propagation does not play such a big role for the method of adjustable thresholds, but somewhat more for the method of latencies.

The exact propagation characteristics can be modulated in many different ways (Rasche, 2005a). In the above example, the traveling wave has a width of a single spike, but can be tuned to show a broader width by changing parameter values of the map or by increasing the radius of the local connections. Likewise, the waves can be made faster or slower by changing parameters, something we will exploit to perform motion detection (chapter 8).

6.4 Signaling Contours in Gray-Scale Images

6.4.1Method of Adjustable Thresholds

We now return to the idea of signaling contours within a network of connected ganglion cells. We take the same map as discussed in the previous section and add the mechanism discussed in figure 29c. We do not emulate the fast process explicitly, but take the luminance distribution of an image directly as the membrane potential of the entire map. A fixed offset value is added to each neuron, which represents the adjustable spiking threshold. Then, in the slow process, the charge propagates and will trigger spikes at steep luminance edges (contours). And once such a contour front is signaled as a line of spikes, it will start traveling across the map. Figure 32 shows this for two objects. After the first two simulation steps (t=1 and t=2), the high contrast contours are already signaled. After further propagation, lower contrast contours are detected as well. As a comparison, the contours found by a popular computer vision algorithm are shown (Canny, 1986).

It should be pointed out that the contours are signaled independently of the absolute luminance level. In a contour profile (of our visual environment) the contrasts can be at any level and the level itself often varies along a contour. The mechanism of figure 29c automatically takes care of that. Thus, there is only one parameter in this network, the offset for the adjustable spiking thresholds. An increase or decrease of the offset value will cause the network to detect higher or lower contrast contours respectively (see figure 33). This offset parameter roughly corresponds to the threshold values used in the Canny algorithm.

6.4.2Method of Latencies

If one used this method without the laterally connected network (without the propagation network), then noisy pixels are signaled ahead of the area they are placed in. The charge propagation counteracts that a bit, by smoothening the areas slightly and thus leveling out noisy pixels. Figure 34 shows preliminary results with this method.

Figure 33: Effects of varying offset values. Compare also to figure 32. a. low more low-contrast contours are signaled. b. high only high-contrast contours are detected. Time steps 2 and 4 are shown only. From Rasche 2004.