin; Repeating the steps by moving the digital camera to the next photographing position; From the coordinates of the three ground control points and the ground auxiliary point, and the image coordinates of the remaining two control points that do not coincide with the image pub, the focal length, which is the internal parameter of the camera, and the coordinates of the image, and the position of the camera, which are external parameters Determining an angle of rotation of the camera; Constructing a collinear condition equation (center projection equation) of the left and right cameras from the camera parameters; Deriving the spatial coordinates of the vertices constituting the joint surface from the image coordinates projected on the image from the relationship between the collinear conditional expressions of the left and right cameras; Determining a normal vector of the joint surface from the spatial coordinates of the joint surface; and determining the inclination direction and the inclination angle of the joint surface from the normal vector of the joint surface.

Description

Method for surveying the characteristics of joint on rock slope using image}

The present invention relates to a method for investigating the geometric characteristics of joints of rock slopes, which is essential for the design and stability analysis of exposed rock slopes. In addition to obtaining a large number of survey data, the survey data are accurate and accordingly provide high reliability in the results of statistical processing of joint data. It is about.

The stability of rock structures, including rock slopes, depends on the geometric and physico-mechanical properties of the discontinuities such as joints, which are inevitably present in the formation of rock masses.

In the construction and maintenance of rock slopes, the quantification of joint characteristics, a representative discontinuity, is a very essential task. Therefore, the joint characteristics serve as an important input element in the design process for rock with stability analysis. The geometric and physico-mechanical properties of the joints are then quantified from investigations and tests, respectively.

Conventional methods for measuring the geometric characteristics of joints include a scan line irradiation method, a scan window irradiation method, a borehole wall logging method, and a drilling core irradiation method. The irradiation method and the irradiation window irradiation method is a method performed manually by using a clinometer and a tape measure.

The survey method has a problem that the survey data is difficult to access in a difficult access area and the scope of the survey is limited, so the reliability of the survey data is low and the heavy manual work must be performed. The survey window survey method is difficult to set the survey window on the rock slope. There is a problem that heavy manual work must be performed, and the borehole wall logging and drilling core irradiation method has a problem that the irradiation range is limited and the absolute direction of the core is difficult to measure.

As a method for solving the problems of the conventional manual survey, there is a method for examining the geometrical characteristics of objects in space by an image. The general method is performed in the following order.

(1) Analysis target setting

(2) Shooting position selection and shooting arrangement design of survey origin

(3) setting or distribution of control points

(4) control point coordinate surveying

(5) shooting

(6) camera parameter determination

(7) Extended shooting by moving the shooting position and rotating the shooting direction

(8) Repeat (3) to (6) by setting new control point

(9) Calculation of spatial coordinates of arbitrary points

(10) Determination of the length and shape of an object by spatial coordinates

Representative methods of geometric characteristics of spatial objects using images include parallel stereogrammetry, convergent stereogrammetry, luminous flux adjustment, DLT method, Tsai method using computer vision. There is an eight-point algorithm.

This representative method is similar to the general method described above, but differs in the method of determining camera parameters.

Photogrammetric and computer vision-based images derive the spatial coordinates of an arbitrary point by the corresponding image coordinates when an arbitrary point of an object in space is projected onto the image by a central projection relationship, and from the derived spatial coordinates. A method of analyzing geometrical characteristics by constructing the length and shape of an object.

In the parallel stereophotogrammetry method, as shown in FIG. 1, two cameras having the same focal length are installed on both sides of a device of a camera base, and the optical axes of these cameras are set to be parallel to each other. A method of deriving a spatial coordinate from an image coordinate by an equation) is performed in the following order.

(1) mounting the camera to the camera base

(2) Adjust camera interval within camera base according to shooting distance

At this time, an appropriate photographing interval / shooting distance is 1/20 to 1/5 m.

(3) Shooting direction setting

(4) camera height measurement

(5) shooting

(6) Derivation of spatial coordinates of arbitrary points of an object

At this time, the visual difference formula is applied and the rotation angle is fixed so that no camera parameters need to be determined.

(7) Determine the length and shape of the object from spatial coordinates

The parallel stereoscopic survey method has the advantage that the camera's shooting direction is fixed (rotation angle fixed) so that camera parameters are not determined, but camera intervals are limited according to the shooting distance, and the range of analysis is reduced due to the small image overlapping range. There is a disadvantage, requiring a camera base.

In the convergent stereophotogrammetry method, as shown in FIG. 1, two cameras having the same focal length are installed on both sides of the camera base, and the optical axes of these cameras are set to converge correctly so that the image is obtained by the central projection equation. As a method of deriving the spatial coordinates from the coordinates, the same process as the parallel stereoscopic photogrammetry method is performed, but the photographing direction of the camera is converged on the camera base. Camera parameters are determined by measuring or determining the angle of convergence (rotation angle Φ).

Converging stereoscopic photogrammetry has the advantage that the camera's shooting direction is fixed (rotation angle fixed) does not require the determination of camera parameters, but camera distance is limited according to the shooting distance, there is a disadvantage that requires a camera base.

As shown in FIG. 2, the bundle adjustment method distributes control points to an object to be analyzed and uses the spatial coordinates of the control points, the corresponding image coordinates, and the initial approximation of the camera parameters. After the camera parameters are determined, the central projection equation is constructed to derive the spatial coordinates of the arbitrary points. The method is performed in the following order.

