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551 
THE ACCURACY OF CONTROL POINTS 
FOR CLOSE RANGE PHOTOGRAMMETRY 
DR. YOUSSEF I. ABDEL-AZIZ 
University of Petroleum and Minerals 
Dhahran, Saudi Arabia 
ABSTRACT 
Control points are needed in close-range photogrammetry for orientation 
the photographed object and for camera calibration. The intersection method 
by two theodolite is used for providing the photographed object with the 
necessary control points. The accuracy of these control points are very im- 
portant in estimating the accuracy of the photogrammetric measurements. 
This article gives the mathematical and the experimental proofs of newly 
developed formulas for estimating the accuracy of control points coordinates 
for any theodolite positions and the optimum theodolite positions that maxi- 
mize the accuracy of these control points. 
I. INTRODUCTION 
The three-dimensional coordinates of several targets, in close-range 
photogrammetry, are needed for i) providing the photographed object with the 
necessary ground controls and ii) constructing three dimensional ground con- 
trols test area for camera calibration purposes. Target marks are fixed on 
the position of the control points on the object. The horizontal and the ver- 
tical directions of these targets are measured from two theodolite stations. 
Target coordinates are calculated from the measured directions, the measured 
horizontal and the vertical distances between the two theodolites. The proce- 
dures of the measurements and the calculations are given in Abdel-Aziz (1), 
Abdel-Aziz-Karara (2), Faig (3), Malhotra-Karara (4), Tolegard (5) and many 
others. These investigators were interested only on the values of these co- 
ordinates and the values of the obtained accuracy. The expected accuracy, the 
formulas which express the accuracy of geodetic control points and the optimum 
position of the two theodolite station have not yet reported in neither 
photogrammetric nor surveying literature. 
The expected accuracy of the calculated coordinates, for a given object, 
is functions of the measurements errors and the position of the two theodo- 
lite stations relative to the object. The theodolite positions are defined by 
i) the horizontal distance (B) between the two theodolite stations, ii) the 
horizontal distance (D) between the object and the theodolite stations and 
iii), the theodolite elevation relative to the object E. At different values 
of B, D and E, the measurements errors have different effects on the accuracy 
of the calculated coordinates. There are specific values of B, D, and E which 
minimize the effect of the measurements errors on the calculated coordinates. 
These specific parameters of B, D and E are called the optimum base Bo, the 
optimum object distance Dg and the optimum elevation Eo. This article gives 
the values of the optimum base Bg, the optimum object distance Do and the 
  
Reports on studies supported by Saudi Arabian National Center for Science 
and Technology (SANCST) (Grant AR-052). 
1