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The Bamiyan valley, as seen by Ikonos (courtesy of Space Imaging, Inc., Denver, CO (Grant Street)).

The Bamiyan valley, as seen by Ikonos (courtesy of Space Imaging, Inc., Denver, CO (Grant Street)).

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In the valley of Bamiyan, Afkhanistan, approximately 1700 years ago, two large standing Buddha statues were carved out of the sedimentary rock of the region. They were 53 and 38 in high and the larger one-figured as the tallest representation of a standing Buddha in the world. In March 2001 the Taleban government militia demolished the colossal sta...

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... the Bamiyan valley ( Fig. 1), at an altitude of 2500 m, three big statues of Buddha and a great number of caves were carved out from the sedimentary rock of the region (Figs. 2 and 3). There were two big standing Buddha statues, which stood about 900 m apart, while in the centre there was a smaller image of a seated Buddha (Fig. ...
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... metric images were acquired in August 1970 with a TAF camera (Finsterwalder, 1896;Finsterwalder and Hofmann, 1968). The TAF (Terrestrische Ausrüstung Finsterwalder) is a phototheodolite camera (Fig. 16, left) that acquires photos on 13 · 18 cm glass plates. Two fiducial marks are present on the longer sides of the photos while a pointer defines the image horizon with an index that moves ...
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... original photos were scanned by Vexcel Imaging Inc. Graz, Austria with the ULTRA SCAN 5000 at a resolution of 10 lm. The digitised images each resulted in 16 930 · 12 700 pixels (Fig. ...
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... multi-photo geometrically constrained (MPGC) least squares matching software package, developed at the Institute of Geodesy and Photogrammetry at ETH Zürich, was applied to all three image data-sets ( Grün et al., 2001Grün et al., , 2003. The automatic surface reconstruction (Fig. 11) works in fully automated mode according to the following ...
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... the MPGC approach, sub-pixel accuracy matching results and 3D object coordinates can be obtained simultaneously (Fig. 12) and also, through covariance matrix computations, a good basis for quality ...
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... differences between each other. In these cases the cross-correlation technique used in the first step to extract the approximations for the MPGC matching normally encounters difficulties. In order to solve these restrictions rectified images are used. The rectified images are generated using a vertical plane fitted to the control and tie points (Fig. 13, left). Then each pixel of the original image is projected onto the vertical plane by using the known orientation parameters. The relationships between the original and rectified images can be calculated using the collinearity ...
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... . 12. Epipolar geometry between the metric images to get the correct matching (upper row). MPGC matching results (patch resampling) and computed 3D object coordinates (lower ...
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... in image scales and rotations, the initial values of the reshaping parameters in MPGC matching can be predetermined by using the collinearity conditions for the four corner points of the image patches. The corresponding rays of these four corners in the template image should intersect in object space and their object coordinates can be determined (Fig. 13, right). Through the collinearity equations the corresponding image coordinates in the search image can be determined. The initial values of the four reshaping parameters are determined from these four points and their ...
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... of the tie points were obtained semi-automatically with adaptive least squares matching (Grün, 1985). The final average standard deviations of the object point coordinates located on the Buddha itself and on its immediate vicinity are r x,y ¼ 0AE13 m and r z ¼ 0AE30 m. The recovered camera poses and the tie and control points used are shown in Fig. 14, ...
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... the surface reconstruction, due to the scale and rotation differences among the images, the modified version of the developed MPGC matching algorithm was applied. A point cloud of approximately 6000 points was obtained. Some gaps are present in the results (Fig. 14, centre) because of surface changes due to the different times of image acquisition and to the low texture in some areas. For the conversion of the point cloud to a triangular surface mesh, a 2AE5D Delaunay triangulation is applied, which is clearly sub-optimal. The textured 3D model is shown in Fig. 14, ...
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... Some gaps are present in the results (Fig. 14, centre) because of surface changes due to the different times of image acquisition and to the low texture in some areas. For the conversion of the point cloud to a triangular surface mesh, a 2AE5D Delaunay triangulation is applied, which is clearly sub-optimal. The textured 3D model is shown in Fig. 14, ...
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... final orientation parameters were recovered with a bundle adjustment (Fig. 15, left). The final average standard deviations of the object point coordinates located on the Buddha itself and on its immediate vicinity were r x,y ¼ 0AE12 m and r z ¼ 0AE17 ...
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... modified matching procedure on the tourist images resulted in 5585 points. Some blunders were deleted by manual editing and the final point cloud and the related textured model are shown in Fig. 15, centre and right. The relatively low image resolution of the tourist data-set results in a coarse but quite complete 3D ...
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... all TAF images the principal point (PP) is defined as the intersection of the straight line joining the two fiducial marks on the upper and lower side of the image and the horizontal line passing through the horizontal index defined on the right side of the image (Fig. 16, centre). The focal length of the camera (160AE29 mm) is given in Kostka (1974), where the acquisition procedure is also described (Fig. 16, right). The images were acquired in the normal case, with a double baseline and at a distance of about 130 to 150 m from the statue (Fig. 16, ...
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... intersection of the straight line joining the two fiducial marks on the upper and lower side of the image and the horizontal line passing through the horizontal index defined on the right side of the image (Fig. 16, centre). The focal length of the camera (160AE29 mm) is given in Kostka (1974), where the acquisition procedure is also described (Fig. 16, right). The images were acquired in the normal case, with a double baseline and at a distance of about 130 to 150 m from the statue (Fig. 16, ...
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... the horizontal index defined on the right side of the image (Fig. 16, centre). The focal length of the camera (160AE29 mm) is given in Kostka (1974), where the acquisition procedure is also described (Fig. 16, right). The images were acquired in the normal case, with a double baseline and at a distance of about 130 to 150 m from the statue (Fig. 16, ...
