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New perspectives to save cultural heritage
Altan, M. Orhan

CIP A 2003 XIX th International Symposium, 30 September - 04 October, 2003, Antalya, Turkey
distance between the perspective centre and the photographed
object point is measured, the spatial position of each pixel
can be computed in the ^r| C, image reference system (see
Fig. 1 and (1) and (2) equations):
0 = arctan—
£ 0 = d - cosa • send
r] a = d ■ send (2)
C Q =d- cosa-cos0
where r|j are the image coordinates of the current pixel of
the image, 0 and a are the two angles that define the direction
in the space, d is the distance value between the centre of the
perspective and the object point, £o, r|o and Q) are the 3D
coordinates of the object point.
The distance values are stored in an additional matrix that has
the same size as the RGB ones (in terms of rows and
columns). Therefore a “solid image” consists of a 4 level
matrix: RGB and distances d (see Fig. 2).
Distances of the object points are obtained from a dense 3D
model (DDEM), easily acquired by a laser scanner. To
calculate these distances, the laser scanning and the photo
should be taken from two points close each other, in order to
reduce the number of pixels that are not visible from the
scanner (hidden areas) and therefore not determined in their
3D position.
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Figure 2. Structure of the solid image
If the external orientation parameters (X 0 ,Y 0 ,Z 0 , CD, (]), k) are
also known, it is easy to transform the 3D image co-ordinates
into the absolute system XYZ, by a simple roto-translation.
2.2 Image calibration
In order to fill the matrix "d" with a correct value of the
distance to every object point, it is necessary to calibrate the
image. The calibration process consists of the estimation of
the internal orientation parameters of the camera. In
architectural surveys, often cameras are not metric. In this
case, the lens distortion parameters have to be determined.
This can be achieved by measuring the image coordinates for
a sufficient number of points, the object coordinates of which
are known (control points). The procedure can be completely
automatic if a laser scanner is used for this purpose.
Some reflecting targets are placed on the object. The laser
scanner is able to measure, in addition to the 3D point
positions, the reflectivity of the object. Special reflecting
targets (markers) have the property to almost totally reflect
the laser pulse, while natural points do not do the same. If the
marker size and their mean reflectivity are known, it is easy
to determine the marker’s position in the laser DDEM and in
the image, in a completely automatic way. Once the marker’s
position is defined, one can estimate the calibration
parameters of the camera and its external orientation by using
a classic bundle solution.
2.3 Projection of the cloud of points
If the internal and external image orientation parameters are
known, it is possible to project the DDEM (“cloud of points”)
onto the digital image. The mathematical model used for this
operation is the central perspective model. The radial
distortion components At, and At] the are added to the
collinearity equations:
£ ~£o + AÇ-c
r l =T 1o + Arj-c
r u {X yY 0 ) + r 2l (T y Q ) + r 3l (Z Z 0 )
r l3 {X-X 0 )+r 2i {Y-Y 0 ) + r i3 {Z-Z 0 )
r l2 {X-X 0 ) + r 22 (Y-Y 0 ) + r 32 (Z-Z 0 )
r l3 (X-X 0 ) + r 23 (Y-Y 0 )+r„(Z-Z 0 )
The distortion components are modelled by:
A£ = ($-0-( Vp 2 +Vp 4 +Vp 6 )
Ari=(ri-ri 0 )-(k x -p 2 +k 2 -p 4 +k 3 -p 6 )
where‘if) is the distance from the centre of the image (radius)
and ki, k 2 and k 3 are the radial distortion coefficients. Other
types of distortion have not been considered.
2.4 Interpolation of the distance matrix
The density of the pixels in the digital image is usually
greater than the density of the cloud of points obtained by the
laser scanner device. For this reason, when the laser points
are projected onto the digital image, the distance matrix is not
completely filled in every element: the values of distance are
associated only to some pixels.
In order to fill the distance matrix it is necessary to integrate
the missing values with an interpolation procedure.
Figure 3. Interpolation of the distance matrix
The “average weighed method” has been used. The four
nearest pixels, which the value of distance is known, are
considered (see Fig. 3).