Bernal S D_2010.pdf - University of Plymouth

Chapter 4
Methods
This chapter describes in detail a theoretical and computational model which employs the maih-
emaiical tools described in Chapter 3, namely Bayesian networks and belief propagalion, lo
simulate some of the anatomical and physiological properties of the ventral visual palhway,
embodied in the HMAX model, rurthermore. the model tries to reproduce some of the ob­
served phenomena described in Chapter 2, such as feedback modulation and illusory contour
completion.
The chapter is organized as follows. Section 4.1 sums up the differeni layers and operations of
the HMAX model and describes a how this model can be fonnulated as a probabilistic Bayesian
Network implementing belief propagation. Section 4.2 specifies the exad network parameters
of three different HMAX archilcclures and describes the corresponding Bayesian network thai
captures each sci of parameters. Section 43 examines the learning methods used to generate the
conditional probability tables of the Bayesian network, and how these weights approximately
capture the original prototypes and operations of the HMAX model. Section 4.4 details how the
selectivity and invariance operation of the HMAX model are approximated using the Bayesian
belief propagalion algorithm. Section 4.5 describes how feedback is implemented inherently
in the proposed Bayesian network through the belief propagation algorithm. Additionally, it
discusses the solutions implemented lo deal wiUi the problem of having multiple parents and
loops in Ihe network. Finally, Section 4.6 recapitulates and justifies the different approximations
used by the model.
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