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a 01 02 WS WS dE 65 Vo 
  
  
  
Figure 2. The errors in the corner points of a rectangle 
as a function of the slope 
6. INFLUENCE OF A NOISE 
On the scattering of the coordinates of the objects also 
influences a noise. If an image is represented as the poisson 
random point field, the variance in the coordinates x,, y, of the 
centroid and in the side a of a rectangle is equal (Bakut, 
Troitsky, and Ustinov, 1976) 
D* = 2 a 
n, (r = 1) 
for the angle orientation ¢ = 0° , where r is the ratio signal / 
background ( r >> 1), n, is the average value of signal points 
located within a rectangle. 
Depending on the angle of orientation and the ratio of the sides 
of a rectangle, the sides length, and the ratio signal/background, 
the variance D* can be either less or more then corresponding 
variance D that conditioned by the effect of digitization. 
7. SOME APPLICATIONS OF THE RESULTS 
The derived results let us to minimize geometrical errors of 
aerial pictures scanning for photogrammetry and the other 
applications by means of optimum orientation of the lines of 
scanning or the objects. Such approach can be used to select the 
templates with optimal angle of the orientation in stereo 
matching and other registration problems for mapping (see, for 
example, Erosh and Zolotar, 1999). The estimations of the 
errors can be also used to define more exactly a distance 
between the objects, their dimensions, shape and geometrical 
features such as area, perimeter (Pisarevsky et al., 1988), shape- 
factors (Warl, 1983). The other fields of theirs application are 
the objects reconstruction, for example, the straight lines and 
buildings reconstruction in 3-D (Suveg and Vosselman, 2002), 
the man-made objects detection (the roads and their 
intersections (Lu et al, 2002), the buildings, means of transport, 
etc.), synthesis of the images, computer graphics, and so on. 
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B1. Istanbul 2004 
8. CONCLUSION 
The results of this paper enable to minimize geometrical errors 
of aerospace pictures scanning for photogrammetry and the 
other applications. The derived results can be spread to the 
objects with non-mutually perpendicular boundary segments 
and the other grids (rectangular, hexagonal, etc.). It allows us to 
extend the sphere of applications of the results on arbitrary 
objects in aerial and other images. 
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