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in 2.2 are not correct. When solving the minimization, one should of course
avoid these local optima. The method developed in [12] solves this problem by
always starting from an approximate reconstruction of the scene from a previous
bundle adjustment iteration, and then adding just a couple of new views to it.
Additionally, these new views are first roughly positioned using RANSAC based
on the point matches. This incremental approach ensures that an intermediate
solution is always close to the global optimum, thus helping the gradient based
Levenberg-Marquardt algorithm. The downside is that a lot of computation time
is spent on re-optimizing parts of the scene that were already reconstructed, as
(3) always considers all points and cameras.
3Propo edM thod
3.1
Splitting the Global Scene
While considering the whole scene in (3) gives the most reliable result, it is
clearly not optimal w.r.t. time. We propose a divide and conquer approach,
splitting the scene into several overlapping subsets of size
S
with overlap
O
.
Then each subset is optimized seperately, after which the results are combined.
Figure 1 shows an example. Ideally a subset consists of cameras positioned close
to eachother. The problem is that we generally do not know the positions of the
cameras in advance. However, in practice it is often the case that pictures taken
close together in time, are also close in space. Thus we subdivide the scene based
on the order in which the images were acquired. To keep things manageable, we
use a constant
S
and
O
. One could think of a dynamic splitting scheme where
S
and
O
change based on the quality of feature matches, or closeness of initial
image transformations. However due to the large number of possibilities we leave
this as future work.
The values of
S
and
O
determine the balance between speed and accuracy,
where accuracy is defined as the difference between the combined subsets and
the result we get without splitting. Smaller subsets require less time to optimize,
but are prone to wind up in local minima. Smaller overlaps decrease computation
time as well, but also decrease the accuracy of the combined result. The reason
for this is that the bundle adjustment can only position cameras in relation to
Fig. 1.
Splitting a global scene into subscenes, with
S
=8and
O
= 2. The black dots
are the (unknown) camera positions.
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