Basis of the Orthoimage Generation Method 
Zygmunt Paszotta, Renata Jedryczka 
Chair of Photogrammetry and Remote Sensing 
Olsztyn University of Agriculture and Technology 
10-957 Olsztyn-Kortowo , 1 Oczapowskiego Street, Poland 
Commission lll, Working Group 2 
KEY WORDS: Generation, Orientation, DTM, Error, Image, Orthoimage, Aerial 
ABSTRACT 
The generation of digital orthoimage is a process whose full formal description is very difficult. In this paper we 
attempted to do it by the use of terms coming from the image processing. The transformations between various 
geometrical coordinate systems also need a formal description starting from the digital image coordinate system 
through image space and model system to local ground or object coordinate system. We outline the way of treating 
the aerial photographs and also the orthoimages as functions. 
We aim is to provide precise conditions of existence of the point in the orthoimage. The analysis of the reasons of the 
existing errors in computing the ground coordinates in DTM is made. After the orthoimage generation the analysis of 
the errors of the pixel position in the various parts of the image is discussed. 
1 INTRODUCTION 
The image of the terrain obtained after the scanning 
process of the aerial photograph has the features which 
we usually want to change; it can be the position of the 
observer, the size of the cartometric features and other 
geometric or radiometric characteristics of the image. It 
means that we want to have an image of the object in 
other projection than this in which its registration was 
done. The changes of the type of the transformation i.e. 
parameters of the projection should be made not only by 
changing the parameters of the camera or its position but 
also by suitable calculations done in the digital process of 
the image. 
When we consider an orthoimage it means we have to 
obtain an image not only in the orthogonal projection. 
We require also it to be an orthogonal projection on the 
plane parallel to XOY plane in the ground coordinate 
system and at the given (determined) scale. To generate 
this image we should first recreate the situation of the 
moment the image was taken. The central projection in 
which the photo was taken is determined explicitly by the 
positions of the projection plane and the projection 
centre. The connections between the position of the point 
(X, Y,Z) in the terrain and its projection position (x,y) in 
the image can be expressed analytically by the projective 
transformation and in the particular case by the 
collinearity equations of the form: 
844(X- X9) a45(Y - Yg)* a45(Z- Z9) 
  
  
X-X9g*^ k 
813(X- X9) £a53(Y - Yo) *a33(Z- Zo) (1) 
P 844(X- X9) a55 (Y - Yg) *ao4(Z- Zg) 
a454(X- Xo) *ao4(Y- Yo) *à34(Z- Zg) 
where: 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996 
e X,Y,Z ground coordinates of the point, 
e Xy,-c, image coordinates 
« X,,Y,,Z, coordinates of the projection centre 
e X, ,y, coordinates of the principle point of the 
image, 
e C, focal distance of the camera, 
* 8 ,,8, ,.,8, elements of the matrix of the 
cosine angles between axes of the ground 
coordinate 
system. 
We will not consider the particular case when two 
different points of terrain lie on the same projection ray 
(on the same line to which belongs the projection centre). 
Then to calculate position of the point in the object space 
(on the ground) on the basis of its image coordinates one 
coordinate in the object (ground) coordinate system is 
missing. If we know the function Z=Z(X,Y) i.e. the digital 
model of terrain (DTM), then from the image coordinates 
X,y we can calculate the object coordinates X, Y and then 
the position of the point X, Y,Z in any other projection can 
be also calculated. To generate orthoimages we should 
know not only the elements of the interior and absolute 
orientations of the photo but also the DTM. 
2 ORTHOIMAGE AS A FUNCTION 
In order to determine the position of the image point on 
the plane it is enough to give its two coordinates. Raster 
im s of the terrain can be described as functions from 
Euclidean R^. space to colour space C. In the space R* 
the coordinate image system x,y is defined. For the tonal 
photograph the section [0,1] can be assumed as a space 
C. For the colour photograph in the RGB palette, the 
cubic 
C - [0,1]x[0, 1]x[0, 1] (2) 
can be assumed as a space C. 
     
  
  
  
   
  
  
    
  
  
  
  
  
  
  
  
  
  
  
  
  
   
  
   
  
  
  
  
    
  
  
   
  
  
   
    
  
    
   
   
   
  
  
  
  
   
   
  
  
   
  
   
   
   
  
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