Computational Approaches to Sensation and Perception

Along with the rapid development of visual neuroscience, there has been an equally rapid development of computational approaches to understanding perception. These approaches ranges from models of large scale like that of Marr (1985) effort at a unified computational theory to more limited efforts such as Krantz, Silverstein, & Yeh's (1992) model of visibility of displays underdynamic lighting. In this section a brief presentation on one computational model being developed by one of the authors will be presented to illustrate some of the power of these models (Krantz, 2000).

The motivations for this effort comes largely from teaching some of the concepts in the last section on Visual Neuroscience. Basically the effort is to try to examine the impact and function of the receptive fields from the retinal ganglion cells, particularly the x cells.

Take a look at the figure below.

The center does not change in any way. Does it look that way. The same is true for the two center squares below - they are identical.

Figure 6. Simultaneous Contrast

This effect is called simultaneous contrast. The model that has been developed will plot the output of many of these cells in a regular array - like an x and y grid. Figure 7 shows the output of this model for using the same simultaneous contrast image as in Figure 6. The receptive fields illustrated are small and would be very good at resolving fine details. The intersections of lines on the figure show where the center of a receptive field was located. So the x and y axes, defining the horizontal plane, represent a set of cells. The height of the surface in the figure represents how fast that cell would respond according to the model. The higher the point on the graph the faster the cell responds.

Figure 7. The model output for a simultaneous contrast image.

There are several interesting and important features of this figure. The most noticeable thing in the output of the model is the edges. If the receptive field does not have an edge in it, then the cell has about the same output whether the input is bright (white), moderately bright (gray) or dark (black). Light filling the entire receptive field is not an effective stimulus for the cell (Kuffler, 1953). So edges are excellent stimuli for cells and that shows up in model in Figure 7 (Troy & Enroth-Cugell, 1993). This finding that only the edges are sent back to the brain for processing agrees with the general finding about vision and it's filling-in of areas. This same process seems to play a role in why we do not see our blind spots.

Now, look at the edges a little more closely. Notice that the hills are next to brighter regions and valleys are next to darker regions. In particular, look at the big hills and valleys where the back background meets the light background (Figures 6 and 7). The square on the left has a hill next to it suggesting it is light and the square on the left has a valley right next to it suggesting a dark regions. This is exactly the illusion. I offer a more complete description of this model, its development, and how it helps us to understand how we see in Krantz (2000).

This model is barely at the beginning of its development. There are many ways to expand this model in the future. So far only X cell responses in the fovea have really been examined. Some of the possible extensions are to model Y cells, add color responses (DeValois & DeValois, 1975), and make the modeled eye jiggle just a little bit all the time like it does in real life (Carpenter, 1977).

While visual neuroscience and computational approaches seem to play a role in revealing new phenomena, reexamination of what are thought to be well established findings can also yield new insights. A recent advance in studies of the earliest stages of sensory information processing was the stunning discovery that the human eye contains a greater variety of cone photoreceptors than previously thought.