Bernal S D_2010.pdf - University of Plymouth

4.2. ARCHITECTURES
4.2 Architectures
This section describes the specific structure parameters of the three different Baycsian networks
employed. They are based on the parameters of two published versions of the HMAX mode
(Serre et al. 2(X)7c,b). For simplicity I have used the same parameter notation employed in
these papers. Note that these parameters can be used to build the HMAX network as well as the
functionally equivalent Bayesian network, as they dehne the topology of the network, i.e. the
structure and the interconnecliviiy between the different elements of the network.
The first two layers of the network are equivalent in all three architectures and their parameters
are summed up in Table 4.1.
4.2.1 Three-level architecture
The parameters for layers S2. C2 and S3 (Serre et al. 2007c) arc shown in Table 4.2 and the
resulting Bayesian network is illustrated in Figure 4.4. The number of nodes at each layer and
band depend on the size of the input image and the pooling (AN) and sampling (E) parameters.
The figure shows the total number of nodes at each layer, assuming an input image of 160x160
pixels and the parameters delined by Table 4.2.
Due to inherent properties of Bayesian networks, each node in the graph can only have a fixed
number of afferent nodes. For this reason, in order to obtain S2 nodes with features of different
RF sizes, AN^ = 4,8.12,16, these are implemented using separate nodes. Therefore, all S2,
C2 and S3 nodes are repeated four times, one for each of the RF sizes. This is not illustrated in
Figure 4.4 because the structure of each of the four sets of nodes is equivalent (as a function of
RF size, ANsi
SI types, Ksi
Scale band
Grid si/e, ANa
Sampling, ec\
Cltypes, Ka
SI parameters
7.9 11,13 15,17 19.21 23. 25 27,29 31,33 35,37
4(0°;45'';90°;135°)
i
8
3
2
10
5
CI parameters
3
12
7
i
4
14
8
5
16
10
{0";45'';90°;135")
Table 4.1: Comparison between two implementations using spiking neurons of graphical models
and belief propagation
150
6
18
12
7
20
13
8
22
15