CIP A 2003 xix"' International Symposium, 30 September - 04 October, 2003, Antalya, Turkey 
Figure 4: Oriented sherd, rotational axis rot, intersecting 
plane et, longest profile line profi(e max , h max 
2.3 Estimation of the Profile Line 
For the extraction of the profile line all vertices that are 
connected by an edge of the face intersecting the plane e* 
are selected. Therefore the Hessian normal form ax 2 4- 
by 2 + cz 2 4- d — 0 is used to determine the distance d to 
the plane. The sign of the distance and the relative distance 
with respect to the maximum distance is used to reduce the 
number of vertices for the estimation of the profile line. 
Vertices with a d < 0 are located on the left side of the 
plane. Vertices with d > 0 are located on the right side. 
Every face consists of three or more vertices, where each 
pair of vertices describe an edge of the face (see figure 5). 
The pairs of vertices, with vertices on different sides of the 
intersecting plane e* are used to estimate the points of inter 
section of the edges and the intersecting plane ¿¿, because 
the vertices of the 3D-model need not be located on the e 
The result of connection of the points of intersection is the 
profile line. 
Figure 5: Vertices p d<0 .oi left (light gray) and right (dark 
gray) of the intersecting plane, edges edge intersect , vertices of 
the profile line p inUrsect (black). 
• First the relative distance (shown in Figure 6 as gray - 
value) with respect to the maximum distance between 
the vertices and the rrz-plane is estimated. Experi 
ments have shown that vertices with a distance larger 
than 1% can not be used for the estimation of the pro 
file line, because the edges, they belong to do not in 
tersect ¿¿. This threshold depends on the resolution 
of the 3D-scanner and can be adjusted, when another 
resolution is used. 
• In the next step the faces fd<o.oi, which contain the 
indices of the nearest vertices Pd<o.oi are selected. 
These faces fd<o.oi are split into edges, for estima 
tion of the vertices of the profile line: A / = {i, j, k} 
connects the vertices p,;, pj and p*., so the edges 
of the face / are described by edge = {(z, j), (j, k), 
(k,i)}. Each of these vertices can have a positive or a 
negative sign, which corresponds to the position with 
respect to intersecting plane. A vertex with a negative 
sign is located on the left side and a vertex with a pos 
itive sign is located on the right side of the plane. So 
the edges e dge intcrscct , which intersect the plane e* must 
contain one vertex with a negative sign and one with a 
positive sign. The points from those edges 
pintersect are selected and the parameters of the line de 
scribing these edges ¿dge. ntersect are estimated. With 
these parameters the point of intersection \> unmeet be 
tween the line and the intersecting plane (equal to the 
xz-plane) is estimated. These points pintersect are con 
nected with their nearest neighbor. They define the 
profile line profile. 
• All vertices Pimersea of the profile have the distance 
y = 0 to the intersecting xz-plane. The ^-coordinate 
is the distance (radius r) to the rotational axis rot and 
the z-coordinate is the height h (see Equation 3). 
profile = {..., (xi, 0, Zj) T ,...} —> {..., (r*, hi) T ,...} (3) 
Figure 6: Oriented sherd and intersecting plane ej. The 
level of gray of the surface of the sherd corresponds to the 
distance of its vertices p to e*. Lighter means nearer. 
2.4 Longest profile line 
For classification and reconstruction only the longest pro 
file line is used. In this procedure multiple profile lines are 
extracted and the longest is selected for further processing. 
All profile lines are used to evaluate the estimation of the 
rotational axis and the registration of the inner and outer 
view (see Section 3).