THE EFFECT OF FEATURE COMPOSITION
ON THE LOCALIZATION ACCURACY
OF VISUAL SLAM SYSTEMS
Mohamed Heshmat and Mohamed Abdellatif
Mechatronics and Robotics Engineering Department, School of Innovative Design Engineering,
Egypt-Japan University of Science and Technology (EJUST), New Borg El Arab, Alexandria, Egypt
Keywords: Monocular Visual SLAM, Feature Composition, Feature Selection Criteria.
Abstract: Simultaneous Localization and Mapping, SLAM, for mobile robots using a single camera, has attracted
several researchers in the recent years. In this paper, we study the effect of feature point geometrical
composition on the associated localization errors. The study will help to design an efficient feature
management strategy that can reach high accuracy using fewer features. The basic idea is inspired from
camera calibration literature which requires calibration target points to have significant perspective effect to
derive accurate camera parameters. When the scene have significant perspective effect, it is expected that
this will reduce the errors since it implicitly comply with the utilized perspective projection model.
Experiments were done to explore the effect of scene features composition on the localization errors using
the state of the art visual Mono SLAM algorithm.
1 INTRODUCTION
Simultaneous Localization and Mapping, SLAM is a
fundamental problem in robotic research and there
exist huge literature dealing with the problem from
different perspectives and approaches.
Traditionally, SLAM exploits sensors that can
measure the depth of scene objects directly such as
laser range finders, ultrasonic range sensors or stereo
camera range finders. Although sensors which
measure depth explicitly always provide better
accuracy of SLAM, the sensors are expensive and
may complicate product marketing and user
acceptance. Therefore, it is challenging to use a
single camera that can infer the depth implicitly
from its motion. Using visual information to solve
the SLAM problem is intuitive, because human
seems to do this and further more, robots are usually
equipped with cameras.
The interest of using camera as the sole sensor
for SLAM systems was active only recently because
of the lack of robust techniques and the belief that it
may be time consuming so that it may not work fast
enough for real applications.
Feature-Based visual SLAM techniques find
distinct visual features in the scene and track them
among frames to recover camera motion and scene
map (Davison et al., 2007), (Jeong et al., 2006), and
(Lee et al., 2007).
The observed features in the scene can be
thought of as a camera calibration target and when
observed through the motion, we can obtain 3D
reconstruction which constitutes a sparse feature
map.
The best known solutions utilize either Extended
Kalman Filter, EKF (Davison et al., 2007), or
Particle filter (Eade et al., 2006). In this work,
Extended Kalman Filter, EKF, was used to solve the
SLAM problem from single video camera. (Civera
et al., 2008) devised one of the successful
approaches to solve the SLAM problem by using
inverse depth parameterization. This
parameterization solved the problem of representing
distant points, with severe nonlinear effects due to
the natural effects of depth. We adopt the inverse
depth parameterization algorithm as implemented by
(Civera et al., 2008). The point features used for
solving SLAM were controlled based on their depth
and the performance was explored.
The key question is whether all detected features
will contribute equally to the accuracy of solving
SLAM. Intuitively, we believe that the geometry of
points affects the SLAM performance. Distant
features contribute to the estimation of robot rotation
419
Heshmat M. and Abdellatif M..
THE EFFECT OF FEATURE COMPOSITION ON THE LOCALIZATION ACCURACY OF VISUAL SLAM SYSTEMS.
DOI: 10.5220/0003868904190424
In Proceedings of the International Conference on Computer Vision Theory and Applications (VISAPP-2012), pages 419-424
ISBN: 978-989-8565-04-4
Copyright
c
2012 SCITEPRESS (Science and Technology Publications, Lda.)
angles but they are computationally expensive since
they need to be represented in inverse depth with
more parameters which slows down the SLAM
algorithm. How much distant point features, and
how much near point features are needed and useful
is the question we try to answer in this paper.
Intelligence will impose the constraint that we
have to select points that will only improve the
accuracy and hence we can justify the added
computational complexity, and consequently added
processing time.
The objective is to find out selection rules of
guaranteed beneficial feature points to the SLAM
performance. This approach of feature management
has not been considered before in the literature to the
best of our knowledge.
The paper is arranged as follows: The next
section outlines the EKF SLAM algorithm based on
inverse depth parameterization. The experiments are
presented in Section 3. Section 4 present the
discussion and finally conclusions are given in
Section 5.
2 EKF SLAM ALGORITHM
The Kalman Filter, KF, is a recursive Gaussian filter
to estimate the state of continuous linear systems
under uncertainty. The Extended Kalman Filter,
EKF is an extension of the KF to model system non-
linearities and detailed information on the Kalman
filters and probabilistic methods can be found in
(Montemerlo et al., 2007), and (Thrun et al., 2005).
The state vector can be described as follows:
=
(
r

q

v


)
(1)
where r

is the camera optical center position
referred to world reference coordinates, q

refers
to the quaternion defining camera orientation; and
linear and angular velocity v
and
relative to
world frame W and camera frame C, respectively,
represents an appended dynamic vector of observed
feature positions.
A constant acceleration is assumed in our state
definition but the EKF will accommodate its
changes as noise or disturbance. The dynamic model
equations can be stated as follows:
=
∆
∆
(2)
=






