Related Work - Hierarchical Neural Networks for Image Interpretation - page 54

(a)
(b)
(c)
Fig. 3.13. Neural field dynamics: (a) vanishing and stable activity; (b) merger and coexistence
of activity blobs; (c) spiral wave in a two-layered neural field (image adapted from [239]).
- explosive type bistable field in which localized excitations up to a certain range
spread out without limit over the entire field, but vanish if the range of excitation
area is too narrow,
- bistable field in which initial excitations either become localized excitations of a
definite length or die out; localized excitations move in direction to the maximum
of the input s , and
- field showing spatially periodic excitation patterns depending on the average
stimulation level.
Most interesting is the coexistence of several stable blobs of activity that is achieved
when the connectivity is positive in the center and negative for a larger neighbor-
hood.
The complexity of the network's behavior increases if one adds a second layer
to the field. In this case, one can further detect oscillatory patterns and traveling
waves. The dynamics of neural fields is closely related to excitable media [156],
which have the ability to propagate signals without damping. Such models have
been used to describe a wide range of natural phenomena.
Wellner and Schierwagen [239] investigated the behavior of neural fields using
simulations that were discrete in space and time. Figure 3.13 shows interesting cases
of the field dynamics. Initial activity vanishes if it is too large or stabilizes if it fits
the excitatory region of lateral interaction. If two small spots of initial activity are
close together, they are merged to a single blob of sustained activity. However, if
they are fare enough apart both blobs coexist.
Neural fields have been applied to several problems arising in perception and
control. For instance, Giese [82] applied them to motion perception tasks. He used