Neural Abstraction Pyramid Architecture - Hierarchical Neural Networks for Image Interpretation - page 66

more abstract
Backward projections
Lateral projections
Forward projections
less abstract
Fig. 4.1. Neural Abstraction Pyramid architecture. The network consists of several layers.
Each layer is composed of multiple feature arrays that contain discrete cells. When going
up the hierarchy, spatial resolution decreases while the number of features increases. The
network has a local recurrent connection structure. It produces a sequence of increasingly
abstract image representations. At the bottom of the pyramid, signal-like representations are
present while the representations at the top are almost symbolic.
decreasing resolution has been used before, e.g. in image pyramids and wavelet
representations (see Section 3.1.1). In these architectures, the number of feature
arrays is constant across all layers. Hence, the representational power of the higher
layers of these architectures is very limited. In the Neural Abstraction Pyramid,
this effect is avoided by increasing the number of feature arrays when going up the
hierarchy.
In most example networks discussed in the remainder of the thesis, the number
of cells per feature decreases from I × J in layer l to I/ 2 × J/ 2 in layer ( l + 1)
while the number of features increases from K to 2 K . Figure 4.2 illustrates this.
The successive combination of simple features to a larger number of more com-
plex ones would lead to an explosion of the representation size if it were not coun-
teracted by an implosion of spatial resolution. This principle is applied also by the
visual system, as is evident from the increasing size of receptive fields when going
along the ventral pathway. The dyadic reduction of resolution is natural to an im-
plementation with binary computers. It allows one to map addresses into adjacent
layers by simple shift operations. Of course, the concept can be generalized to any
pyramidal structure.
It may be desirable that the number of feature cells per layer stays constant, as
in the fast Fourier transformation described in Section 3.1.1. This is only possible
with reasonable computational costs, if the number of accesses to the activities of
other feature cells when computing a feature cell is kept below a constant. If access