A SOLUTION FOR THE GENERAL CASE OF THE THREE-IMAGE ORIENTATION 
Alice Pozzoli, Luigi Mussio, Marco Scaioni 
Politecnico di Milano, Dept. LI.A.R., P.za Leonardo da Vinci, 32 - 20133 Milano, Italy 
e-mail: {alice.pozzoli, luigi.mussio, marco.scaioni}@polimi.it 
Commission III, WG I11/1 
KEY WORDS: Photogrammetry, Orientation, Adjustement, Precision, Accuracy, Reliability, Vision, Education 
ABSTRACT: 
In an easy solution for three - image orientation, each model coming from two images of a triplet is analyzed and the relative 
orientation between them computed, by using an exhaustive research of preliminary values of its parameters. This non-conventional 
approach supplies the orientation of two images, taking into account a priori information among four base solutions. The automatic 
procedure of orientation wants to skip the manual assessment by using three images, which would allow to solve for the ambiguous 
solutions. Once each model has been relatively registered, the absolute orientation is computed by using a linear parameterization of 
this problem. 
1. INTRODUCTION 
1.1 Orientation procedures in photogrammetry 
Orientation procedures play a fundamental role in the object 
reconstruction process of photogrammetry. Traditionally, the 
call for stereo-vision leaded to setup a geometric solution based 
on interior and relative orientations, which are the pre-requisite 
for any further task to extract information from a pair of images. 
The former refers to the determination of 3 intrinsic parameters 
(principal distance and coordinates of principal point in the 
camera reference system), the latter to the computation of the 
baseline vector linking two perspective centres and relative 
rotation of one image with respect to the other; the number of 
unknown parameters adds up to 5, which usually follow one of 
two geometric model, namely the symmetric and asymmetric 
one. By introducing the knowledge of ground information (e.g. 
GCPs) the absolute orientation can be computed and the model 
computed from relative orientation can be transformed into the 
real world, or to a scaled representation of this such a 
topographic map. Research on this topic has been attracting the 
interest of photogrammetrists in the first mid of 20" century 
(Finsterwalder, 1899; Fourcade, 1926; Kruppa, 1913). 
From the 50's to 70's, mathematical fundamentals of analytical 
photogrammetry were established. New formulations of two- 
image orientation were published (Semple & Kneebone, 1952; 
Thompson, 1959; Stefanovic, 1973), while the unexplored field 
of aerial triangulation began to be dealt with (Schmid, 1954; 
Schut, 1955-56). 
Two topic aspects have to be focused concerning orientation 
procedures in photogrammetry up the so called "analytical era": 
e the use of analogue imagery and of purely manual 
measurement for orientation purposes, resulting in the use 
of a small set of accurate points for computing relative 
and absolute orientation; this fact limits the problem of 
blunders to a small number of gross errors (due to wrong 
labelling, image content misunderstanding and the like) 
and to a low fraction of small errors. 
e orientation problems such as formulated in 
photogrammetry are non-linear and they are usually 
902 
solved by a Least Squares approach, after a linearization 
of equations. In this way, L.S. adjustments can run 
automatically and more refined treatments (e.g. robust 
procedures and re-weighted L.S.) can be performed, step 
by step, always solving linear systems. It is obvious that 
all methods can start only if the preliminary values of the 
unknown parameters are known. Aerial blocks feature 
regular shapes, so that approximations may be easily 
derived, because the project for data acquisition define 
these parameters with a sufficient accuracy, or auxiliary 
measurements are available at the time of data acquisition. 
But also close-range blocks, up to 70's show 
configurations, which are very similar to those of aerial 
photogrammetry, offering the same possibility to solve for 
approximations. 
These statements will result fundamental to comprehend the 
changes introduced in photogrammetric orientation approaches 
in the following decades. 
Since the 80's a new challenge defied the community of 
photogrammetrists, given by the possibility of managing and 
processing digital images by computers. Whether the concept of 
a totally digital stereo-plotter (Sarjakoski, 1981) became in few 
years a reality, on the other hand automation of all analytical 
orientation procedures was the topic research issue up to the 
end of 1900 (for a review see Heipke, 1997). 
1.2 Photogrammetry meets Machine Vision 
The development of digital photogrammetry is parallel to that 
of machine and robot vision techniques. Here the problem of 
object reconstruction is needed for specialized and real-time 
purposes, such as object recognition, production and quality 
control, vehicle and robot guidance an so on, not for deriving 
cartography of however a wider description of the space. This 
fact limits the number of digital sensors to be used to the 
minimum: in case of objects lying in a plane, a single image, in 
case of 3D object a two-image configuration will be adopted, 
tuning the interest on relative orientation procedure. For this 
reason, many algorithms have been developed to cope with this 
task, keeping into account the possibility of solving for any 
geometric configuration (no approximation needed) and the use 
    
   
  
    
  
    
  
    
  
   
   
  
  
  
   
    
    
     
    
   
   
   
   
    
   
    
   
   
    
   
   
   
    
   
    
   
   
   
    
   
   
    
    
    
   
   
   
   
   
   
      
  
   
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