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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B6. Istanbul 2004
Figure 2. DTM-grid with two cameras above.
To visualize the camera a square image frame was shown, and
the corners of the square were connected with the projection
center of the camera. Adding a second camera was simple, so
this was done as well. Also the vertical projection of the DTM-
grid onto a horizontal plane is shown. A typical graph obtained
with this sheet is shown in figure 2.
The resolution is better than shown here, but the shape of the
"deformed" grid in the images did not show up well enough. To
show this in a better way, separate graphics were created for
each image to show the "image" itself with good resolution.
Now however, the coordinates of the image points had also to
be calculated in the image coordinate system.
Figure 3. “image” graphic of a DTM-grid.
No attempt was made to limit the drawing of the image to the
inside of the image frame or in any other way.
This gives rather strange situations in extreme cases, as
mathematically the image plane is unlimited and image points
are calculated as the intersection of a straight line — defined by
the object point and the projection center — with the image
plane. There is a critical plane, which is parallel to the image
plane and passes through the projection center. Object points in
this plane are theoretically imaged infinitely far away,
practically a “Division by zero” error happens and they will be
imaged to position (0, 0). Points just a little in front of this
plane will be imaged very far away to one side, while points
just behind it will be far away to the other side. A perhaps short
joining line of two such points (on either side of the critical
plane) can thus result in a very long image line!
Figure 4. landscape with image 2 partly “outside”.
This only happens, if the critical plane passes through the object
area. The effect was considered rather curious than nasty, as
such extreme situations were not meant to be used. For more
"normal" situations the fact that part of the drawing is outside
the image frame can sometimes be considered illustrative for
the danger of errors in the coverage by errors in the camera
inclination.
Restitution
To demonstrate the effect of orientation errors on the geometry
of the restituted object another set of cameras. (restitution
cameras) was introduced. The differences between the
parameters of the restitution cameras and those of the original
cameras are kept as parameters in the parameter sheet, being the
"changes to the original parameters".
In a new calculation sheet the changed parameters were
calculated, then for each image point its location in the object
coordinate system was calculated using those changed
parameters of the camera.