Is this “t” or “I”?

Most humans familiar with the Roman alphabet would say that this is the letter “t”.  It has a cross-bar, which “I” has not.

This is obvious to you, but you have about a billion neurons, all working at once, to figure out what you are seeing.  What might a computer with only one processor (or even with a mere thousand processors) note as features of this image? 

Any of several feasible processes will detect the nearly-vertical stroke.  The computer may then detect the rather large bumps on the sides, which for us form the cross-bar, but it may not.  To define the concept of rather large, an adjustable parameter and/or special-case programming is necessary .  These are dirty words in the computing world because, according to the most well-established rule of computer science, no matter how complicated a process defines the adjustable parameter, some special case soon occurs, for which the result is wrong.

In the present case, rather large seems not very large at all, when we note that

  • The total extent of the bumps perpendicular to the nearly-vertical stroke (< 4 + 4 pixel widths maximum, ~ 3 + 3 pixel widths mean) is less than the width of the nearly-vertical stroke (9 pixel widths).

  • The sum of the areas of the bumps is less than 6% of the black area in the image.

Even if the computer decides those bumps are really there, it also has to decide whether they in fact constitute a cross-bar.  The additional difficulty is that

  • Each bump has more extent parallel to the nearly-vertical stroke (5 pixel widths) than perpendicular to it (< 4 pixel widths maximum, ~ 3 pixel widths mean).

The more we consider this image, the more adjustable parameters and special cases we find necessary, and the less is the probability of a process proving reliable.

Quadrupole convolution provides a clear resolution to the problems posed here.

Up to What Quadrupole Convolution Can Do.