Bernal S D_2010.pdf - University of Plymouth

4.1 HMAX AS A BAYESIAN NETWORK
4.1 HMAX as a Bayesian network
4.1.1 HMAX model summary
Tile HMAX mode! (Riesenhuberand Poggio 1999, Serre el ai. 2007b), which captures the basic
principles of I'eedforward hierarchical object recognition in the visual system, has already been
described in some detail in Section 2.1.2. This model was chosen as a starting point, firstly
because it reproduces many anatomical, physiological and psychophysical data from regions
VI, V4 and IT. The second reason is that it has been repeatedly argued that the main limitation
of the HMAX model is that it docs not account for the extensive feedback projections found
in the visual cortex (Serre 2006, Walther and Koch 2007). Our proposed methodology, namely
Bayesian nelworks and belief propagation, is ideal to tackle this problem and provide such an
exiension. Below is a brief technical outline of the different layers and operations in the original
HMAX model, which will faciUtate understanding of the proposed model. I'igure 2.4 provides
a graphical representation of the dilTerent layers in HMAX.
SI layer - Units in this layer implement Oabor filters, which have been extensively used lo
model simple cell receptive fields (RJ-). and have been shown lo fit well the physiological daia
from striate cortex (Jones and Palmer 1987). There are 64 types of units or fillers, one for each
ofthe KsK^ 4) orientations (0°, 45°.90°. 135") xA/Vsi(^ 16) sizes or peak spatial frequencies
(ranging from 7x7 pixels to M x 37 pixels, in steps of 2 pixels). The four different orientations
and 16 different sizes, although an oversimplification, have been shown to be sufficient lo pro­
vide rotation and size invariance at the higher levels. Phases are approximated by centring the
Gabor filters at all locations. The RF size range is consistent with primate visual cortex (0.2" lo
1 °). The input image, a gray-valued image (160 x 160 pixels Rs 5''j.'i° of visual angle) is filtered
at every IcKaiion by each of the 64 Ciabor fillers described by the following equation;
Gij. = expl--i ^- '-—^ •• '-\ xcosi 2;r-(j:cose + .vsine)-|-iJ
The paraniciers in the equation, that is, the orientation 6, the aspect ratio 7. the effective width
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(4.1)