OBJECT RECONSTRUCTION WITHOUT INTERIOR ORIENTATION
J.Shan
Department of Geodetic Science, Stuttgart University
Keplerstrasse 11, D-70174 Stuttgart, Germany
Commission III, Working Group 2
KEY WORDS: Algorithms, Reconstruction, Geometry, Vision, Photogrammetry, Vision Sciences
ABSTRACT:
This paper develops an algorithm for linear object reconstruction without interior orientation. First we introduce
the Thompson and Longuet-Higgins equation as well as the fundamental matrix. After defining the affine model,
we show that some of its components can be linearly withdrawn from the fundamental matrix, which in turn is
linearly determined up to a scale factor by minimum eight image correspondences. This decomposition of the
fundamental matrix leads to a full use of the information within a stereo. Unlike the well-known DLT algorithm
where minimum six known points are required on each image of a stereo, our algorithm requires that only four
of them appear on the other one. In addition to the fully compatible accuracy with the DLT algorithm, tests
with an aerial stereo show the robustness of this algorithm as well.
1. MOTIVATIONS
For quite a long time it seemed to be a rule that the
interior orientation has to be completed before any
other photogrammetric computation is done. This
was overthrown by the time the well-known DLT (Di-
rect Linear Transformation) algorithm was publisched
by Abdel-Aziz and Karara in 1971 (c.f, Slama, 1980,
pp.801-803). It directly relates the object point to
its oblique image coordinates. This problem seems
to be fully solved if we neglect the drawbacks of the
DLT algorithm. In fact it recovers an object directly
from its images rather than from its photogrammetric
model, therefore, the inherent information behind the
stereo is not fully utilized. Moreover, it requires at
least siz known points on each of the images to re-
construct the object. Keeping those issues in mind,
the question arises that, how could we reconstruct an
object without knowledge of interior orientation by
fully employing the information behind a stereo ?
Our motivation also has its deep root in computer
vision and close-range photogrammetry, where un-
calibrated camera is widely adopted and the interior
elements are either unknown or different from image
to image.
Linear solution always benefits a lot, especially in
computer vision and close-range photogrammetry,
where finding reasonable initial values is crucial to
the success of iterative algorithms.
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International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
Regarding to these backgrounds, our purpose is to find
a linear solution for object reconstruction without in-
terior orientation, which can fully use the information
behind a stereo and has less requirement on known
points than the DLT algorithm.
2. REVIEW OF THE RELATED WORK
AND OUR SCOPE
As our topic falls both in photogrammetry and com-
puter vision, the related work in both areas should
be mentioned. Photogrammetrists seem to rely much
on the DLT algorithm and hence on sufficient number
of known object points. In contrast, besides paying
interests in camera calibration, scientists in computer
vision area have fully studied the problem ” motion
or relative displacement estimation from uncalibrated
camera”. Most recently, quite a few literatures are
focused on this issue. They claimed that without in-
terior elements the object can be reconstructed up
to either an affine or a perspective transformation
(Faugeras, 1992; Hartley, 1992; Hartley, et al, 1992).
Obviously this is of fundamental importance for object
reconstruction without interior orientation ( Faugeras,
1993; Hartley, et al, 1993).
A linear solution for model reconstruction may date
back to the well-known contribution of Longuet-
Higgins (1981) in computer vision. However, the
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