Computational Geometry in the Human Brain - Discrete and Computational Geometry and Graphs - page 148

only the local information. This causes ambiguity in the direction of the detected
motion, in the following sense.
Suppose that, as shown in Fig. 5 , a neuron receives visual data in a small
circular area of the retina, and detects displacement of an edge for which both
terminal points are outside the circular area. Then, the neuron can tell that the
edge moves, but cannot tell in which direction. There are many possibilities for
the direction of the motion, as shown by the arrows in Fig. 5 . This ambiguity
is called the “aperture problem” [ 13 ]. In other words, a neuron can only detect
motion perpendicular to the edge, no matter which direction the edge actually
moves.
Fig. 5. Aperture problem.
On the basis of these two observations, we can explain why the Ouchi illusion
arises. Suppose that the Ouchi pattern moves slightly on the retina. In the central
part of the Ouchi pattern, horizontal edges prevail, and, consequently, primarily
vertical motion will be detected. In the surrounding part, on the other hand,
vertical edges prevail, and, consequently, primarily horizontal motion will be
detected. As the result of this, the central and surrounding parts appear to
move differently. This is a typical way of explaining the Ouchi illusion [ 8 ].
One might think that this illusion would become stronger if the elongated
checkerboard patterns were replaced with stripes, because the edge directions
would then be more uniform. However, this is not true. The illusion becomes
weaker if we replace the central part of the Ouchi pattern with horizontal stripes
and the surrounding part with vertical stripes. This can be understood in the
following manner. When a neuron becomes excited, it suppresses the excitation of
its neighboring neurons. This is called lateral inhibition. If a moving edge is long,
the excitation of a neuron covering part of the edge will suppress the excitation
of the neurons covering the neighboring parts. In this way, the excitations of
neurons cancel each other, and the illusion becomes weaker.
A straight edge will stimulate only those neurons that detect the direction
perpendicular to that edge. If the edge direction deviates slightly, such as like