Photogramatric Measurement of the Attitude of Planar and Linear Features by SangGi Hwang, PaiChai University, Korea Abstract This study demonstrates a simple automated measuring method for planar or linear features on the rock excavation surface. In this method, the attitudes of geological planar or linear features are measured using digital images. Spatial coordinates can be calculated from overlapped stereo images, captured from juxtaposed two cameras. Factors used in the calculation are (1) local coordinates of the left and right images, (2) the focal length of cameras, and (3) the distance between two cameras. This method requires at least three points in a planar feature and two points in a linear feature. The measured spacial coordinates are interpolated to calculate the attitude of the planar or linear feature using the least square method. Although the concepts are simple, capturing images and the selecting the matching points on both images require a large amount of time, and significant errors in measurements can also occur. To solve the problem, a simple image capturing device is constructed and incorporated with an image treatment routine coded by Visual Basic and GIS components A test of the device and software shows a promising result for casual application. It shows less than 1 cm error when a point is measured from 179 cm in distance. However, the accuracy becomes much improved for the vertical space which is parallel to the two camera line. Computerized process helps to measure and calculate the 3D coordinates visually, and the measurements of the orientation data on the rock surface is faster than the conventional compass when the initial setting is completed. Automation of the matching points from two images has also been attempted. A linear laser beam is projected to the outcrop surface so that it acts as a refracted linear target on the irregularly broken rock excavation surface. Since the broken surface tends to follow geological features such as joint, fault, foliation and bedding planes, straight portions of the laser beam are compared with both images, and the matching points of such images are selected to calculate the orientation of the particular plane. This method works well in an ideal model which is constructed in laboratory. However, it is not so realistic in the field. There are much room for improvement to image processing process of this method, and such an attempt is ongoing project of this study. Introduction Geologists are often requested to measure a large number of planar or linear features on a single outcrop. This is especially important in engineering projects such as rock slope and tunnel constructions. When the size of the outcrop is not manageable, measuring the attitudes of planar and linear features using traditional compass is not easy. Considering the importance of the amount of data required for stability or safety analyses of the rock excavation surface(Mauldon and Ureta, 1996; Tsoutrelis, 1990), remotely controlled data acquisition method can be an important tool for such studies. In remote sensing studies, attitude of the topographic surfaces are measured from DEM (Chorowicz et al, 1991; Koike et al,1998), and topographic surface shape has been successfully modeled by photogrammetric methods. Similar approach can be applied to measure the orientation of rock partings but only limited numbers of such attempts have been made. Multi-

model photogrammetry methods (Dueholm and Pillmore, 1989; Dueholm, 1990; Dueholm, 1992) are adopted to analyze fracture orientation of quarry outcrops in South India (Garde, 1992). The multi-model photogrammetry method generates 3D DEM model from two overlapped ordinary color slides (typical 35mm color slide) of a model area. Dip and strike of fracture planes are measured from the DEM by a computerized measurement technique (Chorowicz and Bread, 1991). It is an affective technique, however, it requires a sophisticated analytical machine for the DEM modeling. The current study introduces a simple and relatively economic DEM generation method for measurement of rock partings on an excavated rock surface. Concept If the coordinates of three points on a surface are measured, the 3D orientation of the surface could be established. The 3D coordinates can be measured from two stereo images. Fig. 1 illustrates the concept of photogrammatric survey method. Two stereo photograph (A and B) are aligned along a straight line. The lenticular objects (O1, O2) are the positions of the two camera lenses and C is the focal length of the camera. Three points (Pt1, Pt2, Pt3) on a plane are illustrated. Note the straight lines between the index point (Pt1) and the points on the photograph (P1, P2). If the straight line between the center of the right lens (O2) and the point on the photograph (P2), moves to the left image as in Fig. 1, the triangle O1-P1-P2 has similar shape as that of Pt1-O1-O2. Therefore following relationship can be established. P1-P2 : O1-O2 = C : O3-Pt1 ------------------ � The 3D coordinates on the target surface could easily be measured by following equations, if the focal length of the camera (C) and the distance between the two camera lenses (D) are known. X = (x1 / x1-x2) D Y = (y1 / x1-x2) D = (y1 / x1-x2) D ------------------ � Z = (C / x1-x2) D

Fig. 1. A schematic illustration of the stereoscopic photogrammetry measurement of the 3D coordinate. A plane equation (ax+by+cz+d=0) can be derived from more than 4 points on a target surface using following least-square method (Koike et al, 1998).

