In: Wagner W„ Székely, B. (eds.): ISPRS TC VII Symposium - 100 Years ISPRS, Vienna, Austria, July 5-7, 2010, IAPRS, Vol. XXXVIII, Part 7B 
information. For this reason some studies (Swiderski 1993) 
have tried to exploit the 3D information from non invasive 3D 
scanners, such as laser scanners, to extract area and volume 
measurements. One of the most significant studies (Richtsmeier 
1992) has worked on soft tissue landmarks, creating a 
geometrical model that approximates the facial features with 
flat 
triangles in which vertexes have been represented by the facial 
landmarks. This approach has provided a simple and direct 
methodology for supporting the evaluation of facial areas and 
volumes. However, while the morphological behaviour of the 
face is characterized by smooth surfaces, this methodology of 
working with flat triangles is able to provide only a first 
approximation of the face behavior and neglects a series of 
features. Considering that 3D scanners provide accurate point 
clouds, it would be more useful to use methodologies that can 
exploit the entire point cloud morphology. 
Therefore, starting with this concept, we propose a 
methodology that employs geometrical features for 
approximating the facial shape, but instead of using only a 
tetrahedron for describing the face morphology, this 
methodology employs different 3D geometries that can better 
fit the face morphology. 
2. THE PROPOSED METHODOLOGY: 
GEOMETRICAL FETURES BASED APPROACH 
To identify the geometries required to develop a geometrical 
features-based model, it was necessary to define how to 
decompose the facial morphology. Starting from the head 
modelling guidelines (Coombes 1991) and from the coordinates 
of the facial soft tissue landmarks (Table 1), the face has been 
divided into four different regions (Fig.l), sectioning the model 
with a series of planes passing through the vertex, the upper and 
lower part of the nose, and the chin. 
Name 
Abbreviation 
Nasion 
N 
Pronalase 
Pm 
Subnasale 
Sn 
Labiale superius 
Ls 
Stomion 
Sto 
Labiale inferius 
Li 
Sublabiale 
Sis 
Pogonion 
Pog 
Tragi on 
Light ” Left 
Nasal alar crest 
alright ■ alien 
Chelion 
^bright “ ch] e ft 
Gonion 
S^right “ §Oleft 
Vertex 
V 
Table 1. List of soft tissue morphological reference points 
Once the four regions are defined, it is necessary to determine 
which geometry would be the most suitable fit for the different 
possible shapes in each zone. Starting with the number of 
landmarks that characterize every identified region, the 
available 3D geometries, and all the different possible facial 
morphologies, and working with hypothesis developed from the 
correlations between the cranial shapes and polygons (Raby 
1997), it has been possible to identify the best fitting geometries 
(Hyun 1998): 
Zone 1 (upper face portion): This region could be described 
by an ellipsoid (Fig.2). 
Figure 1. Soft tissue landmarks and face decomposition 
Figure 2. Upper face portion geometrical feature: a) landmarks, 
b) ellipsoid 
Zone 2 (middle face portion): This region could be described 
by a cylinder with an elliptical shape (Fig.3). 
Figure 3. middle face portion geometrical feature: a) 
landmarks, b) cylinder