In: Wagner W., Székely, B. (eds.): ISPRS TC VII Symposium - 100 Years ISPRS, Vienna, Austria, July 5-7, 2010, IAPRS, Voi. XXXVIII, Part 7B 
N-ALS 
N-ALD 
N-SN 
N-PRN 
SN-ALS 
SN-ALD 
ALS-PRN 
SN-PRN 
ALS-ALD 
N 
ALS 
PRN 
ALD 
Figure 5. Nasal Pyramid 
Connecting those five points we have been able to determine 
nose graph characterized by ten lengths. We have used a graph 
matching method (Fazl-Ersi, E., Zelek, J. S., Tsotsos, J. K., 
2007) for the recognition. This is a geometric identification 
method and starts with the consideration of nose graph (G), filli 
graph K 5 that has as vertexes V(G) = {P, PRN, SN, ALS, ALD} 
and as edges E(G) = {a, b, c, d, e, f, g, h, i, 1}. 
This graph has been considered as weighed graph where weighs 
associated are the distances. Then, we have considered the 
dissimilarity between the geometry of the graphs as 
(Bevilacqua, V., Andriani, F., Mastronardi, G., 2009): 
where G¡ = {(en, e i2 , e^} (MODEL GRAPH) and 
Figure 6. Map of points of repere detected 
For the recognition has been implemented PRN Graph 
Matching. This approach is based on the matching of the 
distances calculated regarding a point of reference (PRN point). 
In this technique are considered 9 points of reference and PRN 
for a total of 9 distances to match. 
SCLD1 
Gj = {(©¡j, e j2 , ..., e jn } (TEST GRAPH). 
This method works considering Gj as the graph to identify, so 
Z-coefficients are calculated for all the graphs of the database. 
At the end the graph G, that minimizes better Z is associated to 
Gj. 
3.2 PRN Matching 
Differently from previous approach we have implemented other 
algorithms for the search of points of repere, considering also 
the points of the eyebrow arched. An unstructured organization 
of points as that obtained from ASE file is complicated to 
manage, because it is impossible to move easily in the cloud. In 
this context has been useful to have the points organized in a 
YY matrix where each position has the relative Y value. This 
matrix has been obtained through the creation of a polygonal 
mesh that interpolates the terns of the point cloud. This 
approach permits a more easier scansion of the surface of the 
face using the easy management of the data in the matrix 
structure. The search of points of repere has been done by the 
scansion of the face made by the use of a “sliding vector” on the 
polygonal mesh, in order to determine the geometric-statistic 
features typical of the face. The “sliding vector” is an 
observation window that contains some elements of the YY 
matrix that at every step “scrolls” along the particular direction 
of movement. 
This methodology allows the individuation of the following 
points: 
Figure. 7. PRN Graph 
The technique as that of K5 Graph Matching (Bevilacqua, V., 
Mastronardi, G., Piarulli, R., Santarcangelo, V., Scaramuzzi, R., 
Zaccaglino, P., 2009) is based on the use of the dissimilarity 
coefficient: 
z{G i ,G l )= x - J<Saz*L 
n ^ («,») 
k=1 
where G¡ = {(e¡i, e¡ 2 , ..., e in } (MODEL GRAPH) 
and Gj = {(eji, ej 2 , ..., ej n } (TEST GRAPH), 
where e^ are the edges.