Bernal S D_2010.pdf - University of Plymouth

4.1. HMAX AS A BAYKSIAN NETWORK
(7. the phased and the wavelength A. determine the spatial receptive field of the SI units. These
parameters were adjusted so ihal the tuning profiles nf SI units match those of VI parafoveal
simple cells in monkeys (Serre and Riescnhuber 2004).
CI layer - Units in this layer correspond to cortical complex cells showing a bigger RF size and a
certain degree of position and si/e invariance. Liach CI unit receives input from a AWci x ANc\
square array of reiinotopically organized SI units with the same orientation, thus preserving
feature specificity. CI units arc arranged in 8 scale bands, where units at each scale band pool
from two SI Ri' sizes, e.g. CI scale band I pools from SI units with RH sizes 7 and 9. The
pooling grid size, ANn. ranges from 8 pixels to 22 pixels, in steps of 2 pixels, according to the
CI scale hand. The pooling operation used is the mac operation, i.e. Lheactivily of eachCI unit
is determined by the strongest of its (AA'n x ANci positions x 2 RF sizes) afferent SI units.
This is shown in the following equation:
CU..|.;^.,,,.n,*= max (Sl,(,„r,,,,|,i) (4.2)
where k represents the feature (in this case the filter orientation),
f>c\^x.c\.yc] represents the band and location of the CI unit,
{bi,Xi,yi} represents the hand and location of the afferent SI units, and are given, as a function
of the CI unit's band and location and the network parameters, by the following expressions;
i,e{2-ici-l,2fin} (4.3)
Xie{\ + {xn - 1) •ei,(fc(i),-... \+{xn ~ I)-fv,(bn) + AA'n(tn)} (4.4)
yie{\+(yn-\)-eci{hn).---,i+(yc\-i)-£ciibci) + ANci{bci)} (i.5)
This means each CI unit represents a Gabor-like feature of the same orientation as the SI
units thai feed into it. but with a certain position and size invariancc. Additionally. CI units
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