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Generating a 3D model of a Bayon tower using non-metric imagery 3. Data Acquisition The main goal of the Bayon field campaign was the taking of small format camera balloon images over Bayon for the 3D reconstruction of the complete and utterly complex temple. Balloon images where also taken over the Northern Library of Angkor Wat and over the several Prasat Suor Prat buildings. During the mission a sequence of small format terrestrial images was taken with a Minolta Dynax 500si camera (c = 35 mm) of one of the Bayon towers on the third platform in the north-eastern corner of the temple. The 13 images covering the full horizon were meant as a test of photogrammetric procedures rather than a serious project aiming at a complete recording of the object. Figure 3 shows the arrangement of images, as they were used for bundle triangulation around the tower. Since a 360 degree azimuth coverage was necessary and the light conditions were fairly extreme the production of good, evenly illuminated pictures was practically impossible without artificial lighting, which was not available at the site. Therefore, the images suffer under strong variations of the illuminated and shadow areas. Also, the shadow and light parts will vary from image to image, depending on the time of the day the images were taken. This will cause problems with texture mapping from multiple images, if an even distribution of light is aimed at allover the 3D model. Thus a great deal of our work went into a modification of the standard procedure of texture mapping. We developed a specific technique of view-dependent texture mapping, which is object face oriented and picks for each object face a combination of the best possible corresponding image patches for texture mapping.  Figure 3: Images used for bundle triangulation 4. Triangulation In order to obtain a realistic and geometrically correct 3D model of the Bayon tower, 13 images covering the whole horizon were triangulated as follows:
Unknown and unstable parameters of interior orientation, film unflatness and the lack of fiducial marks are essential features of non-metric small format cameras. Several methods have been developed to eliminate or reduce these shortcomings. To overcome the lack of fiducials, corners of the frame are commonly calculated as intersections of frame edges. In this paper, the coordinates of fictitious fiducial marks were determined by indirect measurement in several analog images. On an analytical plotter two points on adjacent edges of the image frame were measured and intersecting points were calculated (Figure 4a). As a result individual sets of coordinates in the machine coordinate system were obtained for all images. An affine transformation was performed in order to relate the different coordinate systems to a unique image coordinate system (Figure 4b).  Figure 4: (a) Indirect measurement of fiducial marks on an analytical plotter (points A - D for the fiducial mark 1), (b) Image coordinate system with the principal point located by intersection of diagonals. 4.2 Image measurement for triangulation The image measurements for triangulation were performed on an analytical plotter using the approximate interior orientation (camera constant 35 mm, no lens distortion, zero coordinates of the principal point and estimated coordinates of fiducial marks). The optimal spatial distribution of orientation points was not possible due to incomplete frame fill. Altogether about 170 points were measured in 13 images around the tower. Each object point is imaged in two to six images.  Figure 5: Cartesian object coordinate system and three control points with coordinates given in meters For the absolute orientation of the whole block two full control points and one depth control point were used. Control points 1 and 2 are defined as marks on a vertical scale-bar. Depth control point 3 is situated on a small decorated stone to the left of the southern tower side. These three control points define the right-handed Cartesian object coordinate system with z-axis going towards the southern projection centers (Figure 4). Since control points are only visible from the southern tower side, the absolute orientation on the analytical plotter was performed in two models only. 4.3 Bundle adjustment with self-calibration The bundle adjustment of the whole image sequence was performed in a stepwise mode. For that purpose the procedure was started with the first absolutely oriented images number 1, 2 and 3. Consequently additional images were added with manually obtained approximations for exterior orientation elements and new object points. This stepwise mode was necessary because, with the available coarse first approximations, the complete block did not converge simultaneously. After the establishment of a stable adjusted image block, ten additional parameters (Brown, 1971) were used to model systematic errors: focal length correction, principal point coordinate offsets, five parameters modelling radial and decentering lens distortion and two parameters for a differential scale factor and shear (Beyer, 1992). The radial distortion amounted to 810 microns at an image radius of 20 mm. |