Elias Benussi – Monocular Slam Project: personal
contribution
DTAM
Dense Parallel Tracking and
Mapping
INTRODUCTION
DTAM is a recent implementation of Monocular SLAM. DTAM stands for
Dense Tracking and Mapping, due to the way the algorithm uses mutual
dependent tracking and mapping in order to localise the position of the
camera in the space and to map the surrounding environment.
As for the PTAM, the algorithm is self sustaining, due to the recursive way in
which it handles mapping and tracking, i.e. at each stage the calculation only
needs the raw data just obtained from the camera and the output from the
previous stage [3.1]. This, and the improvement of the supporting hardware,
allows its use in real time simulations.
The improvement with respect to the PTAM originates from the dense
mapping technique used. The mapping algorithm in fact doesn’t just rely on
simple triangulation and stereo initialisation techniques, but also creates an
inverse depth 3D mapping of the surfaces observed and then feeds it to the
tracking system [3.1].
This system allows accurate and detailed mapping and simulation of the
environment and improves the weaknesses of point based systems, e.g.
related to blur of the image due to rapid motion [3.1].
Furthermore, before the calculations are approved to be fed back into the
algorithm, the photoconsistency of the data is checked based on previous
depth estimations and given a reliability rating [3.1]. This diminishes the
importance or random error or imprecisions.
The tracking process tracks the movement of the camera so that the
algorithms is always aware of the current relative position of the camera.
INVERSE DEPTH MAPPING
Inverse depth mapping is a technique used in slam simulations which reduces
delays and uncertainties in parametrising points. Also this method uses the
Extended Kalman Filter standard [3.3].
The key concept is that the parametrisation is done using as reference the
point where the location was first observed from. This allows a great deal of
precision even for features with low parallax [3.4].
The parallax angle is a key concept in measurements of distances and it is
used in many different fields. A common application is in astronomy, to
measure the distance of stars from Earth. In simple words, the parallax angle
would be half the angle a telescope would need to be rotated by, in order to
observe a star from a particular location on Earth in the two moments of
maximum displacement (that is when Earth, Sun and the star under
consideration form a right angle). In the picture below this is represented by p''
Image source: [3.5]
Inverse depth mappings have two main advantages: [3.4]:
• The algorithm is undelayed, meaning that features are immediately used to
improve estimates, regardless their weights [3.4].
• Even though the initial frames are used as a reference, these are
continuously updated thus increasing accuracy.
One downside is that it needs a 6-D representation rather than a classic 3-D
XYZ Eucledian one. [3.3]. This obviously contributes to make the algorithm for
the DTAM more computationally complex.
DENSE MAPPING
The dense mapping part of the algorithm can be divided into three substeps
[3.2].
1 First thing is to calculate the photoconsistency of the data just collected with
respect to the reference. The latter is calculated initially (first step of the
algorithm) on the initial measurements via a PTAM like method. This
step is skipped in later calls of the algorithm. The photoconsistency is a
way to give a weight of importance to the newly gathered data, so that
they influence the simulation only if consistent enough with what is
known already. What is problematic in this filtering process is that the
system is not linear, and to linearise it is computationally very
expensive. To avoid this approximations are made, introducing new
variables whose value can be optimised via heuristic research [3.1].
2 The next step is to create (and subsequently update) an inverse depth map,
as described above.
3 Next the information is put together to improve the capability of the
algorithm to make accurate predictions for future data based on the
movements of the camera handled during tracking.
Image source: [3.2]
DENSE TRACKING
As mentioned above, the tracking process must both localise the camera and
associate with the position the change in the image of the environment. This
is done in two steps: estimate and refinement.
• Estimating the pose of the camera in real time is done by simulating a
motion that matches with the live video model and then extrapolating
the best fitting parameters of motion in a process called constrained
inter-frame rotation estimation [3.1]. This uses the results given by the
mapping in order to assess the reliability of the estimate.
• The refinement of the calculation relies on an accurate 6DOF (6 degrees of
freedom) full pose refinement, again against the live model offered by
the mapping [3.1]. This process is more accurate but less stable and is
thus performed second.
CONCLUSION
As illustrated above, the algorithm is very performant in terms of accuracy,
and gives much more accurate results than previous methods.
