CIPA 2003 XIX th International Symposium, 30 September - 04 October, 2003, Antalya, Turkey
The number of profiles, which are extracted depends on the
resolution of the 3D-scanner and the size of the sherd. Ex
periments have shown that 12 extracted profiles have the
best ratio between performance and accuracy. In Figure 7
four multiple intersecting planes e* are shown as light gray
rectangles aligned along the rotational axis. The rotational
axis is shown as vertical black line starting at the point
of origin. The gray object is the 3D-model of the sherd
and the black lines around this model are the intersection
between the sherd and the planes e*, representing multiple
profile lines profileInstead of estimating the distance d for
Figure 7: Sample of intersecting planes e*
each vertex to an intersecting plane e*, the sherd is rotated
so that the intersecting plane is the xz-plane. Afterwards
the y-coordinate is the distance d to the intersecting plane.
Experiments have shown that the rotation is ten times faster
than using the Hessian normal form, because a single ma
trix multiplication for the rotation is done faster than a loop
of multiplications and additions with MAT LAB.
The sherd has to be rotated 12 times by 7* (see Equation 4).
= max{C v {6)) — min(C v (9)) ien=u (4)
n
As the rotational axis is identical to the 2-axis the rotation
is done by using R z (7). This rotation positions the sherd
so that the intersecting plane ei is the x2-plane. After this
rotation the distance for every vertex at every intersection
is equal to the y-coordinate of each vertex. After every
rotation a profile line is extracted and the arc length is es
timated. Afterwards the arc length is estimated and the
profile with the longest arc length is selected.
flat. The y-axis in both figures shows the radius in cm and
the x-axis shows the height in cm. For the evaluation of
(a)
(b)
Figure 8: (a) Multiple profile lines using a correct esti
mated rotational axis (b) Multiple profile lines using an in
correct rotational axis
the registration the minimum and maximum radius of each
profile is estimated in addition to the registration error de
fined in (Sablatnig and Kampel, 2002). In case of pottery
the radius is measured as the orthogonal distance between
the rotational axis and a point of the sherd. The difference
between the minimum and maximum radius is the thick
ness of the sherd. As the range of the thickness of a sherd
is known a priori, a lower threshold (e.g. 0.5 cm) and an
upper threshold (e.g. 2 cm) can be set. These two thresh
olds depend on the material used and the manufacturing
process and are given by archaeologists. The radius and
the standard deviation of the mean radius of the profiles
from Figure 8a and Figure 8b are shown in Figure 9a and
Figure 9b. The x-axis in Figure 9 shows the elevation 0
in degree and the y-axis the z-normalized diameter in cen
timeter.
(a) (b)
Figure 9: Maximum, mean and minimum radius.
3.1 Reconstruction of the Pot
3 EXPERIMENTS
For evaluation of the estimation of the rotational axis the
mean diameter for each profile is estimated. If the stan
dard deviation of these mean diameters exceeds a certain
threshold given by archaeologists (i.e. 0.5 cm) the estima
tion of the rotational axis was not correct. Extracted mul
tiple profiles based on a correct estimated rotational axis
are shown in Figure 8a. The multiple profile lines have
similar shape and position with respect to variations of the
surface and the breakage. In Figure 8b the rotational axis
was not estimated correctly, because the fragment was to
For the reconstruction the vertices p pro fii e , which define
the longest profile line, are copied n times. Each copy
p p r 0 fi( e of the vertices of the longest profile is rotated,
using R z (n*7r/180). The faces of the reconstructed object
are estimated by connecting each point p m with its neigh
bors to quadrangular mesh. Quadrangles have been cho
sen, because of the arrangement of the neighboring points
to each other:
Let k be the number of vertices of the profile line, than the
indices of the neighbors of p m are: m + 1, m + k and
m + k + 1.
