6Retina Circuits Signaling and Propagating Contours

6.1The Input: a Luminance Landscape

The retina absorbs the luminance distribution of our visual environment and transforms it into a signal useful for the analysis in higher areas in cortex. Before we worry about how this transformation is carried out in neural terms, it is sensible to understand the characteristics of the input and too see how computer science approaches have dealt with it.

If one plotted the luminance distribution (or gray-scale image) as a 3D plot with the third dimension being luminance, then one could see a profile reminiscent of a landscape. Fu has nicely expressed this view by describing it as a geographic structure made of plains, slopes, ridges, valleys, shoulders and feet (Lee and Fu, 1981). To extract contours and segments of the image, they created algorithms to detect each of these geographic features. Most other contour-detection approaches have not adopted such a specific viewpoint, but have merely extracted ‘general’ edges. Each of these algorithms has its advantages and drawbacks. They roughly work in two steps. Firstly, the gradient at each image point (pixel) is determined by looking at its immediate neighborhood, e.g. a 3x3 array with the center pixel taken as the investigated image point. Secondly, neighboring gradients with similar orientations are connected to form contours. The output of such algorithms is thus a list of contours, which can be readily used to filter geometrical features like we did in chapter 5.

The visual system performs this contour extraction a little bit differently. The retina does signal the contours somehow, but the contours stay in the 2D visual field - and are not extracted as lists. This transformation from the luminance landscape to a contour signal is discussed next.

6.2 Spatial Analysis in the Real Retina

The retina consists of roughly 5 neuron classes: photoreceptors, bipolar cells, ganglion cells, horizontal cells and amacrine cells (Dowling, 1987). The first four cells generate only analog potentials: they are non-spiking. The ganglion cells are the only spiking cells, with axons projecting to the thalamus. There exists a so-called direct pathway from the photoreceptors via the bipolar cells to the ganglion cells, whose transformation can be summarized as follows: the luminance (gray-scale) value hitting the photoreceptor determines its analog potential, which is linearly transformed into a spike frequency in the ganglion cell (see figure 29a, number 1 and 2). The analysis of this transform has been carried out with small spotlight stimulations and

has led to the picture that the spatial analysis in the retina occurs point-wise, and that a frequency code is at work. It is however not exactly clear, what happens when an edge is presented (see figure 29a, number 3). If the edge was transmitted as two frequencies, a low and a high frequency respectively, then cortical cells would have to disentangle the frequencies to detect an edge (or contour piece). Because the specific transformation is actually not clear in detail, we here suggest two alternate transformations. One exploits the possibility that spiking thresholds are adjustable and that leads to detection of edges. We call this now the method of adjustable thresholds; the other transformation employs a latency code to separate edges in time. We call this now the method of latencies. In addition, both transformations make use of the idea of wave propagation.

6.2.1 Method of Adjustable Thresholds

Let us assume - as we did in the introduction already -, that the retina signals contours, specifically that it responds to large luminance edges (Rasche, 2004). Furthermore, the output of the neuron should only be a single spike because that can suffice for shape analysis. The transformation process can then be described as: we need a process that generates a single spike in response to a large contrast edge (figure 29b).

We imagine that this may occur with a combination of two separate processes, a fast one and a slow one (figure 29c). In the fast process, a receptor potential determines the initial membrane potential and the adjustable spiking threshold of its successor (spiking) neuron, which we call ganglion cell now. For reason of simplicity, the second layer (bipolar and horizontal cells) is omitted. The adjustable spiking threshold of the ganglion cells is set above the initial potential with a fixed offset. This fast process is not explicitly shown in figure 29c but merely its ’end result’, which is at t=0 of the time axis of the slow process. In the slow process, the charge spreads laterally through the network of connected ganglion cells (time steps 1 and 2 in figure 29c). The spiking thresholds stay fixed during this slow process. The charge of a high potential ganglion cell will spread towards its neighboring ganglion cell with a lower potential as well as a lower spiking threshold, and cause it to fire (time step 2).

The motivation for the fast process is that receptors directly determine the membrane potential in their successive ganglion cells, whereas they indirectly determine their adjustable spiking threshold through an extra-cellular process. For example it has been shown for various brain cell cultures, including retinal preparations, that calcium waves can spread quickly through the gap-junctions of the glia network (Charles, 1998). These calcium waves can alter the extracellular calcium concentration rapidly and substantially, and could