Bernal S D_2010.pdf - University of Plymouth

4.4. FEEDFORWARD PROCESSmG
240 prototypes or S3 slates. This increases the invariance to position at the top level.
The learning process for the 4-layer architecture is not described in detail as it is a trivial exten­
sion of the methodology employed for the 3-layer architecture.
4.4 Feedforward processing
4.4.1 Approximation to the selectivity and Invarlance operations
For the feedforward recognition results presented in Chapter 4 we therefore assume that the
network is a singly-connecied tree, so that the k messages can propagate to the root node
without being affected by top-down messages (see Figure 3.9 in Section 3.3.3 for details). This
is the same strategy used during the learning process. This facilitates the approximation to the
HMAX operations and greatly reduces the computational costs to process each image. This is
specially important when testing a large image datasei over a large parameter space.
Note that even if the root nodes and 7i messages were initialized to a flat distribution, they would
still modulate the hotlom-up A messages, as n messages are multiplied by the CPT before being
combined with die A messages. In oUier words, as long as there is bottom-up evidence, it will be
modulated by top-down messages even if the lalier exhibit flat distributions. This was illustrated
in Figure 3.7. Several recognition simulations were also perftirmcd without this assumption, in
other words, with flat top-down messages that modulaied the feedforward A messages, in order
to compare results and establish ils validity. These revealed that a similar invariant recognition
perforniunce can be obtained even when including the feedback K messages (using loopy belief
propagation), but performing a detailed systematic test over the complete dataset and parameter
space is infeasible due to the high computational resources required.
The singly-connecled tree assumption allows the selectivity operation in HMA.X to be approxi­
mated as shown in liquation 4.9. Note thai the original Radial Basis lunction operation has l>een
replaced by an approximately equivalent dot-product operation as proposed by Serre (2006).
Serre et al. (2005a), and this dot-product operation is then approximated using the belief prop­
agation equation. More precisely, the weighted sum over SI locations and features is approx­
imated as a sum over the features and a product over the locations. This can be interpreted as
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