(1) Set and distribute at least three control points to the analysis target (actually apply many control points)

(2) Spatial coordinate measurement of control points

(3) Camera parameter determination by resection

Least squares method, requires initial approximation of camera parameters

(4) Composition of collinear condition

(5) Calculation of spatial coordinates by forward intersection

(6) Determination of the length and shape of the object by spatial coordinates

The luminous flux adjustment method can freely set the shooting direction, has high accuracy and theoretically can use at least three control points, but this requires an initial approximation of the camera parameters. In practice, the disadvantage is that a large number of control points are used and the computational time required for nonlinear optimization is required in the camera parameter determination process.

The DLT method (Direct Linear Transformation Method) is a volume distribution of five or more control points to the analysis object as shown in Figure 3 and by using the least square method using the spatial coordinates and the corresponding image coordinates of the camera A method of deriving the spatial coordinates of an arbitrary point by determining a parameter and constructing a DLT equation modified from the central projection equation is performed in the following order.

(1) Volume distribution of at least 11 control points to the analysis object

(2) control point spatial coordinate measurement

(3) Derivation of DLT coefficients by least squares method

(4) DLT type configuration

(5) Spatial coordinate calculation

(6) Determination of the length and shape of the object by spatial coordinates

The DLT method has the advantage that it is possible to set the shooting direction freely and to calculate it more quickly than the luminous flux adjustment method. However, since the value of the camera element is an approximation, it is not accurate and in practice, more than 11 control points must be applied. have.

The Tsai method of the computer vision (Tsai's Method) is to distribute the control points of more than seven points on the two surfaces as shown in Figure 3, and the least square using the spatial coordinates and the corresponding image coordinates of these control points After the camera parameters are determined by the method, a center projection equation is constructed from them to derive the spatial coordinates of an arbitrary point, which is performed in the following order.

(1) Distribution of control points of at least seven points on two sides

(2) control point spatial coordinate measurement

(3) Derivation of Tsai Coefficient by Least Square Method

(4) Composition of central projection equation

(5) Spatial coordinate calculation

(6) Determination of the length and shape of the object by spatial coordinates

The Tsai method has the advantage that it is possible to freely set the shooting direction and can be calculated faster than the luminous flux adjustment method. However, a specific black paper is required, and in fact, many adjustment points of 7 points or more must be applied.

As shown in FIG. 4, the 8-point Algorithm Method secures a coincidence point of at least 8 points in two left and right images, such as edges or corners, which appear in the image through image processing. A method of constructing epipolar geometry using feature points as control points and deriving spatial coordinates through image restoration is performed in the following order.

(1) Take a picture so that at least 8 matching points appear in the left and right images

(2) Epipolar geometry

(3) Essential matrix composition

(4) Fundamental matrix composition

(5) 3D reconstruction

(6) Composition of central projection equation

(7) Spatial coordinate calculation

(8) Determination of the length and shape of the object by spatial coordinates

The 8-point algorithm has the advantage that it can be automated without the need for any initial information about camera changes or elements, but it can be applied only when the difference between lines and intensities in the image, such as artificial structures, is contrasted. have.

The present invention has been made to solve the above-described problems of the prior art, it is possible to set the shooting direction freely to enable the analysis of the joint surface that does not appear in the image due to the intersecting characteristics of the joint, and by applying a minimum control point Easily determine camera parameters, calculate spatial coordinates and calculate joint orientation quickly, and process large amounts of data to increase the reliability of joint data statistical processing. The present invention provides a method for investigating the geometrical characteristics of rock slope joints using images that can directly use digital cameras that can take advantage of the same digital image.

Method for investigating the geometrical characteristics of rock slope joint by the image of the present invention for achieving the above object comprises the steps of establishing a shooting plan according to the analysis target and site conditions; Installing a digital camera at a predetermined position according to the shooting plan; Installing a spatial coordinate measuring device at the survey origin for coordinate measurement: setting three control points on a rock slope to be analyzed; Measuring the spatial coordinates of the control point using a spatial coordinate measuring device installed at the surveying point: Taking a photograph of the subject: The camera controller is adjusted so that any control point coincides with the center of the image in the photographed image Photographing a photographing surface by adjusting a photographing direction of the camera using the photographing method; Installing a ground assist point device such that a ground assist point is located on a collinear line connecting the control point of the image pit and the rock slope; Measuring spatial coordinates of the ground auxiliary point using a spatial coordinate measuring device installed at a survey origin; Repeating the steps by moving the digital camera to the next photographing position; From the coordinates of the three ground control points and the ground auxiliary point, and the image coordinates of the remaining two control points that do not coincide with the image pub, the focal length, which is the internal parameter of the camera, and the coordinates of the image, and the position of the camera, which are external parameters Determining an angle of rotation of the camera; Constructing a collinear condition equation (center projection equation) of the left and right cameras from the camera parameters; Deriving the spatial coordinates of the vertices constituting the joint surface from the image coordinates projected on the image from the relationship between the collinear conditional expressions of the left and right cameras; Determining a normal vector of the joint surface from the spatial coordinates of the joint surface; and determining the inclination direction and the inclination angle of the joint surface from the normal vector of the joint surface.

1 is a view showing a conventional parallel and convergent stereogram method;

2 is a view showing a conventional luminous flux adjustment method;

3 is a diagram showing a conventional DLT method and a Tsai method;

4 shows a conventional 8-point algorithm;

5 is a layout view showing the correlation between the position of the ground control point, the camera, the ground auxiliary point, the survey origin, the image pub for performing the geometric characteristics of the rock slope joint of the present invention,

6 is a photograph showing a camera controller used in the irradiation method according to the invention,

Figure 7 is a photograph showing a ground assist point apparatus used for irradiation according to the present invention,

8A illustrates spatially the geometric relationship of the arrangement of the input elements of FIG. 5 to determine camera internal parameters according to the invention;

8B is a plan view showing the geometric relationship of FIG. 8A;

9A is a view illustrating a rotation angle that determines a rotation matrix of a camera that determines a direction of a photographic image in a spatial coordinate system assumed based on a survey origin; FIG. 9B is a rotation of an image plane in a spatial coordinate system assumed based on a survey origin; Showing the relationship between the direction cosine between the collinear and spatial coordinate system

10 shows image coordinates (x, y) of C ₁ or C ₃ actually photographed and image coordinates (x ', y calculated by a rotation matrix composed of rotation angles ω, Φ, and χ = 0 determined by a straight line I. Coordinate system,

11 is a diagram showing a value between y coordinates between c ₁ ', c ₃ ' determined when the control points C ₁ , C ₃ are projected on the image c ₁ , c ₃ and ω, Φ and x = 0 determined;

12 is a view in which the direction of the surface is expressed by strike, dip or dip direction α, and dip angle β;

13 is a converging photographing arrangement diagram by two cameras,

14 is a diagram showing a relationship between a joint surface and a normal vector;

15 is a view showing a state in which a normal vector is configured in a relative spatial coordinate system in determining the direction of the joint using the components of the joint normal vector;

16 is a view showing the setting and movement of the control point in the extended analysis,

17 is a view showing a state performed by moving the photographing surface to the left in the field verification of the extended analysis.

* Explanation of symbols for main parts of the drawings

0: survey point P: projection center point (camera position)

o: Video Tavern G: Ground Assist

C ₁ , C ₂ , C ₃ : ground control point

Hereinafter, the present invention will be described in more detail with reference to the accompanying drawings.

5 is a layout view showing the correlation between the position of the ground control point, the camera, the ground auxiliary point, the survey origin, the image pub for performing the geometric characteristics of the rock slope joint of the present invention.

Method for investigating the geometric characteristics of rock slope joint by the image of the present invention is divided into an outdoor working process and an indoor working process, the outdoor working process comprising the steps of establishing a shooting plan according to the analysis target and site conditions; Installing a digital camera at a predetermined position P according to the shooting plan; Installing a spatial coordinate measuring device at the survey origin 0 for coordinate measurement: setting three control points C ₁ , C ₂ , and C ₃ on the rock slope to be analyzed; Determining the spatial coordinates of the control points C ₁ , C ₂ , C ₃ using a spatial coordinate measuring device installed at the survey origin 0: Taking a photograph of the subject: Image pub that is the center point of the image in the captured image Adjusting the photographing direction of the camera by using the camera controller so that the control point C ₂ and the control point C ₂ coincide with each other; Installing a ground auxiliary point device such that the ground auxiliary point G is positioned on a collinear line connecting the image pub o and the control point C ₂ of the rock slope; Measuring a spatial coordinate of the ground auxiliary point G by using a spatial coordinate measuring device installed at a survey origin 0; It consists of repeating the above steps by moving the digital camera to the next photographing position.

In FIG. 5, the XYZ coordinate system is a spatial coordinate system whose origin is the position of the spatial coordinate measuring machine, the coordinate system of xyz is a spatial coordinate system whose origin is the camera position, and the x _p -y _p coordinate system is a planar image having the image principal o as the win point. Where f is the focal length of the camera and c ₁ , c ₃ are the image coordinates corresponding to the ground control points C ₁ , C ₃ .

In establishing the shooting plan according to the analysis target and site conditions, the number of shots that may include the analysis target according to the size and shooting distance of the analysis target, the installation position of the camera according to the shooting environment, and the ground assist point G position The survey origin 0, which is the origin of the relative spatial coordinate system, is determined.

In the step of installing the spatial coordinate measuring instrument at the survey origin for the coordinate measurement, a known total station is used.

In the step of setting three ground control points C ₁ , C ₂ , and C ₃ on the rock slope to be analyzed, the ground control points are set at a location that is easily accessible to the operator.

The camera adjuster for adjusting the photographing direction of the camera so that the image main point o and the control point C ₂ coincide with each other and is configured as shown in FIG. 6 to allow left and right rotation and up and down movement of the camera. The upper part of the camera adjuster is fixed to the camera and the lower part is provided with a tripod fixed to the ground.

The ground control point device in which the ground auxiliary point G is located is configured as shown in FIG. 7, and is configured with a horizontal feed control unit and a shanghai transport control unit. It can be located on the collinear connecting C ₂ .

The spatial coordinates of the three ground control points C ₁ , C ₂ , C ₃ and the ground auxiliary point G on the rock slope are measured by the outdoor work process as described above. The spatial coordinates of these four points and the ground control points C ₁ , C ₃ are measured. The image coordinates c ₁ and c ₃ projected on the image are used as initial input elements for deriving the relative spatial coordinates of the vertices of other spaces forming the joint surface.

Next, the indoor working process will be described.

The indoor working process includes determining camera internal and external parameters from the spatial coordinates of the three ground control points C ₁ , C ₂ , C ₃ and ground assist point G; Constructing a collinear condition equation (center projection equation) of the left and right cameras from the camera parameters; Deriving the spatial coordinates of the vertices constituting the joint surface from the image coordinates projected on the image from the relationship between the collinear conditional expressions of the left and right cameras; Determining a normal vector of the joint surface from the spatial coordinates of the joint surface; and determining the inclination direction and the inclination angle of the joint surface from the normal vector of the joint surface.

First, the steps of determining the camera parameters from the spatial coordinates of the three ground control points C ₁ , C ₂ , C ₃ and ground support point G will be described.

Camera parameters have internal and external parameters.

The camera internal parameters are the focal length f of the camera and the image pub o, which is the center point of the image. In general, the internal parameters of the camera are applied to the specifications provided by the camera manufacturer, but in the present invention, the ground assist point device is used to derive the focal length of the camera, and the image pub o is the maximum resolution of the camera (1600 × 1200 (800, 600) pixel coordinates are applied. The image coordinate of the image pub o is used as it is, the process of obtaining the focal length f using the pixel coordinates of the camera as it is. FIG. 8A is a view showing spatially the geometric relationship according to the arrangement of the input elements of FIG. 5 and FIG. 8B is a view showing this in plan.

The image liquor o and the intersection point of the ground auxiliary point repair defined as a control point intersection of repair down to I in C ₁ to the linear equation passing through G I d C ₁ 'and down to the line I in the same manner control point C ₃ When C ₃ ′, the length of each of these repairs is u ₁ , u ₂ .

The focal length can be calculated using the proportional relationship between the lengths u ₁ , u _{2 in} space and the lengths d ₁ , d ₂ projected on the photograph. Before using the proportional relationship, the ground control point C ₂ (xc ₂ , yc ₂ , zc ₂ ) and the ground auxiliary point G (x _G , y _G ) located on the collinear line with the image point o to find u ₁ , u ₂ . Deriving the equation of the straight line I in space passing through, z _G ) is shown in Equation 1.

[Equation 1]

The direction numbers of the straight line I are shown in Equation 2.

[Equation 2]

here,

Therefore, the direction cosine is as shown in Equation 3.

[Equation 3]

The length u ₁ of the waterline on I in C ₁ (xc ₁ , yc ₁ , zc ₁ ) and the intersection point C ' ₁ (xc' ₁ , yc ' ₁ , zc' ₁ ) of the straight line I with the waterline are expressed by Equation 4 You can get it.

[Equation 4]

here ,

Therefore, the length u ₁ of the repair line is expressed by Equation 5.

[Equation 5]

_{C 3 (xc 3, yc 3} , zc 3) length u ₂ and a straight line I and the intersection point _{C '3 (xc' 3,} yc '3, zc' 3) in the repair of repairs made to the I in the equation (4), mathematics Through the same process as Equation 5 can be obtained as shown in Equation 6.

[Equation 6]

here,

The length u ₂ of the repair line is shown in Equation 7.

[Equation 7]

The relationship shown in Equations 8 and 9 can be obtained from the proportional relationship between ΔC ₁ PC ₁ ′ and Δc ₁ Po and ΔC ₃ PC ₃ ′ and Δc ₃ Po in FIG. 8B.

[Equation 8]

[Equation 9]

Subtracting Equation 9 from Equation 8 results in Equation 10.

[Equation 10]

Therefore, the focal length f of the camera can be determined as in Equation (11).

[Equation 11]

The following describes the process of determining camera external parameters. Camera external parameters define the camera's position (projection point, P) and rotation angle within the overall spatial coordinate system.

The rotation matrix of the camera for determining the direction of the photographic image is determined by the rotation angles (ω, φ, χ) representing the degree of rotation of each axis as shown in FIG. 9A. By applying ground control points and ground control points, the camera's rotation angles (ω, φ, χ) can be simplified through the directional cosine of the collinear equations (spatial linear equations of the optical axis) formed by the image dominant, ground control points, and ground control points. Can be induced. The following is the derivation process. Fig. 9B shows the directional cosine relationship between the spatial coordinates (linear I in the direction of the camera, the optical axis z axis) and the spatial coordinate system according to the rotation of the image plane in the spatial coordinate system based on the survey origin.

The linear equation of the optical axis calculated by Equation 1 is shown in Equation 12.

[Equation 12]

here,

Direction cosine is defined as in Equation 13.

[Equation 13]

Directional cosine;

The configuration of the rotation matrix by the direction cosine is shown in Equation (14).

[Equation 14]

Equation 15 corresponds to the arrangement between the rotation matrix component and the direction cosine of the collinear line (linear I, optical axis z).

[Equation 15]

The rotation matrix configuration according to the rotation angles ω, β, and x is expressed by Equation 16 below.

[Equation 16]

The components of the rotation matrix formed by the directional cosine and the rotation angle, respectively, must match, so that in Equation 14, Equation 15, and Equation 16,l=r ₃₁, m =r ₃₂, n =r ₃₃Is the same asl= sinφ, m = -sinωcosφ, n = cosωcosφ holds. Thus, straightIThe rotation angles ω and φ can be obtained from Eq. The sign of the rotation angle is also determined from the direction cosine.

[Equation 17]

The rotation angle x can be obtained from the spatial coordinates of the ground control points C ₁ and C ₃ and the image coordinates obtained from Equation 17. First, the image coordinates of C ₁ and C ₃ are calculated from the rotation matrix when the rotation angles ω, Φ, and x = 0 obtained from Equation 17, and the image coordinates of C ₁ and C ₃ measured in the photograph are compared. Determine the value of the angle x rotated about the center.

FIG. 10 shows image coordinates (x, y) of C ₁ or C ₃ actually photographed, and image coordinates (x ', y) calculated by a rotation matrix composed of rotation angles ω, Φ, and x = 0 determined by a straight line I. FIG. Coordinate system indicating ').

The angle between the vectors represented by the two image coordinates is the rotation angle x about the Z axis of the camera. The square angle (x) is calculated using a scalar product as shown in Equation 18.

Equation 18

Therefore, the rotation angle x can be obtained as shown in Equation 19.

[Equation 19]

The sign of x is between c ₁ ', c ₃ ' determined when the control points C ₁ , C ₃ are projected on the image c ₁ , c ₃ and ω, Φ determined by Equation 17, and x = 0. The values between the y coordinates may be determined by comparing the values as shown in Equation 20.

[Equation 20]

If c _{3, y} 〉 c _{3, y} 'then x 〈0, else x〉 0

By using ω, Φ, and x in Equations 17 to 20, a complete rotation matrix of Equation 16 can be constructed.

The position of the projection center point, which is a potential vector component, is derived using the linear equation I of G and the optical axis when the distance between the ground auxiliary point G and the projection center point P is g as shown in FIG. 8B. Presence projection center point g if enough away from C ₁ points in meeting the waterline down to the line I C ₁ 'and the projection center point and the distance s ₁ between P C _1' projection central point in that on the same straight line and the straight line equation (I) of the optical axis G The distance to is t ₁ . Similarly, the distance t of these relationships when _two days in between the C ₃ points in meeting the waterline down to the line I C ₃ 'and the distance s ₂ from the to the projection center point P C _3' from the ground auxiliary point G is expressed as shown in Equation (21) Can be.

[Equation 21]

Therefore g is equal to (22).

[Equation 22]

t ₁ and t ₂ can be obtained from the spatial coordinates of G, C ₁ 'and G, C ₃ '. Therefore, the spatial coordinates of the projection center point P can be obtained as in Equation 23.

[Equation 23]

Where l, m and n are the direction cosines of the equation of the straight line I.

As described above, the spatial coordinates of the camera's external parameters, that is, the rotation angles ω, Φ, x, and the camera's position, that is, the projection center point P, can be obtained.

Next, a step of constructing a collinear condition equation (center projection equation) of the left and right cameras from the camera parameters will be described.

The inclined shape of the joint surface constituting the rock is expressed by orientation. There are two general ways to express the direction of the joint. As shown in FIG. 12, the direction of the surface may be represented by a strike and a dip or a dip direction α and a dip angle β.

Perimeter refers to the direction of the intersection of the joint and the horizontal plane, which is expressed as an angle measured clockwise with respect to the north direction. The angle of inclination or inclination represents the maximum angle of the joint surface perpendicular to the main line and the horizontal plane. The direction it points to is called the oblique direction and is also expressed in degrees measured clockwise relative to the north.

In engineering, the direction of the joint surface is mainly represented by the inclination direction α and the inclination angle β.

The inclination direction and the inclination angle may be obtained from the spatial coordinates of the points included in the joint surface. This is made possible by the normal vector derived from the spatial coordinates constituting the joint surface. In the spatial coordinate system, the inclination of the straight line in the xy and yz planes parallel to the normal vector of the joint surface can be derived, and the inclination direction and the inclination angle can be calculated from the relationship between the sign of the inclination and the azimuth. Here, the process of deriving the direction of the joint surface using the spatial coordinates of the points on the joint surface derived from the image will be described.

In order to derive the spatial coordinates, a converging photographing arrangement by two cameras is constructed as shown in FIG. 13. Using the internal and external parameters of each camera, we construct a collinear conditional expression representing the relationship between two-dimensional image coordinates and three-dimensional spatial coordinates in each camera.

In the general analysis method using the collinear condition equation, in the two conventional methods where the optical axes of two cameras are parallel or converging, the position of the projection center is used as an input element by surveying, and the projection center point in the X axis direction in the spatial coordinate system. It can be said that there is only a position shift of. However, using the projection center point determined by the ground control point and the ground control point, we construct the collinear condition equation that can move freely in the X, Y, Z direction in the spatial coordinate system. Can be. The location of the projection center point is the transition vector component of the collinear condition.

First, in the left picture, the collinear condition equation (center projection equation) is the same as Equation 24 and Equation 25.

[Equation 24]

[Equation 25]

The collinear condition equation (central projection equation) of Equation (2.25) obtained from the right picture is the same as Equation 26 and Equation 27.

[Equation 26]

[Equation 27]

In equations (24) to (27), the subscript _L means the left picture, _R means the right picture, X _p , Y _p , and Z _p represent the spatial coordinates of the projection center point P, the origin of the camera coordinate system, and r ₁₁ The back is an element of the rotation matrix R representing the angle of rotation of the camera, and f is the focal length of the camera.

If the collinear condition equations of the two photographs are simplified by using the substituted variables, the following equations (28) to (31) are used.

[Equation 28]

here,

[Equation 29]

here,

Equation 30

here,

Equation 31

here,

Next, a step of deriving the spatial coordinates of the vertices constituting the joint surface from the image coordinates projected on the image from the relationship between the collinear conditional expressions of the left and right cameras will be described.

Subtracting equation (30) from equation (28) is equal to equation (32).

Equation 32

Therefore, equations (33) and (34) are obtained.

[Equation 33]

[Equation 34]

or

Subtracting Equation 31 from Equation 29 gives the same as Equation 35,

[Equation 35]

Therefore, equations 36 and 37 are obtained.

[Equation 36]

or

[Equation 37]

or

As shown in Equation 32 to Equation 37, the positional components of any one point (point on the joint surface) shown in the photograph can be obtained with X: 4, Y: 4, and Z: 2, respectively. When accurate measurements are made, the values of the coordinate components are the same.

In this way, the spatial coordinates of the points on the joint surface can be derived.

Next, a step of determining the normal vector of the joint surface from the spatial coordinates of the joint surface vertex will be described.

