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€ Phétograph | 
  
Figure 2: The geometry of relative orientation. 
Additional notations used in Fig. 2: 
fi Focal length of photograph 1 
€, Focus of photograph 1 
01 FC of photograph 1 
$3, 6 Nearest points on Line 1, Line 2 to each other 
V3 A vector from t; to $4 
The geometry of relative orientation of this algorithm is shown 
in Fig. 2. To determine how two adjacent photographs of a 
common sight are relatively located and oriented, in terms of the 
coordinate system provided by photograph 0, the relative 
location and orientation of photograph 1, represented as a point- 
vector defined by point c, and vector e,-o;, is derived by the 
geometry shown in Fig. | through an invariant go and two 
variants s, and s, proposed initially by photograph 0. The 
correcting vectors vy and v4 (not shown here) are used to guess" 
closer coordinates of s, and s; to g; and g;, respectively. 
Ideally, the norms of v; and v, should be zeros, but we usually 
set a threshold, such as two- to five- pixel width length, to 
proceed. 
3. PATTERN RECOGNITION 
One of the two major topics to enable fast georeferencing images 
is pattern recognition of images. Although the author presents 
in this paper first with two generalized geometric 
photogrammetric algorithms since they are of the very 
fundamental enablers of photogrammetry, the most resource- 
consuming task lies in pattern recognition. Just as Celikoyan et 
al. (1999) pointed out that it takes a lot of time to match the 
continuous non-geometric items. It is of the most key 
techniques since we must first identify the common features of 
two different images of a common sight of interest, and the 
previously developed algorithms can then be used to calculate 
the relative orientations of a group of images. Only when this 
technique is developed can we finally design an eligible 
“automatic” digital photogrammetric system. 
   
  
  
   
  
    
   
  
  
  
  
  
  
    
   
  
   
  
  
   
   
  
   
   
  
  
   
   
   
   
   
   
    
  
   
   
  
    
  
  
  
  
  
   
   
   
  
   
   
   
   
   
  
   
  
  
    
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B1. Istanbul 2004 
3.1 Pattern matching and feature extraction 
Pattern matching techniques are mostly used to compress 
images by replacing several duplicated, or almost the same, 
patterns in one or a sequence of images, and their applications in 
this field are proved to be very effective. These techniques can 
also be used to extract a feature by recognizing the pattern and 
its geographical relationships with other features of the same 
image space. And the procedure is often called a "feature 
extraction", Lay et al. (2004) have shown a feature extraction 
method through the use of basic grid arithmetic, and this 
technique is also used in the proposed algorithm. 
^ 
Uu 
Un 
   
(a) (b) 
Figure 3: Pyramidal process and mapping of a regular raster 
space into a hexagonal space and an n-row regular 
space is tansited into a 2n-row hexagonal space. 
The transition is used as the first-step of pyramidal 
process in the algorithm. (a) Consecutive pyramidal 
processes of the algorithm. The first two steps are 
shown in this diagram. (b) Diagram of the mapping 
algorithm. 
Although the processes used in pattern matching and feature 
extraction are practically the same, they have a major difference 
in their basic ideas: pattern matching is intended to locate where 
there are patterns of as many as areas in images are, to their 
most extent and under acceptable errors, the same; whereas 
feature extraction used in photogrammtry application is 
intended to find where there are similar features, and most 
importantly, where they are going to differentiate? These minor 
differences are just as important as matched features are in 
photogrammetry . 
3.2 Hexagonal space 
Hexagonal spaces is adopted by the algorithm, and the reasons 
are listed below: 
— Distances from any hexagonal grid to its six adjacent 
neighbours are equal. 
— For small anges of rotation, images of hexagonal space 
have shown to have a better representation over 
regular square space (Tirunelveli et al., 2002). 
— Mapping from a regular raster space into a hexagonal 
space can easily be done by simple grid arithmetic (Fig. 
3). 
—  Hexagonal spaces provide six equally scaled profiles 
for use of pattern matching (Fig. 4).