=

+(
+
)∆

+(
(
+
)
∆)
+
+
(3)
where

are linear and angular
acceleration, respectively, (
(
+
)
∆) the
quaternion of the rotation vector
(
+
)
∆.
Here, the prediction is the standard for EKF,
using the previous state vector and the dynamic
model. The EKF update is done in two stages, one
using low innovation inliers, and the other using
high innovation inliers (Civera et al., 2010).
In the inverse depth parameterization of 3D
point, 6 elements vector is used to descibe features
and can be defined by
=


(4)
This vector describes a ray whose optical centre
lies at (


) from which the point has been first
observed.
,
are the azimuth and elevation angles
in the world frame, respectively,
is the inverse
depth of the point along the ray.
represent 3D
feature through this equation:
=
+
1
(
,
)
(5)
where
=
(
cos
sin
,−sin
,cos
cos
)
(6)
The point observation can be represented as a
ray from the camera to the point, expressed in the
camera frame:
ℎ
=ℎ
ℎ
ℎ
(7)
ℎ
=



−

+(
,
)
(8)
The camera observes its projection in the image
plane according to the camera pinhole model:
ℎ=
=
−
ℎ
ℎ
−
ℎ
ℎ

(9)
where u
,v
are the image centre coordinate, and
f
,f
are the focal lengths measured along x, y
directions respectively. Because in the real world
usually there is distortion, a distortion model has to
be applied (Civera et al., 2008, 2010).
3 EXPERIMENTS
The code implemented by Civera, based on the
inverse depth parameterization, is used throughout
VISAPP 2012 - International Conference on Computer Vision Theory and Applications
420
this work (Civera website., 2011) together with the
dataset provided. Figure 1 shows the program
interface, inside which a) shows a frame from the
used data set and the detected features with colour
circles overlaid on it, and b) shows the map and the
camera motion.
In the code, the FAST corner detector is used to
detect point features (Rosten and Drummond.,
2006), but it is possible to use any other detector.
The only constrain is to have plenty of features to
select among them.
In camera calibration literature, features
geometric diversity is known to affect the calibration
accuracy (Tsai., 1987). Therefore, viewing features
as a dynamic calibration target, we intuitively expect
that the same could have a similar effect on robot
localization accuracy.
The feature diversity or composition is measured
here in terms of what we call as the Perspective
Factor, PF which is described by
=
1
1
−1
∑

−
̅

̅
(10)
where N is the number of frames, L is the features
number, d
is the depth of the ith feature, and d
is
the average depth. This value represents the standard
deviation of features depth normalized by their
average depth from camera.
Through the experiments the values of the
perspective factor and the averaged sum of squared
error, SSE of the robot position and orientation were
computed.
The Perspective Factor values are controlled by
removing some features, but with preserving the
minimum number of features required in the
experiment.
The case where the whole detected features is
taken as a reference for our results, as we are
concerned here with the relative relations not the
absolute accuracy of the results (Kummerle et al.,
2009).
We controlled the scene features at first by
selecting, two terminal cases, namely near features,
and distant features. The near features are defined to
be less than 3 meters in this case. On the other hand,
the distant features are considered to be more than 7
meters. The position error in X, Z, and its’
uncertainty along the frames are registered. Also,
The XZ motion of the camera is registered for each
case.
We examine the effect of selecting only the near
or distant features on the accuracy of localization.
Figure 2 shows the XZ path of the camera and the
resulting errors and uncertainty in motion trajectory
along the X and Z axes for near features, where the
black (solid) line represents the error value and the
red (dashed) lines represent the uncertainty bounds.
While, Fig. 3 shows the case when distant points are
only used.
As shown in Fig. 2, the near features give good
results in terms of the error values and the
convergence of the uncertainty. In contrast, as
shown in Fig. 3 the distant points give large values
of errors, and uncertainty divergence.
On the side of the XZ motion of the camera, the
near points show good tracking of the reference
path, but the distant points do not.
From this part of the experiment it is shown that,
the near features have strong effect on the
localization accuracy.
4 DISCUSSION
The localization error can be quantified by
(a) (b)
Figure 1: The program Interface, a) sample frame of the test scene, and b) the camera motion and the detected features with
uncertainty represented by ellipses in XZ plane.
THE EFFECT OF FEATURE COMPOSITION ON THE LOCALIZATION ACCURACY OF VISUAL SLAM SYSTEMS
421
(a) (b) (c)
Figure 2: The camera path of experimental data set and associated localization error when using near features only. a)
Camera motion path. The localization error (solid) and the associated uncertainty bounds (dashed) in b) errors of
X-direction, and c) errors of Z-direction.
(a) (b) (c)
Figure 3: The camera path of experimental data set and associated localization error when using distant features only. a)
Camera motion path. The localization error (solid) and the associated uncertainty bounds (dashed) in b) errors of
X-direction, and c) errors of Z-direction.
computing the difference between the reference
values and the estimated values of robot location or
orientation through complete tour. This can be
described by:
=
1
(

