In: Wagner W., Szekely, B. (eds.): ISPRS TC VII Symposium - 100 Years ISPRS, Vienna, Austria, July 5-7, 2010, IAPRS, Vol. XXXVIII, Part 7B 
620 
Zone 3 (nose): The nose could be described by a conical 
frustum with an elliptical base (Fig.4). 
Figure 4. Lower-face portion geometrical feature: a) 
landmarks, b) conical frustrum 
Zone 4 (lower-face portion): This region could be described 
by an ellipsoid (Fig.5). 
Figure 5. Lower-face portion geometrical feature: a) 
landmarks, b) ellipsoid 
3. EXPERIMENTAL VALIDATION 
To evaluate the performance of the proposed methodology in 
the area evaluation, the geometrical features-based approach 
was compared with the tetrahedron method (Sforza 2005). First 
the facial areas of five patients were estimated using the point 
cloud meshes and adding the area of every single triangle 
covering the different specific regions. The results from this 
evaluation were considered reference values because the mesh 
approximation is very precise and depends only on the 3D 
scanner device employed for data acquisition. However, using 
the mesh approximation, it is possible to obtain reliable 
information about the soft tissue area modifications, but it is 
impossible to understand, comparing pre and post-surgery point 
clouds, where the face was modified (shift, scaling, rotation). 
With the use of specific geometries, such as those used in the 
proposed method, it is possible to extract spatial information 
together with reliable data about area and volume. From the 
results of the different comparisons, the geometrical features- 
based approach yields data closer to reality than the 
tetrahedrons methodology. 
Looking at the graphical comparison (Fig. 6), it is possible to 
see that for the nose, while the geometrical features-based 
approach gives a good fit, the tetrahedron approach does not 
match the real nose shape. This is verified by the fact that the 
tetrahedral structure is composed of five vertices: nasion, nose 
tip, left and right nose lobes, and nose base. For example, 
looking at the nose top, while the real shape shows one unique 
arc profile connecting the eyebrows, the tetrahedron solution 
employs only one point. 
Figure 6. Feature Based Method applied to the nose: a) Feature 
Based Method, b)Tetrahedron method 
This morphological mismatching between the real nose shape 
and the tetrahedron shape confirms the experimental data that 
show a more reliable area evaluation using with the conical 
frustum instead of the tetrahedron. 
4. CONCLUSIONS 
Face decomposition using solid geometries provides reliable 
information about the soft tissue shift comparable to that from 
traditional cephalometric data, but it also provides a more 
complete set of three-dimensional information, such as facial 
area modification, that is not attainable with traditional 
methodology. The presence of elementary geometries that 
synthesize the real shape is able to support the use of 3D 
scanners for diagnostic purposes instead of point clouds that 
contain a huge quantity of morphological data but are very 
difficult to employ and that sometimes, using inappropriate 
measurements solutions, provide false information. 
Although the method proposed is to study the quantification of 
postoperative changes, it could also be a starting point for other 
applications in medical diagnosis thanks to the ability to 
synthesize facial morphometric data using simple geometrical 
elements, which is more reliable than the simple tetrahedron. 
5. REFERENCES 
Bookstein FL (1991) Morphometries tools for landmark data. 
Cambridge University Press, Cambridge 
Coombes AM, Moss JP, Linney AD, Richards R, James DR (1991) 
A mathematical method for comparison of three dimensional 
changes in the facial surface. Eur J Orthod 13:95-110 
Ferrario VF, Sforza C, Schmitz JH, Santoro F (1999) 
Threedimensional facial morphometric assessment of soft-tissue 
changes after orthognathic surgery. Oral Surg Oral Med Oral Pathol 
Oral Radiol Endod 88(5):549-556 
Hajeer MY, Ayoub AF, Millett DT (2004) Three-dimensional 
assessment of facial soft-tissue asymmetry before and after 
orthognathic surgery. Br J Oral Maxillofac Surg 42:396 ^404 
Harmon LD, Khan MK, Lashc R, Ramig PF (1981) Machine 
identification of human faces. Pattern Recognit 13(2):97—110 
Hoffmann J, Westendorff C, Leitner C, Bartz D, Reinert S (2005) 
Validation of 3D-laser surface registration for image-guided cranio- 
maxillofacial surgery. J Craniomaxillofac Surg 33(1): 13-18