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Figure 6: Optimization of a trihedral corner, (a) Initial position, (b) After optimization using only 
the top view, the corner’s projection matches the image features in the top view only, (c) 
After optimization using both views, the corner’s projections match the image features in 
both views. 
In Figure 6, we show the recovery of such a trihedral corner. Figure 7 shows additional corners recovered 
and superimposed on a manually-entered 3-D wireframe models of the correspondng buildings. Because the 
corners are fully 3-dimensional objects, they can be viewed from different viewpoints in which they match 
the 3-D structure of the underlying objects. 
Note that, in order to accurately recover the corner’s 3-D position, the camera models associated with 
the images must be fairly precise—which they are in the examples presented here. However, if the camera 
models were less accurate, we could still perform the single-view optimization in each image separately. We 
could then feed the results of optimizing several corners to a resection program and refine the camera models. 
Extruded objects. Extruded objects are typically used to model buildings such as those of Figure 7. For 
optimization purposes, we define extruded networks that are composed of a polygonal closed contour that 
corresponds to the roof outline and of vertical edges that correspond to the intersections of the vertical walls 
as shown in Figure 8. As discussed above (see Figure 3), for each view, k , in which the extruded object is 
visible, we define a list A k of edges that are visible and use only those to compute the image energy £j. 
During the optimization, we constrain the “wall” edges to remain vertical. We can also constrain the 
“roof-outline” to be planar and the “roof-edges” to form 90-degree angles. As in the case of 3-D corners, 
these constraints greatly reduce the number of degrees of freedom and allow for better convergence properties.