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Generating a 3D model of a Bayon tower using non-metric imagery 5. Image Matching For the extraction of the 3D surface geometry the images were digitized with a resolution of 1200 dpi (pixelsize 21 microns). Image matching was performed with the commercial software package MATCH-T. However, MATCH-T can only generate the 2.5D model from one stereopair. This is necessarily incomplete for close-range applications because occluded parts of the scene cannot be processed. Therefore four image pairs taken from south, east, north and west (images number 2/3, 5/6, 8/9 and 11/12 in Figure 3) were selected and matching was performed in each model separately. This procedure required a transformation of orientation parameters from the Cartesian object coordinate system to local systems for each geographic direction (so that - like in an aerial case - the z-axis in each model is directed towards the projection centers). As a result of fully automatic matching, four separate surface models with a grid width of 3 cm were constructed. The visualization of matched points has shown that the image matching procedure in MATCH-T works reasonably well in this case. Within the individual models only about 0.2% of the matched points had to be edited manually (Figure 6). In the next step, the four separate point clouds were transformed back to a joint object coordinate system and merged together. In the complete 3D point cloud containing 46 850 points overlapping areas occurred and gaps and outliers between the adjacent models showed up (Figure 7). To achieve a good visualization result, these errors were eliminated automatically in a second editing step (Chapter 6).  Figure 6: Matching result within one model (a detail of the southern face profile)  Figure 7: Mathching result at the connection of two separately processed models withmarked area needing additional editing 6. Editing and Triangulation of the Point Cloud Determining surfaces from a set of 3D points containing outliers is a complex task. Many approaches have been designed to treat this problem, such as 3D deformable surfaces (Cohen et al., 1991) and iterative local surface fitting (Fua and Sander, 1992). The last algorithm fits second order patches around each 3D point and groups points into surfaces. In this iterative process errors are eliminated without smoothing out relevant features. Our procedure is an adapted version of this algorithm without performing resampling and clustering. Because all the points should belong to one unique surface, only those outliers are deleted whose derivation from the fitted surface exceeds after 3-5 iterations the predefined threshold. Finally the errors are eliminated while preserving essential surface features (Figure 8). For the conversion of the point cloud to a triangular surface mesh the 2.5D Delaunay triangulation was applied. Without losing its topology, the 3D surface model of the Bayon Tower was expanded to a plane by transforming the Cartesian coordinate system to a cylinder coordinate frame. In the defined rqz cylinder frame z is the vertical cylinder axis crossing the model center and parallel to the original Y-axis of the Cartesian object coordinate system. r is the Euclidean distance from the surface point to the z-axis and q is the angle around the z-axis. The 2.5D Delaunay triangulation was done in the qz plane. The final shaded model of the triangulated mesh is shown in Figure 8b.  Figure 8: The shaded triangulated point cloud before (a) and after editing (b). Most outliers and gaps appeared at the connection of two separately matched models (marked area) 7. View-Dependent Texture Mapping and Visualization With the technique of texture mapping, gray-scale or true color imagery is mapped onto the 3D geometric surface in order to achieve photorealistic virtual models. Knowing the parameters of interior and exterior orientation, to each triangular face of the 3D surface the corresponding image coordinates are calculated. The gray-scale or color RGB values within the projected triangle are then attached to the face. A common approach of texture mapping is to use one frontal image for a related part of the object. In close-range applications this is often not satisfactory, because not enough image information is available for fully or partially occluded object parts. In the 3D model the texture appears as "stretched" (Figure 9). Moreover, often varying light conditions during image acquisition do not allow regular light distribution allover the object. This causes sharp transitions between neighbouring object parts, which are texture-mapped from different frontal images. To overcome these problems, a new method of texture mapping was developed - a view-dependent texture mapping. |