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.