Achieving undelayed initialization in monocular slam with generalized objects using velocity estimate based classification

2011 IEEE International Conference on Robotics and Automation
Shanghai International Conference Center
May 9-13, 2011, Shanghai, China

Achieving Undelayed Initialization in Monocular SLAM with
Generalized Objects Using Velocity Estimate-based Classification
Chen-Han Hsiao and Chieh-Chih Wang

Abstract— Based on the framework of simultaneous local- objects are available in which manual operations such as
ization and mapping (SLAM), SLAM with generalized objects deleting features on non-static objects are needed. Migliore et
(GO) has an additional structure to allow motion mode learning al. [8] demonstrated a monocular simultaneous localization,
of generalized objects, and calculates a joint posterior over
the robot, stationary objects and moving objects. While the mapping and moving object tracking (SLAMMOT) system
feasibility of monocular SLAM has been demonstrated and where a SLAM filter and a moving object tracking filter are
undelayed initialization has been achieved using the inverse used separately. The stationary and moving object classifica-
depth parametrization, it is still challenging to achieve unde- tion is based on the uncertain projective geometry [9].
layed initialization in monocular SLAM with GO because of
the delay decision of static and moving object classification. In In our ongoing work following the SLAM with GO
this paper, we propose a simple yet effective static and moving framework [5], an augmented state SLAM with GO approach
object classification method using the velocity estimates directly using the existing inverse depth parametrization was pro-
from SLAM with GO. Compared to the existing approach in posed to solve monocular SLAM and bearings-only tracking
which the observations of a new/unclassified feature can not concurrently. A stereo-based SLAM with GO system has
be used in state estimation, the proposed approach makes the
uses of all observations without any delay to estimate the whole been demonstrated [10] in which the observability issue is
state vector of SLAM with GO. Both Monte Carlo simulations solved straightforwardly. In these monocular- and stereo-
and real experimental results demonstrate the accuracy of based approaches, stationary or moving classification of a
the proposed classification algorithm and the estimates of new detected feature is accomplished by comparing two local
monocular SLAM with GO. monocular SLAM results: one is local monocular SLAM
without adding this new feature and the other is local
I. INTRODUCTION
monocular SLAM under the assumption that this new feature
The feasibility of monocular simultaneous localization and is stationary. The difference of these two hypotheses is
mapping (SLAM) has been demonstrated [1], [2] in which temporally integrated using a binary Bayes filter. A threshold
the 6 degree-of-freedom (DOF) camera pose and 3 DOF is determined for stationary or moving object classification
feature locations are simultaneously estimated using a single after a fixed number of updates. Although the modified
camera following the extended Kalman filter (EKF) frame- inverse depth parametrization is used, initialization of these
work. An inverse depth parametrization [3], [4] was proposed monocular and stereo-based systems is still delayed as the
to accomplish undelayed initialization in monocular SLAM. observations of new features during the classification stage
It is also shown that the inverse depth parametrization has are not used in the estimation.
a better Gaussian property for EKF and has a capability for In this paper, we propose a simple yet effective static
estimating features at a potentially infinite distance. However, and moving object classification method using the velocity
SLAM could fail in dynamic environments if moving entities estimates directly from SLAM with GO. A new feature is
are not dealt with properly [5]. classified as stationary or moving using two thresholds which
A few attempts have been made to solve the monocular or are determined intuitively. The number of the time steps
visual SLAM problems in dynamic environments. Sola [6] for classification is not fixed in the proposed classification
mentioned the observability issue of bearings-only tracking method which avoids misclassification due to insufficient
and pointed out the observability issues of monocular SLAM observation updates and reduces unnecessary computational
in dynamic environments. Accordingly, two cameras instead cost in the cases that new features can be easily classified.
of single one were used to solve the monocular SLAM The proposed approach makes the uses of all observations
and moving object tracking problem with some heuristics without any delay to estimate the whole state vector of
for detecting moving objects. In [7], moving object effects SLAM with GO. Both Monte Carlo simulations and real
are removed given that the geometry of known 3D moving experimental results demonstrate the accuracy of the pro-
posed classification algorithm and the estimates of monocular
This work was partially supported by grants from Taiwan NSC (#99- SLAM with GO.
2221-E-002-192) and Intel-NTU Connected Context Computing Center.
C.-H. Hsiao was with the Department of Computer Science and In-
formation Engineering, National Taiwan University, