Bas, Hüseyin Gazi
A MATHEMATICAL MODEL FOR CORRECTING THE PHOTOGRAPHIC COORDINATES
DUE TO ORIENTATION ERRORS (AN APPLICATION IN CLOSE RANGE PHOTOGRAMMETRY)
Hüseyin Gazi BAS
University of Sakarya
Engineering Faculty
Department of Civil Engineering
Sakarya- TÜRKIYE
Working Group V
KEY WORDS: Photographic Coordinates, Orientation Errors, Close Range Photogrammetry
ABSTRACT
Photographic coordinates x and y are fundamental data in analytical photogrammetry. At the
same time these coordinates are functions of interior and exterior orientation elements, and
contain some errors. Therefore some corrections and reductions are applied to the image
coordinates measured in comparators before they are used in mathematical models. Some
corrections and reductions related to the physical error sources inherent in photogrammetric
system are applied to the comparator coordinates, but any correction related to the exterior
orientation elements is not applied to these coordinates. In this study, a mathematical model has
been proposed to correct the photographic coordinates due to the small errors of exterior
orientation elements of camera. The data obtained a close-range test field have been used in the
offered mathematical model and the results have been criticized.
1 INTRODUCTION
There are two different techniques in restituting a photograph or photographic pair in
photogrammetry. The first one is analog method which produces plain, profils or contour maps.
The standart outputs of analog restitution method are in grafical form. Th second one is analytical
or numerical method which depends on the analytical reconstruction of the bundles of rays and of
the stereomodels. In analytical method the main data used in mathematical models are image
coordinates obtained from comparators or digital plotters. These coordinates which called as “raw
data” at the beginning, are functions of interior and exterior orientation elements. Therefore, every
errors in these orientation elements will affect the image coordinates, and these errors will
indirectly reflect to the object space coordinates. In this case, it is apperent that some corrections
related with small errors in interior and exterior orientation elements must be applied to the image
coordinates which will be used in mathematical models. Image coordinates must be especially
corrected due to the small orientation errors for some photogrammetric applications which all of
orientation elements or some of them are a priori known and are assumed errorless (Bas, 1985;
Veress and Sun, 1978; Brandenberger and Erez, 1972); or for photogrammetric applications in
which photos are taken from the same exposure station and are reconstructed with the same
interior and exterior orientation parameters (Dauphin and Torlegard, 1977; Altan 1993).
The aim of this study is to offer a mathematical model and its application in close-range
photogrammetry to correct the image coordinates due to small orientation elements after
transforming the comparator coordinates to the photographic coordinate system.
2 REFINEMENT OF MEASURED IMAGE COORDINATES
2.1 Corrections For Systematic Errors
38 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B5. Amsterdam 2000.
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