Interlinking Vertical and Horizontal Edges

A different approach to the problem would be to use information from the horizontal network to influence the vertical network, and vice versa. Consider the images in Figure 9.3. The first one shows a T junction. The vertical edge can gain no useful information from the horizontal edges, as there is no hint as to which way the gradient should go. However, if the vertical edge in the second image were to trip with a positive gradient, it would form part of a diagonal edge. If it were to trip with a negative gradient, the image would make less sense. So in this situation, we can derive useful information from the horizontal grid.

Figure 9.3: Situations in which Horizontal and Vertical Edges Interact.

An improved network based on this information is shown in Figure 9.4. The horizontal edges are now linked to the vertical edges. In the case of the T-junction in Figure 9.3, the effect of the horizontal edges cancels out, and so there is no impact on the vertical edge. However, in the second image, the intensities of the two horizontal edges tend to reinforce the vertical edge.

Figure 9.4: Network Connections for Horizontal and Vertical Interaction.

The only question remaining is to what extent this reinforcement should take place. In previous resistive grids we have not considered the relative weighting of the links because they were all the same. However, in this case the information to be gained from orthogonal links is clearly not as important as that from parallel links. It is easy to take this into account with the resistive grids, because we can simply make links that represent less compelling data have a higher resistance. It is not clear what particular resistance we should choose in this case, but clearly the resistance should be somewhere between infinity and the resistance for a parallel link. About twice that for a parallel link seems like a reasonable choice.