Fua-7 
that only edges that belong to visible faces are visible. This is effective for convex objects but my fail for 
concave ones. Figure 3 illustrates the strengths and weaknesses of this approach. A better way to compute 
visibility would be to use the Z-buffering capabilities of SGI machines; unfortunately this impractical for the 
time being because the graphics libraries supplied by SGI cannot currently be loaded into RCDE, due to 
limitations of the Lucid Common Lisp compiler. 
Formally, given a set of N images, we define a visibility list A*l <k<N for each image and we rewrite the 
image energy of Equation 6 as 
£• = £ £ 1 - ( 15 > 
1 <k<N 
¿1 = Y *5(/ 5 r fc (x t -,y,-,2,),(Pr /s (x l+ i,y (+ i,2: l+ i)))/ L i,i +1 • ( 16 ) 
l<i<n 
Figure 4: Three-stage optimization of a 3-D Network, (a) The object is hand-entered using RCDE. 
By default the vertex heights are that of the underlying terrain model, (b) The object is 
optimized using only the top view. The object matches the roof outline in the top view 
but not the lower one because the object is higher than the terrain, (c) The height of the 
vertices is computed approximately by searching a range of z values while maintaining the 
shape of the object’s projection in the top view, (d) The network’s 3-D shape is further 
refined by simultaneously optimizing the x, y and z values of the vertices’ positions. Its 
projections then match image features in both views, guaranteeing that the 3-D shape of 
the underlying objects has been recovered. 
The optimization typically is a three step process and is illustrated by Figure 4: 
1. We optimize a snake using a single image. Since a single view underconstrains the three degrees of 
freedom of the individual vertices, we fix one of them for each vertex. The z value is fixed and only 
the x and y coordinates are allowed to change. As shown in Figure 4(b), at the end of this first step,