In cognitive psychology visual perception is conceptualized as a progression from (a) a "raw primal sketch"-- a sort of intesnity map, an initial representation from the senses; to (b) a "full primal sketch", or an intensity map that includes markings for edges, regions of similar intensity, and contours; to (c) a "2-1/2 D sketch", a representation that includes depths and orientations of surfaces relative to the viewer. It is assumed that objects within the visual field are then somehow compared to 3D models-- one for every object in the world-- that are stored in long-term memory so that object recognition may take place. What was discussed in lecture this week relates directly to the concepts of the raw primal sketch and the full primal sketch.

The raw primal sketch, being a simple intensity map, may be equated quite simply to the output of the photoreceptors-- permeability changes that "fairly faithfully copy the pattern of light on the retina." More interesting is the derivation of edges and contours-- the full primal sketch-- from this intensity map, which is the work of the ganglion cells. The shape of the receptive field of these cells, otherwise known as "center-surround cells", is critical to understanding this derivation. The ganglion cell's receptive field, called a "concentric center/surround antagonistic receptive field", is shaped somewhat like a bulls-eye. Energy striking the outer region of this receptive field (in the case of a "center-off, surround-on" cell) results in increased activity in the cell, whereas energy striking the inner region of the receptive field results in decreased activity in the cell. (Alternatively, in a "center-on, surround-off" cell, these excitatory and inhibitory areas are reversed). A cross-section of the excitatory and inhibitory tendencies one of these (center-off, surround-on) cells might therefore look like this:

  
   +1 -2 +1

Where +1 indicates an increased firing rate in response to energy, and -2 indicates a decreased firing rate in response to energy. Using this particular cell as an example, the derivation of edges and contours from an intensity map becomes quite simple.

A piece of the input to the ganglion cells, representing the differing intensities of light falling on the retina, might be represented as a string of numbers (smaller numbers representing lower intensities, and larger numbers representing higher intensities), such as this:

  3 3 3 6 6 6

A ganglion cell with a receptive field of +1 -2 +1 would "read" the first three digits of this series as follows:

 
   3   3   3
  +1  -2  +1

(+1x3) + (-2x3) + (+1x3) or (3)+(-6)+(3), which equals zero. This ganglion cell would continue to fire at its baseline rate, having detected no change in intensity which might indicate an edge.

Given that the receptive fields of the ganglion cells overlap, a more realistic situation might be as follows:

3 3 3 6 6 6 6 +1 -2 +1

+1 -2 +1

Here, this pattern of light intensity is falling within the receptive fields of five separate ganglion cells, each of which will "read" its particular piece of the pattern and produce an output accordingly, as seen above. Specifically, the pattern of output produced by these five ganglion cells will be:

  cell 1:  (+1x3) + (-2x3) + (+1x3) = 0
  cell 2:  (+1x3) + (-2x3) + (+1x6) = +3
  cell 3:  (+1x3) + (-2x6) + (+1x6) = -3
  cell 4:  (+1x6) + (-2x6) + (+1x6) = 0
  cell 5:  (+1x6) + (-2x6) + (+1x6) = 0

Therefore, a pattern of light intensity that looked this:

    6|     _________
 
    |     |
 
    |     |
 
   3|_____|
 
    |_______________

Will be transformed into ganglion cell output which looks like this:

     |
 
  +3|       /\
 
    |_____/    \            ______
 
    |____________\ ______ /______
 
    |              \    /
 
  -3|                \/ 
 
    |

This disrution in the ganglion cell frequency of firing indicates a point of change in intensity, or a probably edge in the world. These cells cannot detect gradual changes in brightness, nor do they give any information at all about areas of same intensity.

As a final note, it is important to consider in understanding edge detection that the receptive fields of ganglion cells come in different sizes, allowing for varying degrees of resolution. That is, cells with smaller recptive fields are often more precise in detecting sharp edges, whereas cells with larger receptive fields are able to detect more blurred-over edges that cells with smaller receptive fields cannot detect. These cells with differently-sized receptive fields work simultaneously to produce a full primal sketch that contains "the best of both worlds."

Wonderful summary, along Marr lines. Which are useful, but leave out an argument which says this way of doing things actually makes sense in some worlds but wouldn't in others. To put it differently, the lateral inhibition network actually ADDS information to the picture in one sense (this is THIS kind of world), while subtracting it in another (ignoring the slow intensity variations). Did you try the simulator on the website? It is set up exactly like your example. PG