ISPRS Commission III, Vol.34, Part 3A „Photogrammetric Computer Vision“, Graz, 2002
Figure 4: Illustration how to determine relative orientation
of an image pair using pois.
Figure 5: If one corresponding point is given the second
camera can only be shifted on the given ray.
POIs of different category are indicated by different color.
As can be seen the POIs are very resistant to affine trans-
formation, thus a great fraction of POIs keeps unchanged.
The relative orientation of a camera has 5 degrees of free-
dom - three for the rotation and two for the pose direc-
tion. We assuming that two adjacent images view the same
plane to some extent. If we extract two vanishing points
belonging to a plane, the rotation of the camera relative to
this plane is determined. Furthermore the corresponding
vanishing points (derived from the same physical plane)
of adjacent images give use the relative rotation between
the cameras. The estimation of the rotation angles be-
tween the physical plane and both cameras are described
in Kraus [6]. In our approach the remaining 2 degrees of
freedom for the base direction are found by searching for
one corresponding point.
This correspondence is obtained by testing a qualified set
of possible POI pairs. For each potential pair the support is
measured using an image based method and the pair with
the maximum support is selected. The position of the left
camera is fixed at an arbitrary position. Furthermore the
rotation of the left camera is used to determine a plane,
on which the POIs of the left image are projected as it is
shown in Figure 4. A correct point pair is found by sam-
pling through all possible combinations. If one potential
corresponding point pair is assigned, the position of the
second camera can only be shifted on the ray that goes
through the corresponding 3D point on the plane, the cam-
era center and the corresponding point in the right image
plane. In Figure 4 this ray is indicated by the black contin-
uous line.
If the right image is shifted along the corresponding ray the
3D points on the determined plane are projected on varying
positions on the right image plane. If we add the constraint
that the distance of a 3D point to the left and right camera
centers only differs to a certain extend, each projected 3D
point lies on a bounded line which is projected into the
right image and is shown in Figure 5. To calculate the
support for a POI pair we are using an additional image
with reduced resolution where the POIs of the right image
are plotted. For each entry a special bit according to its
category is set within the region around the POI. Therefore
the support for a given correspondence can be determined
with low calculation cost. The support is increased for each
line that crosses a region of the same category.
Once the best corresponding points are found, the right
camera has still one degree of freedom as described above.
The final position is found by shifting the camera on the
corresponding ray until the support is maximized.
The maximum support has to be greater than a special
threshold to assign the images to be adjacent. For all im-
age pairs which are assigned to be adjacent the correspond-
ing points are determined for later use. A POI pair is as-
signed to be a corresponding point if the corresponding ray
crosses a suitable region in the additional image plane.
The average calculation time for the mentioned steps on a
Pentium 4 with 1800 MHz is below three seconds. There-
fore it is possible to automatically find adjacent images
within a large set. Although this step requires O(n?) com-
putation time if no other information is available. Such
additional information is provided either by a GPS or INS
based position estimation or by simple using the informa-
tion of adjacent images from the acquisition step.
3.3 Relative Orientation of Image Sequences
So far we have determined the orientation of image pairs
and corresponding points of adjacent images. In order to
calculate the orientation of a continuous sequence we per-
form the following steps:
1. Without loss of generality, the corresponding points
and the relative orientation of the first image pair is
used to calculate 3D points, assuming a fixed base-
line.
2. An adjacent image is added to the sequence. The rota-
tion is obtained from the vanishing points as described
before. To determine the position a cost function is
minimized that sum up the reprojection errors of suit-
able 3D points. Suitable means that there exist cor-
respondences between a POI in the new image and
those POIs that led to the 3D point.
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