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Generating a 3D model of a Bayon tower using non-metric imagery Our method of view-dependent texture mapping is based on the selection of a combination of optimal image patches for each triangle of a 3D model. According to the best possible geometric and radiometric conditions a combination of image content is calculated from all images where a particular triangle appears. The locations of the image triangles are computed from object faces via collinearity equations. The procedure consists of three steps: pre-processing, selection of a geometrically optimal image and texture weighted averaging.  Figure 9: Texture mapping with one frontal image - slopped faces A and B appear with "stretched" texture  Figure 10: View-dependent texture mapping: for each object triangle the optimal texture image is selected (image 1 with the bigger area of projected triangle t) (1) Pre-processing. In order to achieve a bigger local contrast and nearly the same color balance in all images high pass filtering and histogram equalization are used for each RGB channel separately. Similarly to Wallis filtering, the high pass filter enables a strong enhancement of the local contrast by removing low-frequency information in an image. It retains edge details in the specified radius where sharp color transitions occur. We apply high pass filtering with a radius of 50 pixels. Additionally, the equalization is performed for all three channels in all images. With these procedures we avoid color shifts when merging the separate channels together. (2) Selection of a geometrically optimal image (Figure 10). In all image planes where a particular triangle t is projected, the area of the triangle is calculated. The image where the triangle t appears largest contains the most texture information. Thus, it is considered as a geometrically optimal image candidate for texture mapping. However, if we use only one image patch, in case of large differences in image radiometry and in case of strong local variability of the surface patch normals, the result will be a checkerboard-type 3D texture map. Therefore in our procedure the radiometry of adjacent images related to the selected "optimal" image is also considered. (3) Texture weighted averaging. We consider all images where a particular triangle t appears simultaneously. The gray values of these images are averaged according to equation (1) 
where gi = gray values of the "new" image gij = gray values of "old" image j n = number of image patches used for texture weighted averaging wij = weight factors calculated from the areas of projected triangles (equation 2) 
Obviously, the weights are chosen proportional to the area of the image patches, which gives priority to the image patch with the better geometry. Before this weighted averaging can take place the different image patches are transformed by an affine transformation to the geometry of the "optimal" master image. The weighted averaging reduces the effects of radiometric differences in adjacent images. The final textured model can be viewed with our own graphics program disp3D or it can be converted to VRML2 for viewing it with standard visualization packages. The results of view-dependent texture mapping are depicted in Figure11.
Figure 11: Texture mapped 3D model of the Bayon Tower: (a) southern view, (b) eastern view, (c) northern view, (d) western view. Display produced by disp3D. 8. Conclusions We have shown that precise and very detailed complex photorealistic 3D models can be derived using tourist-type amateur photographs and automated processing techniques for image matching, point cloud editing and view-dependent texture mapping. The only manual steps were the establishment of fictitious fidutial marks for fixing the interior orientation and the phototriangulation. While the automation of the first procedure constitutes no problem, the automation of triangulation would require a denser sequence of images in order to simplify tie point measurement by image matching. The geometric and texture quality of the models could be improved and the automated procedures would work more successfully if greater attention would be paid to a balanced illumination of all parts of the object. In the case presented here however, this would require the use of artificial lighting. Also, such cases of very explicit and complex 3D object models need certain modifications to be integrated into the matching algorithm (e.g. multi-images, geometrical constraints, edge matching, handling of occlusions), which were not available in this project. Acknowledgement This is to acknowledge the support given by the JSA (Japanese government team for Safegarding Angkor) project. Above all we would like to thank Prof. Sachio Kubo, Keio University, Tokyo for giving the third author the opportunity to participate in this campaign. Also appreciated is the great help which we received in the field from Prof. Kubo's young and ambitious team of surveying, climatology and economy students. Finally, our thanks go to Yoshito Miyatsuka for navigating and controlling the balloon even under the greatest difficulties, such that no harm was done to the precious instrument. We also thank Nicola D'Apuzzo from our Institute for providing us with his software for visualization and editing of a 3D point cloud. References
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