be defined. The process has to restart with the next pixel 
of the orthoimage. In the present state of the software for 
orthoimage production this step is the most time con- 
suming and needs further optimization. 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
re Position in the Definition of the 
orthoimage: orthoimage 
F^ row, column 
Position on the 
Reference plane: Digital Surface Model 
X.Y 
Position on the Collinearity equations 
Digital Surface Model: and data of exterior 
X. Y,Z orientation 
yes 
Hidden pixel? 
no 
Metric position in the Planar Transformation 
distorted image: Parameters 
X. y 
Position in the 
digitized distorted image: Resampling 
row, column 
Gray value in the 
  
orthoimage: 
g(row, column) 
  
  
  
Fig. 6: Calculation cascade for each pixel 
of the orthoimage 
Using the collinearity equations, the transformed data of 
the exterior orientation and the data of the interior orien- 
tation of the distorted image the metric image coordinates 
in the distorted image are calculated. 
Planar transformations, like affine or projective ap- 
proaches, are usually used for the transformations be- 
tween the metric image coordinates and the matrix of the 
digital images. A meshwise transformation to be inte- 
grated in this calculation cascade is under development. 
The row and column of the point in the digital matrix of the 
distorted image is determined in sub-pixel accuracy. 
The grey value of the point is calculated by resampling 
techniques, like Nearest Neighbour or Bicubic Inter- 
polation, and transferred to its corresponding position in 
the digital image matrix of the orthoimage. In the example 
an improved Bilinear Interpolation has been used. For 
  
Fig. 7: Orthoimage (Scale 1:400) 
colour images only this final step has to be repeated for 
each band. 
Fig. 7 shows a digital orthoimage, derived from the image 
displayed in Fig. 1. This example clearly demonstrates the 
advantages compared to the classical approach (Fig. 2), 
but also the limitations of the new approach compared 
with the optimum solution. Fig. 8 shows an image, taken 
from long distance with a long focal length, which provides 
an impression of the product we would like to produce. 
The calculations have been carried out on a Silicon Gra- 
phics computer with 150 MHz and took about 4:30 min for 
the combined calculation of the DSM and the digital 
orthoimage. The resolution is 2.5 cm on the objects 
surface, the DSM and the orthoimage have 1100 . 2050 
grid elements. 
For white areas no DSM data are available, black pixels 
represent occluded areas. On the upper left part of the 
left tower, we see hidden areas and unsharp regions as a 
result of the extremely small angles between the surface 
of the object and the imaging rays. 
An other problem comes from object elements, which are 
not represented in the Digital Surface Model, like the 
608 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B5. Vienna 1996 
  
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