−)

(11)
where p

is the reference parameter of position or
orientation and p is the estimated value.
Experiments are done using different values of
the perspective factor. For each value of the
perspective factors, the average sum of square errors
of the camera position and orientation (X Z) are
computed.
The effect of the perspective factor on the
averaged SSE in (X, Z,) is shown in Fig. 4.
In the figure, each single point represents the error
accumulated through the same tour for each value of
Perspective Factor. The errors are shown for only
these parameters since those are subject to main
changes. An inverse relationship between them can
be observed, when increasing the perspective factor,
error values decrease.
Euclidean distance is a good measure of total
deviation from reference path and was used for
representing the position errors (Funke et al., 2009).
Figure 5 shows the relationship between the
perspective factor and the Euclidean error distance
of averaged SSE in position (X, Z).
In general, by increasing the perspective factor,
the errors are decreased. Therefore, we are advised
to select among feature points (assuming we have
plenty of points), the set of points which cause PF to
have higher value.
Correlation Coefficient (R
2
) declares the strength
of the relation between two variables.
2
=
(∑
−
)
2
(∑
2
−
2
)(∑
2
−
2
)
(12)
20 40 60 77
-0.01
0.01
0.03
N u m b e r o f F r a m e s
X E r r o r ( m )
20 40 60 77
-0.01
0.01
0.03
N u m b e r o f F r a m e s
Z E r r o r ( m )
-0.3 -0.15 0
0.1
0.2
0.3
X ( m )
Z ( m )
R e f e r e n c e
E s t i m a t e d
20 40 60 77
0
0.04
0.08
0.12
0.16
N u m b e r o f F r a m e s
X E r r o r ( m )
20 40 60 77
0
0.04
0.08
0.12
0.16
N u m b e r o f F r a m e s
Z E r r o r ( m )
-0.4 -0.3 -0.2 -0.1 0
0.1
0.2
0.3
X ( m )
Z ( m )
R e f e r e n c e
E s t i m a t e d
VISAPP 2012 - International Conference on Computer Vision Theory and Applications
422
(a) (b) (c)
Figure 4: The effect of the perspective factor on the localization errors measured in, a) X-direction, b) Z-direction, and c) -
orientation angular errors.
Figure 5: The effect of perspective factor on the Euclidean error distance of camera localization.
Correlation Coefficient between PF and the
averaged SSE in (X Z) were computed and its
values are shown in Table 1. The high values, shows
strong correlation between PF and the errors values.
Table 1: The correlation coefficient between Perspective
Factor and localization errors.
Parameters Correlation Coefficient, R
2
Averaged SSE of X 0.8539
Averaged SSE of Z 0.8704
Averaged SSE of  0.9427
This table confirms that Perspective Factor is a
strong factor that limits the localization errors.
Generally, to have higher localization accuracy, we
should increase the perspective factor by proper
selection of features.
5 CONCLUSIONS
In this paper, the effect of features geometric
configuration was studied on the SLAM algorithm
performance using Civera inverse depth algorithm.
A new factor was introduced, called the Perspective
Factor, which expresses the degree of features depth
variance normalized by features average depth from
camera.
It was found that the localization error is highly
correlated with the perspective factor. When features
showed sufficient depth change compared to its
mean depth from the camera, the estimation of the
camera motion was more accurate because the
feature geometrical content gave sufficient cues for
the inference process.
Hence, selecting features points based on
perspective factor is useful to reduce localization
error when we have plenty of features in the scene to
select from.
0.5 0.65 0.8
2
5
8
11
x 10
-3
P e r s p e c t i v e F a c t o r
E r r o r o f E u c l i d e a n D i s t a n c e
0.5 0.65 0.8
1
4
7
10
x 10
-3
P e r s p e c t i v e F a c t o r
A v e r a g e d S S E o f Z ( m )
0.5 0.65 0.8
1
3
5
7
P e r s p e c t i v e F a c t o r
A v e r a g e d S S E o f T h e t a ( d e g )
0.5 0.65 0.8
1
3
5
x 10
-3
P e r s p e c t i v e F a c t o r
A v e r a g e d S S E o f X ( m )
THE EFFECT OF FEATURE COMPOSITION ON THE LOCALIZATION ACCURACY OF VISUAL SLAM SYSTEMS
423
ACKNOWLEDGEMENTS
The first author is supported by a scholarship from
the Ministry of Higher Education, Government of
Egypt which is gratefully acknowledged.
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