Elemental Operations

4. Elemental Operations

The following sections will provide a brief description of several potential elemental operations.  Although these operations may not actually be used by the human visual system, there is some evidence (physiological and psychological studies) indicating so.  Greater details regarding the operations are given in the paper.  It should be noted however that not all elemental operations are known and tyhere are probably many more than the operations described here.

4.1 Shifting of Processing Focus

This operation refers to the ability to control the location to which operations take place, or in other words, the ability to selectively apply our visual attention.  Since visual attention is directed to some particular location, it suggests that processing of visual information does not occur simultaneously at all locations and aids in keeping the amount of information being processed to a minimum.  This shift of attention can be achieved partly through eye movements however, it can also occur witout any eye movements at  all.  Finally, plenty of psychological studies (for example see [1]) and physiological studies indicate the ability to direct visual attention (see [3], [5] for further details regarding the visual attention system).

4.2 Indexing

As described above, we are capable of directing visual attention (or shifting the processing focus) to particular locations.  How are these particular locations actually selected?  According to the author, we select locations with the elemental operation referred to as indexing, which directs processing focus to locations which are drastically different than their surroundings (such locations are also referred to "odd man out" locations).  As an example of such an odd man out location, consider the example illustrated in figures 8a,b.  In figure 8a, each line contains 10 letters "A", each of which is identical.  Figure 8b is identical  to figure 8a except for the single "A", which is red instead of black.  This red A immediately "jumps" out and is easily noticeable.  This "A" is referred to as an indexable location.
 
Figure 8.  Indexable Location.

The Indexing operation itself consists of the following three subdivisions:

  1. The properties used for indexing are computed using the information available in the base representation.  The "indexable" properties may include color, motion, curvature, and texture in addition to others, and are computed in parallel.
  2. Using the information computed in the step above, odd man out locations are located by comparing regions of the base representation to their surroundings and computing a difference image.
  3. Finally, processing focus is shifted to the location corresponding to the strongest difference signal.  After processing has been completed at this location, items similar to the indexed item in close proximity to the indexed item are processed next.  Studies also indicate that this final step may itself be further subdivided (see paper for further details).

4.3 Coloring

Coloring refers to the same operation described earlier with respect to the inside / outside relations and consists of marking or activating some region surrounding a point.  There are several problems associated with this operation however.  For example, referring to figure 9, the small target red circle is inside the larger circle.  However, the boundary of the circle is actually a broken line and as a result, the coloring procedure would reach infinity and it would be erroneously concluded that the point is outside the circle.
 
Figure 9.  Breakdown of the Coloring Method.

Clearly the human system is capable of correctly determining the target is inside the circle and does not ahve the shortcomings associated with the given the coloring  algorithm.  Unfortuanely, the exact coloring process carried out by the human system is not entirely known.

4.4 Boundary Tracing and Activation

This operation allows for the tracing (following) of contours in the base representation and is actually a useful routine employed in a variety of tasks.  For example, as shown in
figure 10, it can be used to determine whether two points are on the same contour.  This can be accomplished as follows:
  1. Start at one point and mark this point (marking is described below)
  2. Trace the contour until one of the following occurs: a) The next point is encountered - in this case, both points are on the same contour.  b) The original starting point is encountered - in this case, both points are not on the same contour.
Figure 10.  Boundary Tracing and Activation Example.

In a similar manner, determining whether a curve is closed or not can also be accomplished using a similar method.  This is accomplished by  starting at some point on the curve and tracing the curve.  If the original starting point is encountered then the curve is closed otherwise it is not.

Although the tracing method appears simple, it is actually quite complex and does require certain restrictions.  For example, how are incomplete boundaries traced or boundaries with breaks in them such as the circle of figure 9. -how about tracing across intersections or branches - hich branch is followed?

4.5 Marking

Allows for keeping track ("remembering") locations already processed thereby permitting routines to shift between locations without having return and re-process previous locations again.  Marking may be used determine whether some curve is closed - mark the starting point, trace the curve.  If the marked point is encountered, curve is closed otherwise if tracing continues to "infinity" curve is not closed.