As can be seen in the figure, the triangulated surface has an 
irregular mesh structure and contains regions with a low 
density (eyes, eyebrows). These problems will be dis- 
cussed in the third paragraph of this paper. 
2.5. Visualisation 
The results can be visualised as a rendered model of the 
face (Figure 11). No filters are applied to smooth the sur- 
face and no interpolation between points is done, the figure 
shows raw data. The peaks and discontinuities of the sur- 
face represent measuring errors. One aim of the future 
work is measurements without errors or an automatic re- 
moval of the errors. 
  
Fig. 11: Model of the face 
A photorealistic visualisation can be achieved by draping 
the natural texture of the face over the 3D model (Figure 
12). 
  
Fig. 12: Photorealistic visualisation 
The purpose of the system which we are developing is the 
measurement of human faces for facial surgical interven- 
tion forecasts. The measurement of the face of a patient be- 
fore and after the surgical intervention is then required. 
Figure 13 shows an example of the face models of a patient 
before and after surgery. 
  
Fig. 13: Left: before, right: after surgical intervention 
3. DISCUSSION 
As can be seen in figures 11 and 13, measuring errors oc- 
cur. Three different causes can be distinguished. Firstly, in 
regions where the texture is insufficient because of the 
darkness (e.g. eyebrows) or because of the brightness (e.g. 
regions with strong reflection) the matching process fails 
so that the meshed surface contains areas without meas- 
ured points (Figure 10). A second problem appears in re- 
gions where the projected random texture is not well 
focused. In this case the matching process cannot give 
good results. This problem can be solved by using lenses 
with aperture for the projectors, that will give a larger 
depth of field. However, problems will remain in regions 
where the two projections overlap. The third problem of 
the matching process occurs in places where big differenc- 
es between the template and the search images exist (e.g. 
sides of the nose, the lateral extremes of the face). This is 
due to the convergent arrangement of the cameras and to 
topology of the human face. The use of two more cameras 
or a more accentuated lateral disposition of the five camer- 
as could remove this problem. 
4. CONCLUSION AND FUTURE WORK 
A photogrammetric method for the measurement of human 
faces with high accuracy has been described. The project 
is in the development stage and many improvements of the 
system can be envisioned. Among these, the most signifi- 
cant could be the implementation of a multi-image geo- 
metrically constrained matching algorithm (Grün, 1988), 
which should reduce the matching errors. A second im- 
provement of the method could be the introduction of an 
automatic generation of the seed points, thus increasing the 
automation level of the system. Thirdly, a real 3-D triangu- 
lation of the surface has to be implemented or added to the 
existent method. Until now only a 2.5-D triangulation is 
computed: the mesh is generated with the projection of the 
points onto the x,y plane. A definition of an "intelligent" 
smooth filter to apply to the modeled surface could remove 
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