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# Full text

Title
New perspectives to save cultural heritage
Author
Altan, M. Orhan

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 indices of the nearest vertices Pd These faces fd 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).