is sharp, for slower maps, the tuning curve is broad. Thus, the speed

Figure 43: Speed-tuning curves. a. Obtained from simulation for each map (fast, medium, slow) for a dot stimulation (dashed-dotted lines) and an arrow stimulation (solid lines) stimulation. X-axis: total number of occurred spikes for the entire stimulation. Y-axis: speed number. b. Schematic version of a.

maps are only useful for a rough estimate of speed. In order to determine speed accurately, one could possibly use more maps and try to achieve a narrow tuning for each one, which however would likely result in a tuning ordeal. A better solution would be the employment of a speed pyramid (section 8.2), in which one used the same dynamics for each level. In either case, the creation of such a set of maps to cover all speeds is costly in terms of size - thinking in engineering terms. Instead, it is more size efficient and even more accurate to create a set of neurons reading out a small number of tuning curves, see figure 43b. This idea is analogous to the formation of color sensation with only three photoreceptors tuned to three different luminance sensitivities. For example, a speed-detecting neuron would read the ratio of firing rates from two or more speed maps (see speed number ‘5’ in figure 43), and so accurately determine speed, despite the broad tuning-curves.

8.4 Biophysical Plausibility

If the nervous system used such propagation maps for speed estimation, how might the cortical tissue emulate them? And where are they likely to be found?

Regarding the biological emulation, it is firstly the horizontal connection that demands an interpretation, in particular the subthreshold propagation through the horizontal connections. We have already looked for such horizontal activity spread in the section on ‘fast waves’

(section 7.5): there we were seeking possibilities that would allow for active propagation of contours. Here, we search for a substrate that rather passively propagates activity and that allows for different dynamics selecting different speeds. One possibility for such propagation is the extracellular activity spread through the glia substrate (e.g. (Charles, 1998)). We already suggested this possibility in the retina chapter to motivate the change of spiking thresholds (section 6.2). It was also pointed out by Koch that such extracellular dynamics are not well understood, yet worth to model (Koch, 1999). There is a number of other studies that report about some sort of activity spread through the neural substrate (e.g. (Grinvald et al., 1994; Beggs and Plenz, 2003)). Another possiblity could be activity spread through dendrodendritic synapses. If any of these possibilities could be the basis for passive spread useful for speed detection, then there may also be different dynamics, which would allow for detection of different spreading speeds. Different dynamics maybe caused by different ‘packing’ density of neurons. Alternatively, evolution may have evolved a speed pyramid, which would not require different dynamics but just sparser connections with higher levels (figure 41).

Regarding the location of such maps, one may readily suggest that they exist in area MT (V5), where many neurons seem to signal exclusively for speed ((Perrone and Thiele, 2001), but see also (Priebe et al., 2003)). But some neurons in primary visual cortex seem also to fire for speed only (see (Nakayama, 1985) for a review). A thorough review of these studies may give hints about whether the brain uses for example a speed pyramid. For instance, we imagine that ‘speed-neurons’ in lower areas like the primary visual cortex, may fire for lower speeds, whereas higher areas may possess neurons firing for higher speeds.

In some motion detection studies, a reoccuring issue has been the aperture problem, which addresses the difficulty to estimate the overall, global direction of object motion from local receptive fields. Local receptive fields, as they exist in primary visual cortex, only sense a subset of the visual field and hence the entire object. An edge wandering through the receptive field may therefore not reflect the global motion direction (reviewed in (Nakayama, 1985)). Furthermore, using only local receptive fields, it is also difficult to estimate the exact speed due to that aperture ambiguity. Attentional networks may solve the problem (e.g. (Nowlan and Sejnowski, 1995)), but here we have proposed a speed-estimation architecture, in which this problem does not really appear, because the architecture does not rely on any local receptive fields. In our architecture, motion direction is not computed at all, but merely motion speed is sensed.

8.5 Recapitulation

The purpose of this chapter was to find a neural substrate that can read the direction and speed of a trajectory - whether this is a sym-ax or a motion trajectory. We have approached this task using propagation maps and illustrated how speed can be estimated with them. What we have not addressed is how to read out direction. To perform that for sym-axes, one could use propagation maps with oriented connections. To perform direction selectivity for actual objects, the challenge of solving - or maybe circumventing - the aperture problem still remains.

A hardware implementation of this speed-estimating architecture required firstly the generation of spikes in response to motion, that could serve as input to the speed architecture (see bottom layer in figure 41). This already exists in form of a silicon retina (Boahen, 2002): it generates spikes in response to any object moving at almost any speed. Those spikes would feed into speed maps, which still had to be developed but could be easily derived from an implementation of the propagation map as presented in section 6.3.

The simulations in this chapter gave us the inspiration that shape could be detected analogous as speed is: a structure maybe stored as electric dynamics in a map, which would be activated only if the corresponding structure would ‘run’ across the map: the map would reverberate in some sense in response to the appropriate input structure. We continue this thought in later sections of the next chapter and we will also present a specific idea in chapter 10.

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