Tag Archives: binding problem

Receptive Fields: Simple Cells and Tuning Curves

Receptive Fields

The jumping spider makes use of pattern recognition to distinguish prey from mate. Their eyes allow them to detect specific features or templates, specifically, the bar-shaped feature similar to the legs of other spiders (Land, 1969). Frisby and Stone (2010) discuss the jumping spider because they provide an excellent paradigm for how template matching works through a series of steps.

–       First, the original image is projected on to the retina of the spider’s eye

–       Second, the spider’s eye focuses on a specific feature, in this case the leg

–       Then the leg’s image is cast onto the retina, and receptors project this information to the primary visual cortex (V1)

–       Neurons in V1 receive inhibitory and excitatory input from the receptors in the retina

–       The receptors not blocked by the leg have increased activity and send an excitatory light signal

–       The receptors blocked by the leg have decreased activity and send an inhibitory light signal

–       The neuron gathers the total input and if it exceeds its threshold, firing indicates that a bar is present

Template matching, whether in a spider or human, relies on encoding of a pattern whose shape directly matches the input pattern to be detected. Striate cortex cells in V1 are found in all mammals. These cells receive input from the retinal fibres, and each cell is responsible for a limited patch of the retina (receptive field). Accordingly, cell types in the striate cortex are classified according to their receptive fields (Hubel and Wiesel, 1981). Striate cells are broken down into two parts: simple cells and complex cells.

Templates can, however, be impractical because the amount needed would be exponential resulting in a binding problem (Frisby and Stone, 2010). For example, if we have 18 templates for orientation sensitive to 18 sizes, which are sensitive to 18 shades, you can image the ridiculous amount of templates you would need. This problem is known as a combinatorial explosion.

Simple Cells

Simple cells are named simple because they can be simply mapped into excitatory and inhibitory sub-regions. Simple cells are optimally excited by bar-shapes, which is why it makes sense that simple cells are also called slit- and line – detectors. Slit-detectors respond to a light bar on a dark surrounding, and line-detectors respond to the opposite (Hubel, 1988).  Light on dark or vice versa is important because simple cells respond best to patterns that generate luminance differences, in other words, edges. However, because simple cells are so sensitive to edges, the orientation of a bar is important. The optimal stimulus for a simple cell, to emphasize luminance differences, is one that provides maximum excitation and minimum inhibition (Frisby and Stone, 2010).  To provide maximum excitation and minimum inhibition, different orientations are dealt with by different cells (Hubel and Weisel, 1962). The angle to which each cell is tuned is determined by the pattern of its excitatory and inhibitory regions. ‘Slit’ and ‘edge’ simple cells exist for a full range of orientations, which is reflected by the brain’s wiring; the fibres going from the retina to cortex differ depending on which orientation they represent (Frisby and Stone, 2010).

Population Code

As discussed in the previous section, bars maximally excite simple cells; however, cells still respond even when they are not maximally excited. If part of a cells visual field is activated, a partial response will be initiated. As such, context is vital to making sense of our visual field. For example, a non-vertical stimulus stimulates the vertically oriented receptive field just as well as the vertical but faint edge. In order to distinguish between the two outputs, they must be considered in context of the activities of cells examining the same retinal patch.

Fortunately, having sensitive simple cells makes interpolation between neighboring orientation measurements possible. This “talk” or interpolation between cells is known as a “population code.” Even though there are only simple cells for 18-20 different preferred orientations, we manage discriminations of less than <0.26 degrees (Frisby and Stone, 2010). Communication between cells allows us to discriminate when orientations vary very slightly, in the grey area between defined orientations. Populations of cells that have same preferred value of particular stimulus, like orientation, are called a channel. Scientists are able to measure the preferred orientation of cells by recording the symmetric pattern of firing rates.

Unfortunately, a major consequence of having a limited number of cells tuned to a large number of orientations is that cells taking each measurement need to be “broadly tuned” for “coarse coading.” Cognitive psychologists wanted to know how many channels are necessary to resolve the ambiguity problem. The answer is technically two but then the cells would be so broadly tuned that you would not be establishing any type of context. In addition, the tuning curve would turn far to slow to interpret anything. Unless the input to the cell coincided with the flank of the curve, there would be very little difference between the cells outputs. Hence, the brain uses a large number of broadly tuned cells with tuning so that the most sensitive part of the tuning curve can always be representative of one orientation with the less sensitive parts being representative of slight deviations from the optimal orientation (Frisby and Stone, 2010). 

Tuning Curve

The overall relationship between orientation of input edge and the output of the cell is called the tuning curve (Frisby and Stone, 2010). Tuning curves are important because they allow you to pinpoint which cells are sensitive to what orientation. The flank mentioned in the section above is where the slope of the tuning curve is the greatest; it also represents the point of greatest change in firing rate. This peak in sensitivity is found half way from the top of the curve. The trough or top of the curve is the least sensitive part because the slop is equal to zero. Regan and Beverly (1985) proved that humans do have peaks and troughs in their orientation sensitivity.