If at least three points are connected in the space, the surface may be configured. However, in the present invention, as shown in FIG. 14, the joint surface is assumed to have a rectangular shape. The normal vector of the joint surface including the spatial coordinates can be derived using a vector product between the vectors connecting the spatial coordinates. This is because a vector connecting two adjacent points around any one of the four points constituting the plane exists on the plane and their vector is perpendicular to the joint surface.

Mathematically, vector product is defined by the components of each vector, as shown in equation (38).

[Equation 38]

Here, i, j, k are unit vectors in each axis direction of the spatial coordinate system.

In FIG. 14, components of two vectors connecting two arbitrary points are represented by Equation 39.

[Equation 39]

The product of the two vectors can be expressed by Equation 38 as Equation 40, which is the normal vector of the joint.

[Equation 40]

Next, the step of determining the inclination direction and the inclination angle of the joint surface from the normal vector of the joint surface will be described.

In calculating the joint surface direction using each component of the normal vector N of the joint surface, N may be configured as shown in FIG. 15 in the relative spatial coordinate system.

The direction of the joint surface can be obtained by calculating the angle between the normal vector and each component constituting the normal vector. The angle between the vectors is calculated using the dot product.

In general, the angle of the two vectors is equal to (41).

[Equation 41]

And the angle between the two vectors is equal to the equation (42).

[Equation 42]

The direction of the joint surface can be calculated by deriving a normal vector when at least three vertices constituting the plane exist as shown in Equation 40. However, since the model is composed of four vertices for more accurate face construction, the direction of the joint can be derived for each component vertex and there are three cases for each. For example, if a direction is derived based on P ₁ , a combination of three vector pairs of Equation 43, Equation 44, and Equation 45 is possible.

[Equation 43]

Equation 44

[Equation 45]

Therefore, three joints can be derived with respect to each of the vertices of the joints configured as in the model. In other words, a total of 12 directions can be calculated for a joint consisting of four vertices, and in the ideal plane they should be the same value. However, the joint surface is not composed of completely flat surfaces, so a more accurate direction can be obtained by averaging or optimizing a plurality of data obtained for one surface.

In each case, the direction of the total of 12 jeolrimyeon is determined by calculating the angle of the normal vector forms with the vector and a Y axis projection on the xy plane depending on the sign of the normal vector x components (N x) of the N and y components (N y) This can be calculated by the dot product of the component vector ( N xy) and the Y-axis component ( j ).

(i) When x component ( N x) of normal vector N is greater than 0 and y component ( N y) is greater than 0 (a> 0 and b> 0),

[Equation 46]

(ii) When x component ( N x) of normal vector N is greater than 0 and y component ( N y) is less than 0 (a> 0 and b <0), Equation 47 is obtained.

[Equation 47]

(iii) When x component ( N x) of normal vector N is less than 0 and y component ( N y) is also less than 0 (a &lt; 0 and b &lt; 0), Equation 48 is obtained.

Equation 48

(iv) When x component ( N x) of normal vector N is less than 0 and y component ( N y) is larger than 0 (a &lt; 0 and b &gt; 0), the equation (49) is obtained.

[Equation 49]

In this way, the inclination direction α of the joint surface can be obtained.

The following describes the process of obtaining the inclination angle of the joint surface.

The inclination angle of the joint surface is determined by the vector relationship between the normal vector N of the joint surface and the z component vector N z of N. The tilt angle is also determined according to the sign of the z component of N as follows.

(i) When c, which is the z component ( N z) of the normal vector N , is larger than 0 (c &gt; 0),

[Equation 50]

(ii) When c, which is the z component ( N z) of the normal vector N , is smaller than 0 (c &lt; 0), the following equation (51) is obtained.

[Equation 51]

In this way, the inclination angle β of the joint surface can be obtained.

The present invention obtains the inclination direction and the inclination angle of the joint surface out of the geometric characteristics of the joint surface as described above. Among the geometric characteristics of joints, items such as the density and length of joints can be derived by implementing the existing irradiation line or irradiation window method through image. In other words, it is possible to derive joint density, joint length, etc. by acquiring survey items required by survey survey method or survey window survey method through spatial coordinate calculation by image and applying them to existing joint data statistical processing.

Next, a process of extending and analyzing the geometric characteristics of the joint surface with respect to the imaging surface 1 to the entire rock reflection surface will be described.

The extended analysis step is a process of determining the inclination direction and the inclination angle of the joint surface by photographing the photographing surface 2 overlapping the photographing surface 1 and using a specific point of the joint surface in the overlapping portion as the ground control point of the photographing surface 2. By using a specific point of the joint surface in the portion overlapping with the photographing surface 1 as the ground control point of the photographing surface 2, the measurement of the ground control point is necessary only on the photographing surface 1, and from the photographing surface 2, the measurement of the ground control point is not required. .

The extended analysis was developed to minimize the number and installation of ground control points that need to be measured using a spatial coordinate meter such as a total station. Because installing ground control points on rock slopes is only possible for workers to access, the ground control points should be installed only in accessible parts at the beginning and the rest of the joints are used to capture the geometric characteristics of the joints. Investigate.

The algorithm of extended analysis consists of using a specific point of an object derived from the previous photographing surface (photographing surface 1) as a ground control point on the adjacent extension photographing surface (photographing surface 2).

Extended shooting is possible by changing the camera's shooting direction or shooting position, and the spatial coordinates of a specific point except the ground control point of the previous shooting surface are derived from the image pair of the previous shooting surface. Therefore, in order to apply the extended analysis presented in the present invention, the extended photographing surface should be photographed by overlapping with the previous photographing surface.

