Field Theory in Vision

During the 19^th century, theoretical physicists made major advances in the study of “fields”.  A field, in the present context, is a physically measurable quantity that has a distinct value at every point in space.  Examples are the temperature at each point in a solid body, and the electric potential at each point in space.

The astonishing feature of a field is that it has not just an independent value at each point.  Rather, at every point, its value is determined by certain conditions, which are characteristic of the type of field.  Since there is an infinite number of points, even in a finite region of space, Nature determines a field by means of an infinite number of processes.  It is only a slight metaphor, to say that Nature uses an infinite number of parallel processors to determine a field.

Even though those 19^th century physicists had only their own brains and hands for computing, they were able to calculate and understand the working of these fields, because they developed highly effective methods and penetrating concepts for the purpose.

In the present work, instead of trying to reproduce the work of many parallel processors in the human brain with one or a few processors in a computer, we go to the opposite extreme.  We make the approximation that an infinite number of processors work in parallel to interpret images in the human brain.  Then, we apply the powerful methods and concepts of field theory, to understand and reproduce some of those processes.