Eight-Way Connected Networks

In the present network, each resistive fuse is connected to four of its neighbours. An obvious solution to the diagonal edge problem would be to simply connect the resistive fuses to each other with eight connections instead of four, as shown in Figure 9.1. This would mean that each edge segment in a diagonal edge would have a direct connection to other edge segments.

**Figure 9.1:** Eight-Way Connected Resistive Grid.
$\begin{figure}\par \centerline{\psfig{figure=fig/eightway.eps,width=10cm,angle=-90}} \par\end{figure}$

However, this only resolves the problem for edges that are at an angle of exactly 45 degrees to the network. Edges at different angles will include edge segments that are separated by two or more pixels, as shown in Figure 9.2. In this case, there is still no direct connection between the horizontal edge segments, and there is little performance improvement. Whatever performance improvement is achieved could just as easily have been achieved by simply increasing the characteristic length of the differential network.

**Figure 9.2:** Edges Showing Staircasing due to Large Gradient
$\begin{figure}\par \centerline{\psfig{figure=fig/grad2.eps,width=7cm,angle=-90}} \par\end{figure}$

Matthew Exon 2004-05-23