Related Work - Hierarchical Neural Networks for Image Interpretation - page 55

temporally asymmetric Mexican hat shaped lateral interactions. Stable solutions
were traveling pulses that followed a motion sequence. The lateral dynamics was
used to integrate activity over time. Vijayakumar et al. [234] used neural fields as
saliency map to control attention and to generate saccadic eye movements for a
humanoid robot.
Cellular Neural Networks. While continuous neural fields facilitate analysis, they
must be discretized to be applicable in practice. Chua and Roska [41, 42] proposed
a simplified model that represents space with discrete cells, the cellular neural net-
work (CNN). This network has a strictly local connectivity. A cell communicates
e.g. to the cells within its 8-neighborhood. The space-invariant weights are described
by templates. A cell is computed as follows:

dt ( t ) = − 1

C dx ij

R x ij ( t ) + A ij,kl y kl ( t ) + B ij,kl u kl ( t ) + z ; y kl ,u kl ∈ N ( ij ) ,
where A describes the influence of neighboring cells, B is the receptive field on the
input u , and C and R determine the time-constant of a cell. Parameter z determines
the resting potential. The output y ij = σ ( x ij ) of a cell is a non-linear function σ
of its state x ij . Frequently, a piecewise linear function that saturates at − 1 and 1 is
used. While above equation is used for continuous time, there are also discrete-time
CNN variants.
The actual computation of the continuous network dynamics is done by relax-
ation within a resistor-capacity network. It is supplemented with logic operations
and analog image memories in a universal CNN machine, used for image process-
ing purposes. Low-level image processing operations, such as spatiotemporal filters,
thresholding, and morphologic operations, have been implemented in this frame-
work.
The CNN cells can also be combined with photosensors to avoid I/O bottle-
necks. Analog VLSI implementations for focal plane processing up to a size of
128 × 128 [143] have already been realized. The massively parallel architecture
achieves a throughput that would require a supercomputer if the same operations
were realized with general-purpose CPUs.
The CNN approach has been applied to areas other than image processing. For
instance, it has been used for the control of a walking hexapode robot [9] with 18

(a) (b)
Fig. 3.14. Cellular neural network model of Chua and Roska [41, 42]: (a) processing elements
are arranged in a grid and connected locally; (b) core cell of continuous time analog CNN.