Bernal S D_2010.pdf - University of Plymouth

4.1. HMAX AS A BAYESIAN NETWORK
NodeX
Message to
parents of X
(U, U^)
Ax(U^)... Ax(U^)
A(X)
A(X)^n^c.(X)
Ac.(X)...^c„(X)
Message from
children of X
(C, CJ
n^(U,)-Bel(U,)/MU,:
Message from
parents o( X
(Ui U,}
Bel(UM ... Bel(U^)
TTx(UO TTX(UM)
n(X)= ^ P(X|U ,U,)n"-(lJ'
n(X)
Bei(X)-a.A(X).TT{X)
T^
Bel(X)
Message to
children of X
_4______j
F/jjiiw J..J; Inienial structure of a node implemeniing belief propagation in a Bayesian network
wilh a polyiree slruciure (more ihan one parent per node). F.acli node combines
the bollom-up A messages from cfiild nodes willi itie top-down n messages from
the parent nodes lo culcuJaie the teliet and the oulpui A messages to the parent
nodes. Nole that the lop-down ouipui messages of the node are made equivalent
lo the belief of the node. Therefore, inpul top-down messages to a ni>de need to
he divided hy the output A message to ohlaiii the eorresponding n' message from
the node above (Pearl 1988). The operations performed correspond to Equations
(3.27) lo (3-31), and were described in detail in Section 3.3,3.
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