The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B5. Beijing 2008 
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4. LINKING IMAGES SEQUENCES INTO NETWORKS 
Our approach presented in Section 2 assumes that individual 
sequences of images are given. It has been validated with a 
large number of wide baseline sequences (Mayer, 2005, Mayer, 
2008). Yet, the experiments with the UAV presented above, 
which led to more or less long independent image sequences, 
made clear, that it is important to be able to treat extended 
image configurations, very often in the form of networks of 
linked sequences, in an adequate way. 
Linking all images independently as, e.g., in (Schaffalitzky and 
Zisserman, 2002), is the generic solution which works for 
sequences, networks, i.e., sequences linked at certain positions, 
or general blocks. (Schaffalitzky and Zisserman, 2002) avoid 
matching all pairs of images by transforming the pairwise 
matching problem into a correspondence problem in feature 
space made up of two stages. In the first a table of point features 
versus views is calculated, giving for each feature point its 
putative matches over multiple views. The second stage 
improves the quality of the matches by a number of 
global ”clean-up” operations outputting a table with 
considerably more correct matches. The complexity of the 
method is 0(n +{»--{».) 
While (Schaffalitzky and Zisserman, 2002) is a generic method, 
it is often far from optimal, as still a hard decision problem has 
to be solved: Are two images related just by chance, or do the 
few matches actually result from wide baseline perspective 
distortion, occlusions, and a small overlap? While a full least 
squares solution can help to improve the reliability (Mayer, 
2008), it is still advantageous to make use of the fact that 
usually images are taken in the form of partial sequences. I.e., 
images which can be matched are often taken directly after each 
other. Using this information should improve reconstruction, 
though we note that it might still be not easy to decide, when a 
sequence ends. Here, again GRIC (Torr, 1997) might be helpful. 
We have analyzed the situation for (partial) sequences and have 
found several configurations, which are shown in Figure 8. 
Figure 8. Configurations for the (internal) linking of image 
sequences. 
The most simple configuration in terms of complexity consists 
of two sequences (1 and 2 in Figure 8) which can be linked at 
one of their ends. 1 For this configuration only four possibilities 
1 We note that also here threefold overlap is necessary. Thus, 
actually in this and all other configurations a third image 
neighbored to one of the pair of linked images has to overlap 
the pair. To make the description more readable, we decided not 
have to be checked. More effort is needed if the end of one 
sequence (Sequence 3 in Figure 8) can be linked to any image in 
the other sequence. 2*(n+m) possibilities have to be checked, 
where n and m are the numbers of images of the two sequences. 
The worst configuration for sequences is if any image of a 
sequence with n images can be linked with any image of the 
other sequence with m images (Sequences 5 and 6 in Figure 8). 
For this configuration n*m possibilities exist. I.e., if « is 8 and 
m is 12 for a set of 20 images, there are 96 possibilities. A 
special configuration is given by Sequence 7 in Figure 8 with an 
intersection inside the sequence. Here it is possible to use the 
camera positions and orientations to predict possibly 
overlapping images and thus to avoid an exhaustive search. 
Finally, if nothing about the order of the images is known, i.e., 
in the extreme case of exhaustive search for threefold 
overlapping images in a set of n images (here we cannot make 
use of neighboring third images as in sequences) 
n! _ 1 a 
(n — 3)f • 3! “ 6 n 
1 2 . 1 
2” + 3' 1 
checks would be needed. For a set of 20 images there are 1,140 
possible triplets. Though the complexity is polynomial, it is too 
expensive in practice and thus the problem can only be solved 
by a strategy transforming the problem into the feature space 
such as (Schaffalitzky and Zisserman, 2002). 
The above discussion shows, that it should be advantageous 
from the point of view of computational complexity, but also 
reliability, to make use of partial order in a set of images. We 
particularly plan to let the user decide how the system should 
proceed. In many cases a strategy should be advantageous 
where one starts with trying to link adjacent images and by this 
means constructs partial sequences. Depending on the user 
knowledge one then ei-ther tries to link the sequences at the 
ends, ends are tested against all images in the other sequences, 
or whole sequences are checked image for image against each 
other all with the goal to construct networks. (Self-intersections 
are in all cases handled automatically as this is not a 
combinatorial problem.) 
If the user indicates, that there is no order in the images, it is 
useful to employ an approach such as (Schaffalitzky and 
Zisserman, 2002). It should also be helpful for linking 
sequences if not only the ends are to be matched. 
5. CONCLUSIONS AND OUTLOOK 
We have shown that from images taken with a weakly 
calibrated camera from a Micro UAV, for which neither a 
reliable positioning was possible due to challenging weather 
conditions, nor even any approximations for position and 
attitude are available, it is still possible to conduct a reliable and 
precise 3D reconstruction without markers or even ground 
control. 
For the future, we plan to make more experiments with an 
up-graded Micro UAV more stable against wind. Another 
possibility for improved results could be a digital camcorder 
with a resolu-tion in the range of Megapixels, which can be 
carried by a Micro UAV. Due to the high frame rate the images 
to discuss this issue in the remainder of the text.