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Visualization of the Buddha model with Cosmo Player plug-in in Netscape. 

Visualization of the Buddha model with Cosmo Player plug-in in Netscape. 

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In the valley of Bamiyan, Afghanistan, almost 2000 years ago, two big standing Buddha statues were carved out of the sedimentary rock of the region. They were 53 and 35 meters high and the Great one figured as the tallest representations of a standing Buddha. In March 2001 the Taleban militia demolished the colossal statues, as they were considered...

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... constraints while the found approximations are used in the following global matching method [Zhang et al., 1992]. In our application, images B and C of the metric data set 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 4 pyramid levels. As result, a point cloud of ca 178 000 points is obtained (Figure 4). Due to the smoothness constraint and grid-point based matching, the very small features of the dress were filtered or skipped. Therefore these important small features had to be measured manually. 3.2.2 Manual Measurements The dress of the Buddha is rich of folds, which are between 5 and 10 cm in width. Therefore only precise manual measurements can reconstruct the exact shape and curvature of the dress. Therefore the metric images are imported to the VirtuoZo stereo digitize module [Virtuozo NT, 1999] and manual stereoscopic measurements are performed. The three stereo-models A/C, A/B and B/C (Figure 2) are set up and points are measured along horizontal profiles of 20 cm increment while the folds and the main edges are measured as breaklines. With the manual measurement a point cloud of ca 76 000 points is obtained (Figure 5) and the folds on the dress are now well visible. based on a relaxation algorithm [VirtuoZo NT, 1999]. It uses both grid point matching and feature point matching. The important aspect of this matching algorithm is its smoothness constraint satisfaction procedure. With the For the conversion of the point cloud to a triangular surface mesh, a 2.5D Delauney triangulation is applied. Due to some holes in the cloud, the created mesh surface includes some big faces. Then the model is texturized with one image of the data set and the result is shown in Figure 6, right. Due to the smoothness constraints and grid-point based matching, the small folds on the body of the Buddha are not correctly measured and the point cloud of the statue and surrounding rock looks very smooth. For the modeling, a 2.5D Delauney triangulation is performed: without losing its topology, the 3D surface model of the Buddha is expanded to a plane by transforming the cartesian coordinate system to a cylinder coordinate frame. In the defined ρθζ cylinder frame, ζ is the vertical cylinder axis crossing the model center and parallel to the original Y-axis of the cartesian object coordinate system. ρ is the euclidean distance from the surface point to the z- axis and is the angle around the z- axis. The 2.5D triangulation was done in the plane and the final shaded model of the triangulated mesh is shown in Figure 7. The model looks a bit “bumpy“. This is due to small measurement errors and inconsistences in surface modeling. Then the central image of the metric data set is mapped onto the 3D geometric surface to achieve a photorealistic virtual model (Figure 8). The lower part of the legs are not modeled because in the used stereomodel the legs were not visible. In the point visualization of Figure 5 it is already possible to distinguish the shapes of the folds on the dress. This point cloud is not dense enough (except in the area of the folds) to generate a complete mesh with a commercial reverse engineering software. Therefore the generation of the surface is performed again with the 2.5D Delauney method, by dividing the measured point cloud in different parts. A mesh for each single point cloud is created and then all the surfaces are merged together with Geomagic Studio []. The folds of the dress are now well reconstructed and modeled, as shown in Figure 9. With the commercial software some editing operations of the meshes are also performed: - holes filling: polygon gaps are filled by constructing triangular structures, respecting the surrounding area; - noise reduction: spikes are removed with smooth functions; - edges correction: faces are splitted (divided in two parts), moved to another location or contracted; - polygons reduction: in some areas, the number of triangles is reduced, preserving the shape of the object. The final 3D model, displayed in Figure 10, shows also the reconstructed folds of the dress. Compared to Figure 7 this represents a much better result. For photorealistic visualization, the central image of the metric data set is mapped onto the model, as shown in Figure 11. Different tools are available to display 3D models, shareware or commercial software, with or without real-time performance, interactive or not. The generated model can be visualized with a software developed at our Institute and called Disp3D. It allows the visualization of a 3D model as point cloud, in shaded or textured mode, as well as with interactive navigation [Gruen et al., 2001]. One of the few portable formats to interactively display a 3D model like the reconstructed Buddha statue is the VRML. With free packages like Cosmo Player or Vrweb we can display and navigate through the model or automatically fly along some predefined paths (Figure 12). Computer animation software (e.g. Maya) is generally used to create animations of 3D models. An example is presented in ddha.mpg. They usually render the model offline, using antialiasing functions and producing portable videos like MPEG or AVI. Finally, a way to display static view of 3D models is based on anaglyph images. An anaglyph mixes into one image a stereoscopic view using the complementarity of colours in the RGB channels. With coloured glasses, one can then filter the image and see the depth information of the model (Figure 13). The 3D computer model that we reconstructed with the manual procedure is used for a physical reconstruction of the Great Buddha. At the Institute of Machine Tools and Production, ETH Zurich, R.Zanini and J.Wirth have recreated a 1:200 model statue of the Great Buddha. The point cloud of the photogrammetric reconstruction is imported in a digitally programmed machine tool (Starrag NF100). The machine works on polyurethane boxes and follows milling paths calculated directly from the point cloud. The physical model is created in three steps: (1) a roughing path, (2) a pre-smoothing path and (3) the final smoothing path. The time needed for preparing the production data was about 2 hours while the milling of the part itself was done in about 8 hours. The computer reconstruction of the Great Buddha of Bamiyan, Afghanistan has been performed successfully using various digital photogrammetric techniques. We have presented here three versions of the 3D model, based on automated point cloud generation using four internet images, automated point cloud generation using three metric images and manual measurements using three metric images. While the automated matching methods provide for dense point clouds, they fail to model the very fine details of the statue, e.g. the folds of the robe. Also, some other important edges are missed. Therefore, only manual measurements allowed to generate a 3D model accurate and complete enough to serve as the basis for a possible physical reconstruction in situ. The problems encountered with the orientation of amateur images and with automated matching could be solved in an acceptable manner. The main difficulties of this project consisted in the transition from the point cloud (including breaklines) to a surface model which can satisfy high modeling and visualization demands. Since automated image matching does not take into consideration the geometrical conditions of the object, it is very difficult to turn such more or less randomly generated point clouds into TIN or wireframe structures of high quality and without losing essential information. Commercial reverse engineering software could also not generate correct meshes (mainly because the point cloud is not dense enough in some parts) and conventional 2.5D Delauney triangulation was used. When measurements are done in manual mode it is crucial for the operator to understand the functional behaviour of the subsequently activated 3D modeler. An on-line modeler would be very beneficial, as during the point measurements, the results of this modeler could be directly plotted onto the stereomodel and the operator could control the agreement of the on-line model with the measurements and the structure of the object. A web site of the work has been established on our server and is available at with more technical details and animations. The authors would like to thank Yuguang Li for the manual measurements on the metric images, Robert Zanini, Joachim Wirth and the Institute of Machine Tools Production, ETH Zurich, for the physical reconstruction of the statue at scale 1:200, Tom Bilson, Courtauld Institute of Art, London, for some Internet images of the Bamiyan statues and all the web sites where we found images and information on the Bamiyan statues. Baltsavias, E., 1991: Multiphoto Geometrically Constrained Matching. Dissertation, IGP, ETH Zürich, Mitteilungen No. 49, 221pages. Finsterwalder, S., 1896: Zur photogrammetrischen Praxis, pp. 225-240. Finsterwalder, S., Hofmann, W., 1968: Photogrammetrie. De Gruyter Lehrbuch, Berlin, pp. 119-120. Grün, A., 1985: Adaptive Least Squares Correlation: A powerful Image Matching Technique. South Africa Journal of Photogrammetry, Remote Sensing and Cartography, 14 (3), pp. 175-187. Grün, A., Baltsavias, E., 1988: Geometrically Constrained Multiphoto Matching. Photogrammetric Engineering and Remote Sensing, Vol. 54, No. 5, pp. 633-641. Grün, A., Zhang, L., Visnovcova, J., 2001: Automatic Reconstruction and Visualization of a Complex Buddha Tower of Bayon, Angkor, Cambodia. Proceedings of 21 th Wissenschaftlich Technische Jahrestagung of Deutsche Gesellschaft für Photogrammetrie und Fernerkundung (DGPF), 4-7 September, Konstanz, Germany, pp.289-301. Grün, A., Remondino, F., Zhang, L., 2002: Reconstruction of the Great Buddha of Bamiyan, Afghanistan. International Archives of Photogrammetry and Remote Sensing, 34(5), pp. 363-368, Corfu (Greece) ...

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