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Measuring the strike and dip of a plane is the final goal of this study, however, the calculation result is from a model space. The model space is established by the orientation of the camera frame. Therefore the strike and dip of the model space need to be rotated to the true geographic space. Such a rotation would be possible, if two reference orientations of true planes are known. Rotation, from model to the true geographic space, can be achieved by establishing a rotation matrix from the reference plane and lineation, and apply the matrix to other planes. The

matrix can be established by following three steps. The first step is to rotate the strike of the model plane to that of the geographic reference plane. The rotation axis is vertical z axis of the geographic coordinate space. The second step rotates the model plane along the strike axis until the dip angle matches with that of geographic space. After the second step, the planes of the model space and the reference geographic plane should be parallel. However, the reference lineation is not necessarily parallel. To establish complete parallelism between the model and geographic space, the reference line must match with that of model space. Therefore the third rotation should be operated along the axis perpendicular to the reference line until the strike of the lineations matches. To establish the final rotation matrix, rotation matrixes of each step are calculated and multiplied. Rotation about a specific axis could be achieved by a quaternion representation (Hearn and Baker, 1994).

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Where v is the rotation vector and � is the positive rotation angle. The 1st(R1) and 2nd(R2) stage rotations are strict. However, matching the reference line by the 3rd stage rotation needs some consideration. A complete match of the two reference vectors, one from the model space and the other from the geographic space, cannot be achieved because of the measurement and instrumental errors. A reference linear vector, such as an intersection line, in geographic space is measured by geological compass, which usually cause �10 degrees of error. Orientation of a reference line, which is measured from model data, also includes some instrumental error. Therefore, these reference lines are never parallel to the reference plane. This error must be adopted by a reasonable rule. Best way of adopting such error is to rotate the model vector until it has smallest angle to the geographic vector. Such condition can be achieved by projecting the reference lineations of the model and geographic spaces to the geographic reference plane and rotate until they are parallel. If the 3rd rotation angle on the reference plane is calculated, the 3rd rotation matrix (R3) could be derived, and all three matrixes could be multiplied to calculate the final rotation matrix. Rt = R1� R2 � R3 ---------------------- � The final rotation matrix can be multiplied to the normal vector of the measured plane in model space to obtain the geographic orientation of a plane. Survey Equipment Simple survey equipments are designed to mount the two close circuit cameras (Fig. 2A) and laser point (Fig. 2B). The survey equipment is designed to rotate the laser pointer horizontally and vertically by two stepping motors (Fig2B). Stepping motors are controlled by CPU 80C196KC micro-controller board and are interfaced with timer 8254 and Digital to Analog Converter (DAC) (Fig. 3). The motors communicate with controller by the serial communication of RS232C. Visual Basic codes are constructed to control the stepping motors

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Since the system uses 640x480 pixel image and small size CCD, the software includes error adjustment function. The coordinates of input points are not read as pixel position but read as two digit real number. The size of the photo is converted to 6400x4800 unit and the proportion between this size and 0.5 inch CCD size is calculated by comparing the actual distance and the calculated distance. For such adjustment, actual distance must be measured by survey machine.

Fig. 4. The GUI form for the 3D coordinate measurements and the strike/dip calculation.

Fig. 5. Orientations of the fracture planes.

Applied Example To test the method and the survey equipment, a rock slope at PaiChai University is selected and the orientation of each plane on the slope is carefully measured by geological compass (Fig. 5). The slope is modeled by the survey equipment. The measured orientation of each plane from the stereo photograph are rotated by reference line and plane. The final result is shown in Fig. 6. As the figure demonstrates, remotely measured orientation matches with the field measurements within 10 degrees error.

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Fig. 7. Image processing routine for error calculation. Software captures left and right image sequentially and calculate the center point of the laser beam while the laser beam scans the grid paper area. Inlets at top right area show detected horizontal and vertical lines by image processing.

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Fig. 9. Measurements of the x and y coordinated of moving laser beam. Automation of the measurements Automation of the measurements of 3D coordinates has been attempted. Since the 3D coordinates of the target point is calculated by finding two matching points on the stereo images, recognizing the same target points on the stereo images has been the major task. To find the target point easily, a point type red color laser beam is emitted to the target surface and the beam positions on the stereo images are read by image processing technique. While the laser beam scans the target surface in equal emitting angle, by operating the two stepping motors, the 3D coordinates of the laser beam positions are calculated. The array of coordinates, which are calculated from the scan process, are interpolated to generate an equal spacing DEM (Digital Elevation Model) data. Once the DEM is generated, 3D shape of the excavation surface and the attitude of the fracture plane can be calculated (Koike et al, 1998). Detail description of this method is beyond the scope of this paper, and therefore, the results and problems of the method will briefly be presented. A small target area of rock excavation surface (Fig. 10) is selected to test above method. The camera is set at about 3 m distance from the rock surface and the 30 x 30 scan points are read. From the 3D array points, 100x100 DEM points are interpolated and the 3D geometry of the DEM is generated by AutoCad (Fig. 11B). Same process is also performed by none target theodolite and the interpolated result is illustrated in Fig. 11A.