Ironically this procedure would have been considered disadvantagious in the
past since it needs to perform texture-mapping of the scene, which is
modelled by millions of vertices. This is itself composed by depth maps built
from bundles of frames. All this makes it a very computationally expensive
algorithm. Nowadays though, with the powerful hardware disposable [3.1], this
is not an issue anymore and the fact that it gives better accuracy has been
exploited even in real time simulations.
PARTICLE FILTER SLAM
Global approach for density
function
INTRODUCTION
Most previous SLAM techniques made use of a Bayesian framework, but in
applications in the real world two main issues occur. Most systems are
dynamic and thus often need nonlinear models for process and measurement.
This creates some problems. Moreover the noise resulting from
measurements and processing can be non-gaussian. In these conditions a
normal Kalman Filter tends to perform quite poorly [3.6].
This led to the creation of more sophisticated algorithms. Non linear filters can
be classified into two categories. The first one uses a local approach in
approximating the probability density function of the sampling particles. The
most prevalent example, which is mentioned several times in other pages, is
the Extended Kalman Filter (EKF) [3.6].
The other approach is a global approach, which is what the Particle Filter
method uses. It works by approximating the posterior density function by
some particular form [3.6]. As its local equivalents, it bases its great accuracy
on modelling a large number of samples which makes it quite computationally
expensive.
OVERVIEW
The implementation was very convenient at the time of invention, because it
allowed to get rid of costly depth mappings. Nowadays however, due to more
powerful hardware this is not necessarily true anymore. During the
implementation of an adaptive particle filter there are two main factors to keep
in mind[3.6]:
• During the selection process care must be taken that not too many samples
with a low weight are ignored. This is done by means of a likelihood
function which being very easily calculated, proves to be an efficient
solution [3.7]. The reweighting process is shown below in image b.
Image source: [3.7]
• The design of a distribution that facilitates predictive sampling in order to
achieve a sufficient overlap with the true state density function. [3.6]
• Image source: [3.7]
• At each step of the algorithm the value of correlation is kept high to obtain a
sufficient number of weighted particles [3.7].
• However, since an excessively large number of samples (or value for the
threshold of correlation ε [3.7]) would slow down the algorithm
considerably, a process of particle annealing is performed: particles are
iteratively focused onto potential modes and in the meantime the value
of ε is reduced.
CONCLUSION
This model performs differently from local approaches. It all depends on the
noise value in the measurements. If this value is lower than a certain
threshold then a local approach, like those based on the EKF will perform
better than this model [3.6]. However with very noisy systems this global
approach will yield to better accuracy, thus making it useful in some real life
applications where measurements are hard to take. Although nowadays this
system seems obsolete as the performant hardware we possess allows us to
make use of complex depth and texture maps, at the time of creation this
algorithm was a optimal solution for real time simulations.
CREDITS AND REFERENCES
REFERENCES
[3.1] Newcombe, Richard A.; Lovegrove, S.J.; Davison, A.J., "DTAM: Dense
tracking and mapping in real-time," Computer Vision (ICCV), 2011 IEEE
International Conference on , vol., no., pp.2320,2327, 6-13 Nov. 2011
[3.2] DTAM slides http://www.slideserve.com/lorie/dtam-dense-tracking-andmapping-in-real-time-newcombe-lovegrove-davison-iccv11
(Accessed
17.03.2015)
[3.3] Civera, J.; Davison, A.J.; Montiel, J., "Inverse Depth Parametrization for
Monocular SLAM," Robotics, IEEE Transactions on , vol.24, no.5, pp.932,945,
Oct. 2008
[3.4]
Inverse
depth
slides.
http://cms.brookes.ac.uk/research/visiongroup/talks/montiel/InverseDepthMon
ocularSLAM.pdf (Accessed 17.03.2015)
[3.5]
Parallax
angle
diagram.
http://www.thunderbolts.info/eg_draft/images/parallax_566x304.jpg (Accessed
25.02.2015)
[3.6] Songlin Piao, Adaptive Particle Filter based on the Kurtosis of
Distribution, Master's thesis, Hanyang Universty Graduate School, February
2011
[3.7] Pupilli, M.; Calway, A., "Real-Time Camera Tracking Using Known 3D
Models and a Particle Filter," Pattern Recognition, 2006. ICPR 2006. 18th
International Conference on , vol.1, no., pp.199,203, 0-0 0
CREDITS
Bootstrap based theme from http://startbootstrap.com/