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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B5. Istanbul 2004
(5, x P) ev, (2)
Where
is the vector connecting the perspective centre to the
AUS em
A
first point along the object space line.
V: ids the vector connecting the perspective centre to the
second point along the object space line.
fp: is the vector connecting the perspective centre lo any
intermediate point along the image line.
Equation 2 incorporates the image coordinates of the
intermediate point, the exterior orientation parameters, the
interior parameters of the camera (which includes the distortion
parameters) as well as the object coordinates of the points
defining the object space line. The constraint in Equation 2 can
be written for each intermediate point along the line in the
imagery. One should note that this constraint will not introduce
any new parameters. The number of constraints is equal to the
number of measured intermediate points along the image line.
In summary, for a bundle adjustment with self-calibration using
straight lines, the end points (points 1 and 2 in the above
example) can be selected in any of the images where the
straight line appears. These points need not be identifiable or
even visible in other images. Four collinearity equations will be
written using the measured end points for each line. The
intermediate point(s) (e.g., point 3 in Figure 1) can be measured
in any one of the overlapping images. These intermediate points
need not be conjugate. A constraint is written for each
intermediate point according to Equation 2. A schematic
drawing to clarify the different scenarios for the end point
selection is shown in Figure 2. Figure 2a shows a case where
the end points of the straight line are selected in one image
(Image 1); while in Figure 2b, they are selected in different
images (Images 1 and 4). Intermediate points are shown in the
same figure.
1 , 1
To, a .
Image 1 Image 2 Image 1 Image 2
a" a” er a"
MSS
S. ~ X2
Image 3 Image 4 Image 3 Image 4
(a) (b)
e End points defining the line in object space
X Intermediate points
Figure 2. Schematic drawing representing two scenarios for the
selection of the end and intermediate points in
overlapping images
Once the calibration procedure has been carried out, the IOP of
the camera that are derived from two different calibration
sessions can be inspected for the purpose of stability analysis.
The methodology used in this research is a bundle coriparison
procedure that quantifies the degrec of similarity between
reconstructed bundles from two sets of IOP, (Habib et al,
2004).
Afterwards, the calibrated camera is used to capture convergent
images for the object to be constructed. Tie points are measured
in overlapping images and incorporated in a bundle adjustment
procedure. For this purpose, an arbitrary datum is chosen and
three-dimensional coordinates are determined with respect to
that datum. The datum for the calibration procedure is
established by fixing six coordinates of three points as well as a
few measured distances
The next section shows in detail a case study for the
reconstruction of a historical church. The conducted experiment
composed of two main parts. The first part is camera
calibration. This includes constructing the test field, capturing
convergent images, incorporating straight lines in bundle
adjustment procedure and stability analysis of the interior
orientation parameters. The second part is the 3D-
reconstruction of a historical church. This includes the capture
of convergent images, measuring of tie points and estimation of
their 3D-coordinates and finally incorporation of these
measurements in a CAD model.
4. EXPERIMENTAL RESULTS
4.1 Camera calibration
To perform calibration and stability analysis on a camera, a
specific detailed procedure is carried out. A two-dimensional
test field consisting of straight lines and points is used for
calibration. The lines are thin dark ropes that are stretched
between nails on the wall, and the points are in the form of
crosses that are signalized targets used as tie points in the
calibration procedure, Figure 3.
The datum for the calibration procedure is established by fixing
a certain number of points as control points that are distributed
in a specific way. To establish a datum, the origin, orientation
and scale need to be fixed. The fixed coordinates of three points
are shown in Figure 3. By fixing the X, Y and Z coordinates of
point El, the origin is established. By fixing the Y and Z
coordinates of points El and E7 as well as the Y coordinate of
point A4, the orientation is established. Finally, the scale is
established by incorporating a distance measurement between
any two points.
Figure 3. Calibration test field with 20 lines and 21 points
For the conducted camera calibration experiments, a total of
seventy two images have been acquired in four different
sessions. Each session contains eighteen converging and
