le for each image 
(3) 
(4) 
ge point corrected 
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e case of Figure 7, 
ssible homologous 
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n process within 
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ortion of the target 
ess takes as input 
yrresponding image 
The main loop iterates over all possible image pair 
combinations. Within this loop, the algorithm computes all 
epipolar plane angles of the two selected images and stores the 
values in an angle array. To find homologous image points, the 
angle array is sorted. At this stage only object point candidates 
are determined. To guarantee a certain accuracy of the candidate 
point coordinates, only rays with a specified minimum 
intersection angle are accepted. An object point candidate is 
classified as accepted if, using back projection, it is found in at 
least one other image. Consequently, the complete triangulation 
information of an object point is built up once it is found to be 
an object point candidate. In the case of ambiguities (Figure 7), 
only one of all possible object point candidates may be accepted 
as the true object point. After rejecting or accepting all object 
point candidates of the image pair, the next two images are 
selected. In the new image pair only epipolar plane angles for 
unassigned image points are computed, which makes the 
computation faster for every new image pair. 
  
Figure 7. Resolving correspondence ambiguity 
using a third image. 
5. BUNDLE ADJUSTMENT AND QUALITY 
MONITORING 
The integrated bundle adjustment forms a logical final step 
within an automated off-line VM computation process. Beside 
the determination of object point coordinates and EO 
parameters, the final bundle adjustment typically includes 
sensor self-calibration. Sensor calibration is a basic requirement 
for the achievement of high triangulation accuracy, especially in 
the case of off-the-shelf digital cameras. Bundle adjustment 
strategies include methods for blunder detection, which leads to 
the idea of employing an initial bundle adjustment for the 
detection and correction of gross errors that arise in the 
automated measurement process. Least-squares adjustment 
methods are well suited to error detection because all decisions 
can be statistically based. 
Considering possible observational blunders in both image 
scanning and point correspondence determination, a correction 
algorithm needs to be developed. There are three types of errors 
that can occur: 
® Recognition errors in image scanning: It is assumed that 
all targets are found correctly and that only a few non- 
target regions (e.g. bright areas or spots) are falsely 
accepted. If a non-target feature is found in at least three 
images, the correspondence process will then find a 
corresponding object point. Because the located object 
point is a real, physical object feature the final triangulation 
network is rarely disturbed. Additionally, these object 
points are often rejected in early iterations of the bundle 
adjustment because of their anticipated larger image 
coordinate residuals. Artificial targets (e.g. retro-reflective 
targets) have a very high centroiding precision which is 
rarely matched by ‘natural’ target features. Consequently, 
the interference of these errors in the automatic 
measurement process is rarely of any practical 
consequence. 
e Correspondence determination errors: This type of error, 
which arises from ambiguities in the epipolar-based point 
matching, can always be expected to be present to some 
extent, although it rarely causes serious concern in strong 
VM networks. In rare situations, often with very dense 
target arrays, unresolved false detections occur. Whereas 
with recognition errors the effect is to generate additional 
object points, here incorrect points with completely wrong 
coordinates might result. Though these observational 
blunders interfere with initial triangulation, they are usually 
rejected in the bundle adjustment if the number of images 
in which they appear is low. 
* Duplicate point errors: Situations can arise such that a 
single target is identified as two (or more) discreet object 
points. This occurs when two or more subsets of images 
exist where the target passes the correspondence test in 
each subset, but not the set as a whole. The algorithm, not 
knowing that the target is unique, assigns it as if it were 
two discreet object points with slightly different XYZ 
coordinates. The correction for this type of error can occur 
later, after the final bundle adjustment reveals that the 
coordinates for these discreet points are coincident. This 
situation occurs when the EO within each image subset is 
relatively strong but not strong between each subset. 
Analysis of the bundle adjustment progress within various 
Australis projects has shown that the first two error types are 
accommodated (bad data rejected) in early iterations of a bundle 
adjustment. Even the third error type can be identified early on 
in the processing because later iterations effect only very small 
shifts of object points and these multi-object points are close to 
coincident in space. These considerations have led to the 
development of a final three-stage triangulation process for 
Australis: 
® A ‘fast’ bundle adjustment: This is an initial adjustment to 
‘near’ convergence, where a larger than usual RMS 
threshold for image coordinate residuals is used as a 
convergent criterion; 0.5-3um turns out to be an 
appropriate threshold range for highly convergent VM 
networks. These networks typically achieve a final RMS 
value of 0.15 — 0.3 um. The camera is not fully self- 
calibrated in this initial adjustment, though the focal length 
and the principal point coordinates are usually carried as 
additional parameters. This results in a performance gain, 
and it is generally a more robust calculation strategy if only 
an inaccurate camera calibration (or no calibration) is at 
hand. 
* Data cleansing stage: Next, a correction process is 
performed where the results of the initial bundle adjustment 
are analysed. Object points with less than three active 
imaging rays are removed and all the corresponding point 
measurements are omitted. This process also corrects 
blunders arising from the first two error sources listed 
above. To correct for duplicate point errors, a simple 
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