Setting and movement of the control point in the extended analysis is shown in FIG. In FIG. 16, the ground control points are C ₁ , C ₂ , and C ₃ on the first photographing surface. Their spatial coordinates are measured using a total station. Ground control points are C ₁ ', C ₂ ', C ₃ 'on shooting surface 2 and ground control points are C ₁ ", C ₂ ", C ₃ "on shooting surface ₃ . to the shooting conditions for shooting, C ₂ that a new sensing surface and C ₂ points of the previous image sensing surface that matches the film picture reduction and the characteristics image liquor of the digital image enlarged does not occur in the printing process as in the case of each shot of The spatial coordinates of the control points of the extended imaging plane can be characterized in all images that can be derived from the image pair, including the control point C ₂ applied in the previous imaging plane.

As shown in FIG. 16, both control points C ₂ of the two photographing surfaces exist in the overlapping area of the photographing surface 2 on the photographing surface 1. Although C ₂ 'point of the photographing surface 2 is selected at any point of the photographing surface 1, the C ₂ point of the photographing surface 1 exists in the overlapping area of the two photographing surfaces. Therefore, the C ₂ point of the previous photographing surface may be applied as the C ₁ 'point or the C ₃ ' point, which is an adjustment point of the new extended photographing surface, which is a special case of the extended analysis method proposed by the present invention. Similarly, in the case of the photographing surface ₃ , a control point may be applied to the C ₂ 'point and the C ₃ ' of the photographing surface 2 and a specific point derived from the photographing surface 2. In addition, the specific point C ₃ "derived from the photographing surface 1 may be used as a control point. This should be flexibly determined according to the range of the object to be analyzed and the clarity of the specific point appearing in the image.

Site verification of the extended analysis was performed by moving the photographing surface to the left side as shown in FIG. The control points are C ₁ , C ₂ , and C _{3 of} FIG. 17 for the first photographing surface 1 for the extended analysis. When the photographing work was completed on the first shooting surface, the shooting direction of the camera was changed to the shooting surface 2 for the next extended analysis.

Control points C ₂ ′ and C ₃ ′ on shooting surface ₂ apply control points C ₁ and C ₂ on the first shooting surface. The C ₁ 'point of the photographing surface 2 was set at the vertices of the specific joint surface existing in the slope to identify both points in the left and right images. The spatial coordinates of the new control point C ₁ ′ of the photographing surface 2 to be applied to the analysis were calculated and input from the left and right images of the photographing surface 1. Therefore, when performing image measurement on the photographing surface 2, the control points C ₁ ', C ₂ ', C ₃ ', which are geometric input elements, are sequentially selected from the image measurement on the photographing surface 1 and then the vertex and control point C ₁ In this case, the survey space coordinates of C ₂ are applied.

Next, in the extended analysis of the photographing surface 3, the C ₁ 'point and the C ₂ ' point of the photographing surface ₂ were set to the C ₂ "point and the C ₃ " point of the photographing surface 3. The C ₁ "point of the photographing surface 3 was applied using the spatial coordinates calculated from the image coordinates of the vertices of the specific joint surface in the photographing surface 2.

The movement and setting of the control points according to the extended analysis are shown in FIG. 17. Even in the extended analysis of the photographing surface, the photographing position should be considered to maintain the convergence angle range so that the joint surface existing in the rock can appear as much as possible in the image. After setting the rock slope to measure the image, the control points of C ₁ , C ₂ , and C ₃ were attached to a part of the rock slope according to the photographing arrangement of FIG. 19. The survey origin was set at the position where all the spatial coordinates of the device can be measured, and a total station was installed. The spatial coordinates of the control points were measured and a camera was installed. Since the shooting distance SD is 3 m, the distance between the cameras is set to about 2.5 m or more so that the convergence angle is 25 ° or more. Photographs were taken after measuring the spatial coordinates of the control points. In every picture, whether or not the image point coincides with the control point C ₂ was determined by checking the image taken by the image analyzer. Whether the auxiliary point is located on this collinear line is also measured by the image analyzer, and when the consistency is confirmed, the relative spatial coordinates of the ground auxiliary point are measured. After confirming the agreement, the ground control point was removed from the collinear line and retaken to determine whether the camera moved.

The direction of the joint surface on the rock slope was analyzed from the photographic image taken according to the photographing arrangement of FIG. 17 by the spatial coordinate analysis algorithm and the direction analysis algorithm. The error degree of the image measurement spatial coordinates was examined by comparing it with the surveying spatial coordinates of three control points, and the direction was set as a reference plane by comparing a value measured using a clinometer with the image measurement value. The degree of error was analyzed. In the case of shooting surface 1, the reference plane was set to 20 specific planes, and in the case of shooting plane 2, three reference planes were set based on the joint surface which is not taken from the shooting plane 1. 4 joints which were not photographed were set.

As a result of camera parameter determination, in case of photographing surface 1, the angle θ of the optical axis between two cameras was 34 ° and the distance CD between the two cameras was 2.8 m. This is a camera arrangement that satisfies the optimum shooting conditions.

The error of the image measurement spatial coordinates of the control point of the photographing surface 1 was compared with the coordinates measured by the total station for the control point. The spatial coordinate measurement errors are shown in Table 1. The difference in image coordinate spatial coordinates on the image plane 1 was within the tolerances expected in the design of the imaging array, which was very good, less than 10 mm, similar to the results of the indoor model verification. The parameter determination results of the two cameras on the plane 1 were judged to be good enough to analyze the direction of the joint surface.

TABLE 1

The imaging direction was calculated using the camera parameters on image plane 1 and the image coordinates of 20 specific joints. The clinometer's direction measurement value was selected as a comparison object, and the measurement was performed five times, one at the center and four at the corner for one joint surface, and the final clinometer measurement was determined as their average. Table 2 shows the degree of error between each measurement result.

