James Olaleye 
  
position vectors (figure 1). This vector space conceptualization enables the use of vector symbology and linear algebra 
to develop compact computational algorithms for the reduction process. 
Although the theoretical bases of the mathematical formulations used in the treatment of a stereogram are well known 
and in fact vector notations have been used to present them, nevertheless, the computational schemes often adopted are 
based on long hand approach in which symbols are used to represent single variables, involving tedious algebraic 
manipulation. This inevitably leads to complicated computational procedures, a devoid of clear geometric meaning 
and insightful appeal. This paper applies the ARDOVS concept [Olaleye 1992], an analytical tool, to the solution of 
the stereogram problem. It is shown how this methodology provides a compact and consistent solution scheme which 
is easy to understand and general application. 
  
  
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Figure 1: Image vector spaces (a) left image space (b) right image space 
  
  
  
  
  
  
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To begin with, the term "ARDOVS" is an acronym for "Apparent and Real Directions of Vector Spaces" and states 
that to every photogrammetric vector space, there is a set of natural directions (as seen by elements within space) and a 
set of apparent directions (as seen by elements outside the space. When two such spaces are to exchange elements, one 
space is always the fixed space, which in the ARDOVS concept is called the R - space with natural directions i,j,k, and 
apparent directions R;,R,,R;, (figure 2a). The other space is then the movable space with natural directions i'j',k', and 
apparent direction C,,C,, and C; (Figure 2b). 
  
658 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 
  
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