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... this information and some control points measured on the contour plot, the first approximations of the exterior orientation were achieved. With the following bundle adjustment all the parameters of the three images were recovered (Fig. 17); the final standard deviations of the object point coordinates located on the Buddha itself and in its immediate vicinity were r x,y ¼ 0AE07 m and r z ¼ 0AE14 m. These high values can be explained by the unfavourable control point distribution covering just a small part of the images (see Fig. 14, bigger ...
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... parameters of the three images were recovered (Fig. 17); the final standard deviations of the object point coordinates located on the Buddha itself and in its immediate vicinity were r x,y ¼ 0AE07 m and r z ¼ 0AE14 m. These high values can be explained by the unfavourable control point distribution covering just a small part of the images (see Fig. 14, bigger ...
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... MPGC matching algorithm resulted in fairly reliable and precise results. From the three metric images, 49 333 points (without the surrounding rocks) and 73 640 points (with part of the surrounding rocks) were obtained. The point cloud data is shown in Fig. 18 (centre), as well as a textured 3D model (right). Although an automatic blunder and occlusion detection process was used, some blunders are present in the 3D point cloud and they were removed with manual editing. As shown Fig. 16. The TAF camera (left) and the interior orientation of the images (centre). The acquisition geometry of the three ...
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... rocks) and 73 640 points (with part of the surrounding rocks) were obtained. The point cloud data is shown in Fig. 18 (centre), as well as a textured 3D model (right). Although an automatic blunder and occlusion detection process was used, some blunders are present in the 3D point cloud and they were removed with manual editing. As shown Fig. 16. The TAF camera (left) and the interior orientation of the images (centre). The acquisition geometry of the three metric images as presented in Kostka (1974). in Fig. 18, there are some gaps in the point cloud, mainly due to the shading effects caused by the variation of the illumination conditions during the image acquisition (typical ...
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... Although an automatic blunder and occlusion detection process was used, some blunders are present in the 3D point cloud and they were removed with manual editing. As shown Fig. 16. The TAF camera (left) and the interior orientation of the images (centre). The acquisition geometry of the three metric images as presented in Kostka (1974). in Fig. 18, there are some gaps in the point cloud, mainly due to the shading effects caused by the variation of the illumination conditions during the image acquisition (typical areas are marked in Fig. 18). As shown in Fig. 19, the dress of the Buddha was rich in folds, which were between 5 and 15 cm in width. Many folds could not be exactly ...
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... camera (left) and the interior orientation of the images (centre). The acquisition geometry of the three metric images as presented in Kostka (1974). in Fig. 18, there are some gaps in the point cloud, mainly due to the shading effects caused by the variation of the illumination conditions during the image acquisition (typical areas are marked in Fig. 18). As shown in Fig. 19, the dress of the Buddha was rich in folds, which were between 5 and 15 cm in width. Many folds could not be exactly reconstructed with the automatic program. Fig. 19 also shows some of the problems that the automated matcher had to deal with: high noise values in the shadow areas, large differences between ...
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... interior orientation of the images (centre). The acquisition geometry of the three metric images as presented in Kostka (1974). in Fig. 18, there are some gaps in the point cloud, mainly due to the shading effects caused by the variation of the illumination conditions during the image acquisition (typical areas are marked in Fig. 18). As shown in Fig. 19, the dress of the Buddha was rich in folds, which were between 5 and 15 cm in width. Many folds could not be exactly reconstructed with the automatic program. Fig. 19 also shows some of the problems that the automated matcher had to deal with: high noise values in the shadow areas, large differences between illuminated and shadow ...
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... point cloud, mainly due to the shading effects caused by the variation of the illumination conditions during the image acquisition (typical areas are marked in Fig. 18). As shown in Fig. 19, the dress of the Buddha was rich in folds, which were between 5 and 15 cm in width. Many folds could not be exactly reconstructed with the automatic program. Fig. 19 also shows some of the problems that the automated matcher had to deal with: high noise values in the shadow areas, large differences between illuminated and shadow areas, and artefacts (straight lines) from the photographic development process. Other reasons for failure are: the image patches of least squares matching are assumed to ...
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... the application, the metric images of Fig. 10(b) and (c) from Professor Kostka were used to reconstruct the 3D model. A regular image grid with 9 pixels spacing was matched using a patch size of 9 · 9 pixels and four pyramid levels. As a result, a very dense point cloud of approximately 178 000 points was generated (Fig. 21). The statue as well as the rock around it is well ...
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... the application, the metric images of Fig. 10(b) and (c) from Professor Kostka were used to reconstruct the 3D model. A regular image grid with 9 pixels spacing was matched using a patch size of 9 · 9 pixels and four pyramid levels. As a result, a very dense point cloud of approximately 178 000 points was generated (Fig. 21). The statue as well as the rock around it is well reconstructed, but due to the smoothness constraint and grid-point-based matching the small folds on the body of the Buddha were filtered or skipped and they are not visible. A 2AE5D Delaunay triangulation was applied for the surface modelling. Without losing its topology, the 3D ...
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... the vertical cylinder axis crossing the model centre and parallel to the original Y axis of the Cartesian object coordinate system; q is the Euclidean distance from the surface point to the z axis and h is the angle around the z axis. The 2AE5D triangulation was done in the hf plane and the final shaded model of the triangulated mesh is shown in Fig. 21, right. The shaded model looks ''bumpy'', mainly due to small measurement errors and inconsistencies in surface modelling. The central image of the metric data-set was mapped onto the 3D geometric surface to achieve a photorealistic virtual model (Fig. 22). The lower parts of the legs are not completely modelled because in the ...
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... final 3D model, displayed in Fig. 25, shows also the reconstructed folds of the dress. Compared to Fig. 21 (right), this represents a much better ...

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