As a result of the comparison, an error of 0 to 9 ° in the inclination direction and 0 to 5 ° in the inclination angle was found.

Generally, according to the investigator, the clinometer measurement error for the same joint surface is about ± 5 ° for the inclination direction ± 10 ° and the clinometer mechanical measurement error is also ± 2 °. It seems reasonable.

TABLE 2

The extended analysis of the photographing surface was performed twice. The results of the camera parameter determination for the photographs of the photographing surface 2, which is the first extended analysis, are shown in Table 3. As a result of camera parameter determination, in case of shooting surface 2, the convergence angle of θ 'of the two cameras was 36 ° and the camera distance CD was 2.8m.

TABLE 3

For shooting surface 3, camera parameter determination results are shown in Table 4. Calculation of the camera parameters showed that the angle of convergence of the optical axis between the two cameras, θ ', was 36 ° and the distance CD between the cameras was 2.8 m.

TABLE 4

To investigate the distribution of the error control of the recording surface, as determined by the camera parameter two points C ₁ ', C _3' and the recording surface 3 control point C ₁ ", C _3". In the case of the photographing surface 2, the results obtained by the calculation and measurement from the photographing surface 1 and the results calculated in the photographing surface 2 were compared with each other. In the case of the photographing surface 3, the results obtained from the photographing surface 2 were compared with those calculated in the photographing surface 3 And analyzed. The result of the analysis showed that the degree of error is less than 10 mm, which is the allowable error distribution obtained from the indoor verification (Table 5).

TABLE 5

In order to analyze the result of the image measurement direction according to the extended analysis, three joints which were not visible in the photographing plane 1 were analyzed in the case of the photographing plane 2, and four joints were additionally analyzed in the case of the photographing plane 3. The analysis results are shown in Table 6.

TABLE 6

The results of the analysis showed similar error ranges as those of the photographing surface 1 and were included in the measurement error range in the direction of the normal joint surface using a clinometer.

The present invention can freely set the shooting direction and can easily and quickly determine the camera parameters while including all the squares of the joint surface in multiple angles.

According to the present invention, the range of image overlap is increased by convergent shooting, so the irradiation range is extended and the shooting direction is not restricted. In addition, many survey data can be extracted because it is possible to survey in the unmeasurable area and is not restricted by the setting of the survey line and the survey window compared to the irradiation line and the survey window survey by the rock slope measurement.

In addition, the present invention can shorten the field measurement work time, the survey data are accurate according to the indoor measurement work, give high reliability to the results of statistical processing of joint data and apply the reliable joint characteristic data to stability analysis and design. Economical construction is possible.

In addition, according to the present invention, the investigator does not have to approach the rock slope directly, so even if there is a slope collapse or a rock crash, a safety accident does not occur.

As described above, the geometric characteristics of the rock slope joint of the present invention can be irradiated in an inaccessible region, shorten the working time, obtain a large number of survey data, and the survey data are accurate and accordingly statistical processing of the joint data. It gives high reliability to the results and has the effect that there is no fear of safety accidents during the investigation work.

Although the invention has been described in detail only with respect to the described embodiments, it will be apparent to those skilled in the art that various changes or modifications can be made within the spirit and scope of the invention, and such changes or modifications are therefore to the appended claims. It will have to belong to the scope of.

Claims (2)

Establishing a shooting plan according to an analysis target and site conditions; Installing a digital camera at a predetermined position P according to the shooting plan; Installing the spatial coordinate measuring machine at survey origin 0 for coordinate measurement: Setting three control points C ₁ , C ₂ , and C ₃ to the rock slope to be analyzed; Measuring spatial coordinates of the control points C ₁ , C ₂ , and C ₃ using a spatial coordinate measuring device installed at the survey origin 0: Steps to photograph the subject: Photographing the photographing surface 1 by adjusting a photographing direction of the camera using a camera controller so that the image circumference o, which is the center point of the image, and the control point C2 coincide in the photographed image; Installing a ground auxiliary point device such that the ground auxiliary point G is positioned on a collinear line connecting the image pub o and the control point C ₂ of the rock slope; Measuring a spatial coordinate of the ground auxiliary point G by using a spatial coordinate measuring device installed at a survey origin 0; Repeating the steps by moving the digital camera to the next photographing position; The three ground control points, the focal length of C _1, C _2, C _3, and ground space coordinates of the auxiliary point G, and the control point C _1, the camera internal parameters from C ₃ a c _1, c ₃ projected on the imaging parameters f And determining the coordinates of the image circumference o and the position (center projection point P) of the camera which are external parameters and the rotation angles ω, Φ, x of the camera; Constructing a collinear condition equation (center projection equation) of the left and right cameras from the camera parameters; here, ego, X _PL , Y _PL , Z _PL are the spatial coordinates of the left camera, and X _PR , Y _PR , Z _PR are the spatial coordinates of the right camera, Deriving the spatial coordinates of the vertices constituting the joint surface from the image coordinates projected on the image from the relationship between the collinear conditional expressions of the left and right cameras; Determining a normal vector of the joint from the spatial coordinates of the joint; And determining the inclination direction and the inclination angle of the joint surface from the normal vector of the joint surface. The method according to claim 1, wherein the measurement of the ground control point is necessary only on the photographing surface 1 by photographing the photographing surface 2 overlapping the photographing surface 1 and using a specific point of the joint surface in the overlapping portion as the ground control point of the photographing surface 2. And from the photographing surface 2, further comprising an extended analysis step in which the ground control point is not measured.