and they reduce the quantity of the object space information mathematically
required.
(b) Constraints of the second group
These constraints are absorbed by the coplanarity and model connection con-
ditions, and they give thus no influences on the relationship between the
model and object spaces. However, these constraints cannot be introduced
regardless of those of the first group.
Based on these properties, the potential regarding the interior orienta-
tion of the system can be difined for constraints to be introduced.
The potential theory derived here is applicable to many photogrammetric
problems such as
. (3) The analysis of overlapped pictures for various special cases in pho-
togrammetry
For example, when one of a stereopair of photographs has known interi-
or orientation parameters, the coplanarity condition can provide seven
independent orientation elements (five exterior and two interior), be-
cause these five constraints belong to the first group. Accordingly,
the relationship between the model and object spaces can be described
in terms of 10 independent orientation unknowns (seven exterior and
three interior).
(i) The self calibration problem of non-metric cameras
Based on the potential theory, it can be explored how many interior
orientation unknowns can be determined under constraints to be intro-
duced into the system. Then, we can see what constraints must be
imposed for providing all the interior orientation parameters of the
used non-metric cameras without object space information. Further-
more, using plane mirrors, constraints among the interior orientation
parameters of the system can be given very easily.
REFERENCES
/1/ Abdel-Aziz, Y.I., Karara. H.M.: Direct Linear Transformation into Ob-
ject Space Coordinates in Close-Range Photogrammetry.
in Proceedings of the Symposium on Close-Range Photogrammetry,
University of Illinois, Urbana, Illinois, (1971), pp. 1-18.
/2/ Faig. W.: Calibration of Close-Range Photogrammetric Systems: Mathemat-
ical Formulation.
Photogrammetric Engineering and Remote Sensing, Vol. 41, No. 12,
(1975), pp. 1479-1486.
/3/ Kager, H., Kraus. K., Novak. K.: Entzerrung ohne Passpunkte.
Bildmessung und Luftbildwesen, Vol. 53, No. 2, (1985), pp. 43-53.
/4/ Koelbl. O.: Selbstkalibrierung von Aufnahmekammern.
Bildmessung und Luftbildwesen, Vol. 40, No. 1, (1972), pp. 31-37.
/5/ Moniwa. H.: The Concept of "Photo-Variant'" Self-Calibration and Its
Application in Block Adjustment with Bundles.
Photogrammetria, Vol. 36, No. 1, (1981), pp. 11-29.
/6/ Okamoto. A.: Orientation and Construction of Models, Part I: The Orien-
tation Problem in Close-Range Photogrammetry.
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