Neuronal Pathways of Vision - Vision with Direction - page 13

the receptive field sizes of ganglion cells in the retina. Likewise, the density changes
of the simple cells reflect corresponding changes in ganglion cell density that occur
with increased eccentricity. The smallest receptive fields of simple cells, which map
to fovea, are approximately 0 . 25 ◦ × 0 . 25 ◦ , measured in eccentricity and azimuth an-

gles. This is the same as those of ganglion cells, on which they topographically map.
The farthest retinal periphery commands the largest receptive field sizes of

1 ◦
for simple cells. Furthermore, the simple cell responses appear to be linear, e.g. [6].
That is, if the stimulus is sinusoidal so is the output (albeit with different amplitude
and phase, but with the same spatial frequency). This is a further evidence that at
least a sampled local spectrum for all visual fields is routinely available for the brain
when it analyzes images. In Sect. 9.6, we will study the signal processing that is
afforded by local spectra in further detail.
Complex cells, which total about 75% of the cells in V1, respond to a critically
oriented bar, moving anywhere within their receptive fields (Fig. 1.7). They share
with simple cells the property of being sensitive to the spatial directions of lines, but
unlike them, stationary bars placed anywhere in their receptive fields will generate
vigorous responses. In simple cells, excitation is conditioned to the bar or edge with
the critical direction be precisely placed in the center of the receptive field of the cell.
Complex cells have a tendency to have larger receptive fields than the comparable
simple cells, 0 . 5 ◦ × 0 . 5 ◦ in the fovea. The bar widths that excite the complex cells,
however, are as thin as those of simple cells,

1 ◦ ×

≈

≈ 0 . 03 ◦ . Some complex cells (as well
as some simple cells) have a sensitivity to the motion-direction of the bar, in addition
to the spatial direction of it. Also, the complex cell responses are nonlinear [6].
In neurobiology the term orientation is frequently used to mean what we here
called the spatial direction, whereas the term direction in these studies usually rep-
resents the motion-direction of a moving bar in a plane. Our use of the same term
for both is justified because, as will be detailed in Chap. 12, these concepts are tech-
nically the same. Spatial direction is a direction in 2D space, whereas velocity (di-
rection + absolute speed information) is a direction in the 3D spatio-temporal signal
space (see Fig. 12.2). Accordingly, the part of the human vision system that deter-
mines the spatial direction and the one that estimates the velocity mathematically
solve the same problem but in different dimensions, i.e., in 2D, and 3D, respectively.
The cells that are motion-direction sensitive in V1 are of lowpass type, i.e., they
respond as long as the amplitude of the motion (the speed) is low [174]. This is
in contrast to some motion-direction sensitive cells found in area V2, which are of
bandpass-type w.r.t. the speed of the bar, i.e., they respond as long as the bar speed
is within a narrow range. There is considerable specialization in the way the the cor-
tical cells are sensitive to motion parameters. Those serving the fovea appear to be
of lowpass character, hence they are maximally active during the eye fixation, in all
visual areas of the cortex, although those in V2 have a clear superiority for coding
both the absolute speed and the motion-direction. Those cells serving peripherial
vision appear to have large receptive fields and are of high-pass type, i.e., they are
active when the moving bar is faster than a certain speed. Area V1 motion-direction
cells are presumably engaged in still image analysis (or smooth pursuit of objects
in motion), whereas those beyond V1, especially V2, are engaged in analysis and