Neural Abstraction Pyramid Architecture - Hierarchical Neural Networks for Image Interpretation - page 86

Layer 0: Foreground/Background. Figure 4.13 summarizes the templates used
for the processing elements of the pyramid's bottom layer features and shows the
stable response of the network to a test pattern consisting of three circles.
The input array I is set to a version of the input image that has been shifted in
intensity to make the mean value equal to 0.5. Furthermore, the image was reduced
in size by a factor of two if it did not fit into a 232 × 88 window, and then smoothly
framed to match the array size of 240 × 96.
The input projections to the forward feature F and the backward feature B have
a center-surround structure. They have been set to differences between 3 × 3 and 7 × 7
binomial kernels. The central weight has an amplitude of 4 . 031 and the projections
have a DC part of ± 1 . 5 . This is offset by a bias of 0 . 75 to the background input
projection. The foreground bias is set to − 0 . 8 , suppressing responses to intensities
that are slightly larger than average. Hence, the forward potentials of the foreground
react best to a dark center that is darker than its neighborhood (a line), and the
forward potentials of the background react best to a bright center that is surrounded
by dark lines (a loop center).
Lateral projections to the two excitatory features have a specific excitatory and
an unspecific inhibitory part. Excitation comes from the 3 × 3 neighborhood of the
same feature and inhibition from a 5 × 5 window of the sum S F B of the two fea-
tures. The feature cells do not excite themselves but inhibit themselves via S F B .
Hence, the lateral connectivity favors blob-like activities that extend over multiple
neighboring pixels and suppresses isolated active cells. The lateral excitation for
the background is stronger than the one for the foreground. The opposite applies
to the inhibition. Thus, the lateral competition between the two features favors the
background. Initial foreground responses are removed if they are not supported by
neighboring foreground pixels or by edges detected from Layer 1.
Top-down support comes from the backward projections which are the inverse
of excitatory forward projections to the edge-features. They expand the edge repre-
sentation to the higher-resolution foreground/background representation. Unspecific
backward inhibition comes from the sum of the edges S E .
Layer 1: Edges. The middle layer of the binarization network is summarized in
Figure 4.14. Four features detect step edges. E T responds to the top edge of hori-
zontal lines and E B to their bottom edge. The left and right edges of vertical lines
excite E L and E R .
The specific excitatory weights of the 6 × 6 forward projections resemble the
oriented foreground/background double line that is characteristic for step edges in
Layer 0. Unspecific forward inhibition comes from S F B weighted with a 6 × 6 bino-
mial kernel. The forward projections have a bias weight of − 0 . 05 to prevent reaction
to spurious edges. The sum of the edge features is computed by S E .
Lateral projections mediate cooperation between aligned edges of same or sim-
ilar orientations by 3 × 3 excitatory kernels and unspecific competition via a 5 × 5
binomial kernel, folded with S E . Since edge cells do not excite themselves, they
must be supported by other edges or line features to survive the competition.