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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B5. Istanbul 2004
they do not have to be precisely measured in the test field.
Instead, we can incorporate the knowledge that a straight line in
the object space is imaged as a straight line in the image space
in the absence of distortion. Therefore, deviations from
straightness in the image space can be modelled and attributed
to distortion parameters in a near continuous way (limited to the
pixel size) along the straight line (Habib et al., 2004).
In summary, utilizing linear features instead of, or in addition
to, distinct points in photogrammetry is motivated by the
following reasons:
» Linear features are easier to extract than distinct points,
especially in a digital environment. Pixels along a linear
feature (or edge pixels) have discontinuity in one direction,
while a distinct point has discontinuities in all directions.
= [n the absence of distortion, straight lines in the object space
appear as straight lines in the image space. Therefore any
deviation from straightness can be attributed to various
distortions that can be modelled using the distortion
parameters.
= [Linear features can be automatically extracted with sub-pixel
accuracy.
» As far as camera calibration is concerned, it is much easier
to establish a test field comprised of straight lines rather than
establishing a traditional test field with numerous ground
control points.
There are a number of approaches for utilizing linear features
for camera calibration. Brown (1971) introduced the plumb-line
method that uses straight lines to derive radial and decentric
lens distortions. The principle behind this method is that
straight lines in object space should project through a perfect
lens as a straight line image. Any variations from straightness in
the image space are attributed to radial and decentric
distortions. This method offers a rapid and practical procedure
for computing lens distortion parameters. However, the results
would be contaminated by uncorrected systematic errors in the
comparator and uncompensated film deformations. Moreover,
we still need to perform a separate calibration procedure for
determining the camera constant and other systematic
distortions such as affine deformations.
Heuvel (1999b) proposed another approach for using straight
lines to recover the Interior Orientation Parameters (IOP). This
method can only be applied whenever we have imagery
containing parallel and perpendicular lines. Similar to the
plumb-line method, the radial lens distortion is estimated first.
Then, the principal point coordinates and the focal length are
determined later.
Prior to incorporating straight lines in the bundle adjustment
procedure, a decision should be made regarding how they
would be represented in the image and object space. Within
most existing literature such as the work of (Mulawa and
Mikhail, 1988; Tommaselli and Lugnani, 1988; Habib, 1998;
Heuvel, 1999a; and Tommaselli and Poz, 1999), a straight line
in the object space is defined as an infinite line using minimal
representation with four degrees of freedom. Habib (1999)
proposed an alternative approach for representing object space
straight lines using two points (six-dimensional representation).
Uniqueness and singularities are the primary reasons for
choosing this representation. Since minimal representations of
object space lines as an infinite one have singularities, they
would not represent all three-dimensional lines in the object
space. In addition, such a representation would require
complicated algorithms for the perspective transformation
between the object and image space, which would make it
difficult to incorporate in existing bundle adjustment programs.
In this research, we use two points to represent straight lines in
object space, as suggested by Habib (1999). Thus, object space
line segments would be well localized. On the other hand,
image space lines will be represented as a sequence of 2-D
points. This representation would allow us to incorporate
various distortions at each point along the line.
As a result, using straight lines in camera calibration can ensure
accurate estimation of the IOP. After finishing camera
calibration, the 3D-construction process of the object under
study can be started. The three-dimensional coordinates of
points, which are required to reconstruct the object, are
measured in overlapping images and incorporated in a bundle
adjustment procedure. The final step is modelling, where the
three-dimensional coordinates produced by photogrammetry are
launched in a CAD system. In this study, AutoCAD was used to
reconstruct the 3D model. Once structural information is
provided for the model, AutoCAD can handle geometric,
topologic and even semantic information. Moreover, texture
and material information can be handled, where rendering and
lighting can be used to make the model more representative to
the real object under study.
In summary, the reconstruction of 3D-historical sites requires a
high accuracy measuring device, affordable cost of the imaging
device and capable CAD system. According to these
requirements, this paper proposes a low-cost 3D modelling
procedure and is organized as follows. Review of the role of
photogrammetry, and in particular the advent of digital
photogrammetry, on the documentation of cultural heritage is
described in Section 2. An overview of the suggested
mathematical model for incorporating straight lines in a bundle
adjustment with self-calibration is described in Section 3. A
case study to evaluate the efficiency of the suggested approach
is demonstrated in Section 4. Finally, concluding remarks and
possible extensions are presented in Section 5.
2. THE ROLE OF PHOTOGRAMMETRY IN
PRESERVING CULTURAL HERITAGE
Natural threats to heritage include earthquakes, landslides,
flood, storms, fires and avalanches, while cultural threats
include war and industrial pollutions. Fire has destroyed more
world heritage sites than all other natural threats (Dallas et al.,
1995). If cultural sites are to be preserved for future
generations, highly detailed records are essential as an
insurance against their destruction by natural and cultural
catastrophes (Chong et al., 2002).
Photogrammetry has been applied to the planning, recording,
reconstruction, and revitalization of world heritage sites. With
the advent of digital photogrammetry and image processing
technology, photogrammetric recording of world heritage sites
has rapidly increased. Working in a digital environment allows
flexibility in the choice of computer hardware and software and
enables non-photogrammetrists to produce accurate data for
recording purposes. Digital object enhancement and 3D-
modelling techniques are also possible and usually give clear
presentation. of heritage sites. They considerably enhance
recognition of construction material, shape and area, and their
