CIPA 2003 XIX 11 ' International Symposium, 30 September - 04 October, 2003, Antalya, Turkey
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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-