Resistive Fuse Grids and Motion

A resistive fuse contains an element of positive feedback to its operation. Consider a fuse that starts off with a large differential voltage across it, and is therefore not conducting. Now suppose that the difference between the voltage sources at the two terminals of the resistive fuse is very slowly lowered. At the point where the voltage difference is just below the threshold, the resistive fuse will start conducting. This will drag the high voltage down and raise the low voltage, reducing the voltage difference in a sudden jump. If the voltages of the two sources are then very slowly made more different, the resistive fuse will not cut off until the difference is considerably more than the threshold. So the resistive fuse reinforces its own behaviour once the threshold is crossed.

This makes the resistive fuse somewhat ``sticky''; it tends to remember its previous state and not switch until there is an overwhelming case to do so. If we consider the situation in which an edge is moving across the image, then we find that the network responds as shown in Figure 8.1. The initial state has the network responding to the edge correctly. When the light pixel adjacent to the edge drops in intensity, because the edge has moved along one pixel, this drags the corresponding output pixel down as well. However, because of the segmentation, there is only one dark pixel working against a large number of light pixels, and so the output pixel does not get dragged all the way down, while some of the dark pixels get dragged down as well. This will continue until the voltage difference over the edge has dropped below the threshold. However, a smooth long gradient has been set up in the meantime, and there is no voltage difference sufficient to cause a new edge to segment. Thus, once the edge starts moving, it will be lost. No matter how much further it moves, it will not be detected.

Furthermore, just moving one pixel across may not even be enough to reduce the voltage difference across the edge enough for it to start conducting again. The edge may have moved by several pixels before this happens. This results in the network being ``sticky'', with edges tending to stay in the same place.

Figure 8.1: Response of Resistive Fuse Grid to Motion.