Fig. 10. A testing area for the automated survey method.

Fig. 11. Model result of the rock excavation surface of Fig. 10. A. The result from theodolite measurement B. The result from laser target and image processing method.

Line type laser beam is also tested for the automated 3D measurements. Since the geological structures are planar, a line will be refracted at the edge of the plane surface. If the edge points could be detected, the orientation of the target plane can be calculated. To test this method, a model is constructed and the cross laser beam is emitted on the model surface (Fig. 12). The linear beam is refracted at the edge of the planar surface as shown in Fig. 12. Position of the laser beam was easily detected by image processing technique as in Fig. 13. To calculate the refracting points, progressive least square fitting calculation is performed from thin line image (Fig. 13). From these attempts, refraction points of the laser beam were detected with certain error range and it is proved that these points can define the orientation of planes.

Fig. 12. Constructed model for line laser beam. Note the line beam refracts at the edges of the planes. Line feature at the right of the photograph is the result from image processing.

Fig. 13. Result from the image processing. Center points of the lines are detected and plotted as dots. Inlet at the left side is the details of edge area and the right side is the least square fit lines from the data points. Discussion and Conclusion Orientation of the planar structures on the excavated rock surface could easily be measured by a simple photogrammatic survey method. It requires simple equipment which hold two closed circuit cameras and image capturing board in computer. A reliable s/w for point selection from stereo images and a few calculation routines allow the remote measurements to be applied for practical uses. The tested error ranges from the simple photogrammatic method shows only 0.6 cm when the 170 cm distance is measured. Further error can be raised from the distance measure between two cameras and the selecting process of the matching points on stereo images. However, this error range could be acceptable, if the normal measurement error of the geological compass is about 10 degrees. The measurements of the planar structures on the rock slope at PaiChai University (Fig. 6) also proved that the measuring result is reasonable. Automation, however, need more studies. Although the targets made from laser beam were recognized by image processing technique, it caused irregular errors. The line laser worked well for the artificially made model object but it is not so practical in real rock slope. Furthermore, image processing for each step of laser beam movement takes unrealistic time. The automated process of the present study is far from practical use. However, some successful results for the automatic extraction of the matching points from stereo images have established in photogrammatric and robot vision fields. Errors caused by finding center position of the round targets and cross targets are well known. Statistical approaches for the pixel RGB values to find the matching points could be one other approach for the further studies. Considering rapid developments in other fields, it is optimistic that the slope shape is modeled fully automatically into 3D shape in the near feature. Acknowledgement

This research has been partially supported by the Nuclear long term planning project of Korea (Development of technology and background for seismic safety evaluation). References Chrowicz, J. and Breard, J. and Guillande, R., 1991, Photogrammetric Engineering and Remote Sensing, 57, 4, 431-436 Dueholm, K.S., 1990, Multi-model stereo restitution. Photogrammetric Engineering and Remote Sensing, 56(2), 239-242 Dueholm, K.S., Garde, A.A., and Pedersen, A.K., 1993, Preparation of accurate geological and structural maps, cross-sections or block diagrams from color slides, using multi-model photogrammetry, J. Struc. Geol., 15, 7, 933-977 Dueholm, K.S. and Pillmore, C.L., 1989, Computer-assisted geologic photogrammetry. Photogrammetric Engineering and Remote Sensing, 55(8), 1191-1196 Garde, A. A. 1992. Close-range photogrammetry studies: field and laboratory procedures with examples from prograde granulite facies orthogneiss, Kerala, South India. Rapp. Gronlands geol. Unders. 156, 53-62 Hearn, D, and Baker, M.P., 1994, Computer graphics, Prentice-Hall International, INC, pp.652 Koike, K., Nagano, S., and Kawaba, K., 1998, Construction and interpreted fracture planes through combination of satellite-image derived lineaments and digital elevation model data, Computers and Geosciences, 24, 6, 573-583 Mauldon, M. and Ureta, J, 1996, Stability analysis of rock wedges with multiple sliding surfaces, Geotechnical and Geological Engineering, 1996, 14, 51-66 Priest, S. D., 1993, Discontinuity analysis for rock engineering, Chapman & Hall, 473p Tsoutrelis, G.E, Exadactylos, G.E. and Kapenis, A.P, 1990, Study of the rock mass discontinuity system using photoanalysis, in Mechanics of Jointed and Faulted Rock, Rossmanth(ed), 103-112