As can be imagined, the resolving of point correspondences for 
EO takes quite some computation time if all point permutations 
on the EO device are considered. A total of 120 (or 5!) 
resections need to be performed for a 5-point array before the 
correct solution is known. On a Pentium II/266 PC, the EO 
device detection takes two seconds whereas the scanning of a 
single high-quality image (1536 x 1024 resolution) is performed 
in only one second. Though computation time is usually not 
critical in off-line VM, an optimised detection algorithm has 
been implemented in Australis to further enhance processing 
speed. If the targets on the EO device are labelled in a specific 
order, the correct EO can usually be achieved with only four 
resections. In the adopted labelling scheme, the point closest to 
the centre of gravity of all EO targets (the raised point in Figure 
4) is initially labelled, and then the remaining points are 
incrementally labelled in a clockwise fashion. EO devices 
which are labelled as such are detected within one second. 
4. POINT CORRESPONDENCE DETERMINATION 
USING EPIPLOAR GEOMETRY 
4.1 Epipolar Plane Angle Geometry 
Epipolar geometry can be employed to locate homologous 
image points in a multi-image VM network. Therefore, 
reasonable approximations of the EO parameters for all camera 
stations are required, this being provided via the EO device. In 
the literature, various techniques having different characteristics 
in relation to speed and robustness can be found for image point 
correspondence determination (e.g. Furnee et al. 1997, Chen et 
al. 1993) All techniques, however, must deal with 
correspondence ambiguities that can easily arise in the case of 
only two images or in multi-image networks where there is a 
dense array of targets (real and false). The technique adopted 
for Australis is based on epipolar plane angles and is similar to 
that proposed by Sabel (1999). It is fast and capable of 
accounting for lens distortion effects in correspondence 
determination, which is often critical when using modern CCD 
cameras. 
The basic principle of the epipolar plane angle method is that 
rays of corresponding image points subtend identical angles to 
any epipolar plane, as illustrated in Figure 6. Epipolar planes 
always contain the projection centres of both camera stations. In 
order to calculate the required angles for image points of both 
images, an arbitrary epipolar plane is first defined. The 
normalised vectors n; and n, are then computed with the applied 
constraints that both the vectors and the baseline are normal to 
each other, and that n, is contained by the defined epipolar 
plane. The corresponding epipolar plane angle for each image 
point in both images can then be calculated: 
y z-R y (3) 
ee 
A =arctan(ñ, +, h, 7) (4) 
Here, x; and y; are the coordinates of an image point corrected 
for lens distortion, R is the rotation matrix for the current 
camera station and c is the corresponding focal length. 
4.2 Resolving Ambiguities 
An image point can have an infinite number of homologous 
points in the second image, the applicable constraint being that 
they all have the same epipolar plane angles, or in other words, 
they are positioned on epipolar lines. When lens distortion is 
taken into account, the epipolar line transforms to a curve. Such 
correspondence ambiguities can be resolved or at least greatly 
reduced by using a third image. Consider the case of Figure 7, 
where the point I, in image 1 has two possible homologous 
points in image 2 (J; and J,), because they are positioned on the 
corresponding epipolar line in the image. The two object points 
P, and P, can be computed and are projected into the third 
image. If one of these projected points is coincident with an 
existing image point (K,), within a given tolerance, the 
ambiguity is resolved and P, is then the correct 3D object point. 
In the resection-driveback image-point measurement process, 
where the object point coordinates and EO are utilised to predict 
image point location, lens distortion has to be considered for the 
back projection to deliver correct image point locations, and 
therefore correct correspondence determination. An inverse 
function for lens distortion is therefore needed. Because no 
closed-form of this function exists, a numerical inversion that 
typically converges within a few iterations is performed. 
43 Correspondence Determination Algorithm 
The entire correspondence determination process within 
Australis, which was designed for highly-convergent VM 
networks where most images 'see' a large portion of the target 
range, is briefly outlined below. The process takes as input 
several images with known EO and their corresponding image 
point measurements. 
  
Figure 6. Epipolar plane angle geometry. 
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