Graphics Reference
In-Depth Information
This update is iterated until convergence (usually three or four iterations), yielding
the combined edge:
C
,Σ
C
k
e
C
=
μ
(2.10)
Node Removal
Consider a node
n
r
to be removed by marginalization, with incident edges
E
r
=
{
e
0
,...,
e
m
}
. Each pair of such edges
(
e
i
,
e
j
)
is composed into
e
according to
(
i
,
j
)
the following cases:
⊧
⊨
e
i
·
e
j
s
(
e
i
)
=
d
(
e
j
)
=
n
r
e
−
1
j
e
i
·
s
(
e
i
)
=
s
(
e
j
)
=
n
r
e
(
i
,
j
)
=
(2.11)
e
−
1
i
⊩
·
e
j
d
(
e
i
)
=
d
(
e
j
)
=
n
r
e
j
·
e
i
d
(
e
i
)
=
s
(
e
j
)
=
n
r
The resulting composed edge is added to the graph between the two incident nodes
that are not
n
r
. If such an edge already exists, the edges are combined, reversing the
composed edge if necessary. Finally, all incident edges
E
r
are deleted from the graph
along with the node
n
r
. An example is shown in Fig.
2.4
.
2.8.3 Edge Pruning
While the node marginalization procedure always decreases the number of graph
nodes and attempts to decrease the number of edges, it might fail to bound the
degrees of nodes and thus the complexity of the graph. Indeed, marginalizing out
all pose nodes results in a completely connected graph over view nodes, with edge
cardinality quadratic in the number of views.
Fig. 2.4
Graph reduction by marginalizing out a node. In this example, the number of edges in the
graph is unchanged
