James Olaleye 
  
(a) 
(b) 
cos f cosk sinw sin f£ cosk + cosw sink 
C, =|-cosfsink | , C, =\—sinw sin Ésin k +coswcosk |, 
sin f — sin w cos f 
— cosw sin f cosk + sin w sin k 
C, = | cosw sin f sink +sinw cosk (1) 
cosw cos f 
Where w ,£,k are the positive angular rotations about the i.j.k, axes that will bring the apparent axes of the movable 
space into the same orientation as the fixed space. 
From an applications viewpoint, the ARDOVS concept serves a dual purpose. First, it may be used to simplify the 
derivation of formulations needed to transform elements between two vectors spaces if the apparent directions and 
other parameters are given: and secondly it may be used to derive computational algorithms to determine the apparent 
direction vectors and other parameters for use in subsequent applications. In this paper, we explore the first application 
of the concept, and for this, we make the assumption that the exterior orientation parameters (R.O + A.O) of the 
stereogram are already computed and that the imaging sensor has been properly calibrated. For our purpose, we shall 
use the exterior orientation data in two stages. First, we use the relative orientation information (R.O) to evaluate eqns 
1 & 2 for the apparent direction vectors needed for the image space operations. Secondly, the absolute orientation 
information (A.O) will be used to evaluate eqns. 1&2 are evaluated with the R.O. elements, they refer to image space 
apparent directions and do not carry a superscript. When evaluated with the A.O. elements, they refer to object space 
directions and carry the star symbol (*) as a superscript. 
Yet, the successful use of the ARDOVS techniques depends on correct identification of the R-space and the C-space 
in any problem situation. For the stereogram problem, this is easily achieved by recognizing that two image space 
(i.e. the left image space, the right image space) and an object space are involved, and by logical reasoning, the fixed 
space is the object space while the image spaces are the movable spaces. Therefore, for operations involving the image 
space and the object space, the image space is the C-space while the object space is the R-space. Moreover, th 
stereogram reduction process adopted in this paper involves transfer of elements between two image spaces which 
according to the ARDOVS terminology, are moving and therefore are both C-spaces. Incidentally, the ARDOVS idea 
does not apply to two C-spaces, hence we must regard one of the image spaces as fixed and the other moving. The 
choice of one or the other space is purely a matter of preference, just similar to the usual practice in dependent pai 
relative orientation in which any of the images may be chosen as fixed while the other is moved. Consequently in thi 
paper, the three vector spaces concerned are identified as follows: 
for the image space operations:- the right image is a movable or C-space while the left image is fixed or R-space (see 
figure 4a & b) 
for the object space operations:- the left image space is the € space while the object space is the R-space (see Figure X 
& figure 4) 
This convention implies that the left image space will have its axes re-assigned when changing from the image spat 
operation (see Figures 3a & b) to the object space operation (see Figure 3). Therefore, the left image space will x 
alternately referred to as the image R-space to object C- space is effected through a re-labelling of the left image axes 
However, as said earlier, the apparent directions needed for all these operations are obtained by evaluating eqns. 1& 
with R.O and A.O elements respectively. 
Having identified the spaces involved in the reduction of a stereogram, the application of the ARDOVS technique is 
premised on three operational rules (Olaleye 1992). 
  
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International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 
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©)