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corresponding to ith feature point. The vector qi is a set of spatial and angular

distances from feature point i to its N nearest neighbors denoted by Qi(x,y,θj),

where j is the jth of the N neighbors. Ni represents a set of neighbors. The

neighbors satisfying both maximum number N and minimum Euclidean distance

dij between two points Vi and Vj are said to be of consequence for i
th feature point.

In order to identify an input graph with a stored one, which might be

different either in total number of feature points or in the location of the respective

faces, two cost values are evaluated [36]. One is the topological cost and the other

is a similarity cost. If i, j refer to nodes in the input graph I and nmyx ′′′′ ,,, refer

to nodes in the stored graph O then the two graphs are matched as follows [36]:

1. The centroids of the feature points of I and O are aligned.

2. Let Ni be the i
th feature point { Vi }of I. Search for the best feature point {Vi’ }

in O using the criterion



ii S





′ =−= min

1 (2.45)

3. After matching, the total cost is computed taking into account the topology of

the graphs. Let nodes i and j of the input graph match nodes i ′ and j ′ of the

stored graph and let iNj ∈ (i.e., Vj is a neighbor of Vi). Let



= ′′








,minρ . The topology cost is given by

.1 jjijjii ′′′′ −=Τ ρ (2.46)

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