8 Motion Detection

The symmetric axes, that we have evolved in the previous chapter, represent a trajectory in a 3D space. For L features, that trajectory is a vector having a certain direction and certain speed, very much like the vector of a motion stimulus. If one attempted to create a neuromorphic substrate that reads out such trajectories, one may as well seek inspiration from models that perform motion analysis and this brings us to the topic of motion detection.

8.1 Models

8.1.1 Computational

The earliest, thorough experimental and computational study of motion detection is the one by Reichardt on the fly’s motion system (Reichardt, 1961). Reichardt measured systematically the fly’s turning response to a large number of schematic motion stimuli. From the collected response patterns he dervied an elaborate algorithm, that consists of a number of stages performing various types of filtering and correlating between inputs. Its very basic gist is shown in figure 40a. The input signals converge to a unit that correlates them: correlation is only successful if the two signals are received in sequence and in preferred order. If the stimulation direction is reversed (nonpreferred), then the unit reports no correlation. There is a number of computational studies that is roughly analogous to the Reichardt approach: these studies model the responses of humans to certain motion stimuli and motion illusions (Adelson and Bergen, 1985; Vansanten and Sperling, 1984; Watson and Ahumada, 1985).

Several neuromorphic implementations of the Reichardt principle already exist in analog hardware (e.g. (Tanner and Mead, 1986; Kramer et al., 1995)). They are implementations of the proposed algorithms using analog circuitry performing the necessary types of filtering and correlation. These motion detectors work well if the motion crosses a substantial part of their visual field, meaning their ‘receptive field’ corresponds to the entire visual field. But one may also intend to develop an implementation in which a motion stimulus is analyzed, when it has only crossed part of the visual field, for example only the left half of the visual field, or speaking in terms of sym-axes, when a trajectory is generated in only part of the visual field. A solution to that may lie in a neural emulation using a retinotopic map.

8.1.2 Biophysical

The computational models mentioned previously have not been specific about an exact biophysical implementation but the proposed algorithms lend themselves toward a neural interpretation. For example

Figure 40: Variants of the delay-and-compare principle. a. Photoreceptors 1 and 2 receive motion input (indicated by two dots). The elicited signals are correlated in the unit C, whereas the second signal arrives with a certain delay Stimulation in the reverse direction would not yield a correlation between the signals. b. Schematics of a dendrite (rectangular shape) and a soma (circle). The four synapses of the dendrite receive sequential inputs from 1 through 4. Each synaptic stimulation contributes to an increasing wave running towards the soma. The ‘comparison’ would take place in the soma.

the correlation unit C (in figure 40a) could be simply a neuron summing or multiplying postsynaptic signals. Because neurons can possibly perform such calculating operations (section 3.7), and because such operations have been proposed (Barlow and Levick, 1964; Koch et al., 1983), this may be one way to develop a retinotopic map for motion detection. But there are also alternative biophysical models: One on the dendritic level, and one on a ‘map’ level.

Dendritic Level A model for the dendritic site comes from Rall, who applied cable theory to the study of dendritic processing (Rall, 1964) (see section 3.7). He proposed that a dendritic cable can act as a direction sensitive ‘wire’ (figure 40b): If one stimulates a dendritic cable sequentially - with stimulations approaching the soma -, then an increasing activity wave runs towards the soma, causing the soma to spike. If stimulations occured into the opposite (non-preferred) direction, the wave would run into the tip of the dendrite where it has no effect. This type of dendritic direction selectivity has been modeled with compartmental models and some researchers have interpreted neurophysiological data according to it (Livingstone, 1998). It has also been implemented into analog hardware ((Elias, 1993; Rasche and Douglas, 2001), see also section 4.3).

Map Level Because of the abundant research performed on a neuronal level, it is tempting to think that the neuron is the sole site