The input image is a movie with luminance
L, varying as a function of space and time—i.e.,
L(
t,
i,
j). Luminance increases (
on channel) are defined by
and luminance decreases (
off channel) are defined by
Remember that all outputs are half-wave rectified ([
x]
+) unless otherwise specified. Inhibitory interneurons, implementing Barlow–Levick inhibition, are governed by
where
ij +
Display Formula
refers to the node next to
ij in the direction of
Display Formula
and
Display Formula
is the direction of motion. Note that although the predecessor model restricted the motion signals to eight directions of motion (Barnes & Mingolla,
2013, equation 11 and after), we have chosen to allow any reasonable fixed number of directions (say from four through 16, depending on the geometry and connectivity of nodes). The direction opposite of
Display Formula
is denoted by −
Display Formula
. This means that the direction-specific inhibitory interneurons inhibit each other if they are at neighboring locations representing motion towards each other. Directional transients (which always computed at equilibrium, because they decay too quickly) are described by
which is almost identical to
Equation 16. The equations for
a() and
b() are very similar, but remember that
a() represents known interneurons that inhibit each other, as well as
b() neurons, whereas
b() represents excitatory neurons that represent motion in a specific direction.
Figure 8 explains the geometrical arrangement of these motion neurons. The signals are combined by adding the rectified
on and
off components to yield elementary motion signals:
Short-range filtering is performed according to:
where
σ1,
σ2 , and
σ3 are the sizes of Gaussian kernels and
F1 and
F2 are constants. The kernel defined by
σ1 is the small isotropic on-center for the same direction and also off-center for
other directions; whereas
σ2 and
σ3 are the anisotropic off-surround for the same direction (as shown in
Figure 8C). This signal is then smoothed using a direction-specific uniform-density circular kernel with radius
σe according to