CIPA 2003 XIX 11 ' International Symposium, 30 September - 04 October, 2003, Antalya, Turkey 
530 
Figure 3: Measurement of tie points (Upper image: photo 
data, Lower image: Intensity image of the laser scanner). 
system can be seen in Fig. 2). The rotations of the local 
sensor co-ordinate systems of the laser sensor in respect 
to the global co-ordinate system could be computed with 
an accuracy of 0.38gon for ui (rotation around the x-axis), 
0.18gon for ф (rotation around the у-axis) and 0.17gon 
for к (rotation around the z-axis). The photo positions 
have an accuracy of 22mm in X-direction, 21mm in 
Y-direction and 46mm in Z-direction with an accuracy 
of the rotations of 0.18gon for u), 0.29gon for ф and 
0.27gon for к. The average accuracy of the tie points is 
17mm in X-direction, 16mm in Y-direction and 28mm 
in Z-direction. Separating the tie points on the statue, 
which are in general much closer to the sensor position, 
from those around the object shows that the accuracy of 
the points on the sculpture is much higher (XYZ: 11mm, 
11mm, 9mm vs. 28mm, 26mm and 61mm). 
Finally, a variance component analysis was performed. 
The following observation groups were examined: 
• image co-ordinates in photos: 0.37pixel 
• fine scan polar co-ordinates: 
horizontal angle: 48mgon; vertical angle: 31mgon; 
distance: 12mm 
• panorama scan polar co-ordinates: 
horizontal angle: 74mgon; vertical angle: 42mgon; 
distance: 16mm 
4 SURFACE MODELLING 
The goal of surface modelling is to get a geometric repre 
sentation of the object’s surface such as a triangulation 
or even a - more or less - continuous surface described by 
NURBS. NURBS (Non Uniform Rational B-Splines) are 
B-Splines, which are (rational) polynomials of usually low 
degree. The (rectangular) NURBS patches are fitted to 
the measured points, minimizing the residual vectors from 
the measurements to the idealized surface. As mentioned 
above, this surface is smooth, which is also the case for 
the original (i.e. the statue), with possible exceptions at 
certain lines and points. A surface composed of NURBS 
Figure 4: Point cloud from 10 fine scans (points with the 
same color belong to the same scan position). 
patches has therefore similar properties to the original 
surface, which makes renderings and texture projections 
- in order to name two applications - more appealing. 
There is another rational for using surface patches, which 
is the data reduction. A patch has typically only few 
parameters and needs therefore less storage capacity than 
the original points, e.g. in a triangulation. 
In this example, surface modelling was performed 
by the use of the software package GeomagicStudio 5.0. 
(cf. [Geomagic, 2003]). 
Only the data of the 10 fine scans (see Fig. 4) were 
eventually used for the modelling process, whereas the 
10 coarse panorama scans and the 22 photos served to 
stabilize the adjustment and increase its redundancy. 
Of course, it would be a promising idea to include the 
photos for the geometric reconstruction of the object, 
especially when thinking of sharp edges, which could 
be measured directly in the photos with a higher reliability. 
Using the parameters of outer orientation obtained 
by the adjustment, each of the fine scans was exported to 
a xyz-file (ASCII). Afterwards, those 10 point files were 
imported to the modelling software. It supports “ordered 
point clouds”, achieved by directly importing the format 
of the original scanner data. Unfortunately, Riegl’s format 
*.3dd is not supported for I/O by GeomagicStudio. So, 
for each scan, the topological information given by the 
raw data matrix was lost, the point cloud was not ordered 
anymore. 
With regard to ordered point clouds, some advan 
tages compared to unordered point clouds arise: Due to 
the implicitly stored topology, nearly all operations on 
the point cloud can be performed much faster, and the 
quality of the results improve (e.g. noise reduction or 
triangulation). Furthermore, GeomagicStudio provides 
a “select best data” operation, which selects the points 
from the “best” scan in overlapping areas, based on the 
angle between laser beam and (estimated) surface normal. 
However, this example - as mentioned above - is restricted 
to unordered point clouds. 
Within GeomagicStudio the modelling process is 
subdivided into 3 main phases: point phase (editing of 
the point cloud), polygon phase (computing and editing 
of the triangulation), shape phase (creating and editing of 
the patches used to generate NURBS). Each one will be 
treated in the following. 
In the first step (the Point Phase) a manual prepro-