Fua - 6 
where S and L are the functions defined in Equation 5. It is optimized using either steepest gradient des< ent 
or conjugate gradient. In Figure 2, we show an example of such a network. When constraints, such as 
planarity or rectilinearity, are imposed on the network, constrained optimization can also be used [Gill tt 
al., 1981, Brechbiihler, 1995, Brechbiihler et al., 1995]. 
Figure 3: Edge Visibility, (a) An RCDE “extruded-object.” Only the visible faces, that is those whose 
normal is oriented towards the viewer are drawn. Note that this heuristic does not account 
for non-convexity, as a result the faces in the lower left corner of the image are improperly 
drawn, (b) The network snake generated to optimize the extruded-object. It includes roof- 
edges and vertical wall-edges. The edges at the back of the building are not drawn—and not 
used during the computations involving these views—because they belong to hidden faces. 
The edges at the base of the building are treated as invisible because their appearance is 
unreliable in typical imagery. 
In the three-dimensional case, one must take into account the fact that not all the network’s edges are 
visible in all views. As a result one must also provide, for each projection of the snake into all the images, a 
list, of visible edges. We compute this list by using the face-visibility methods embedded in RCDE: we assume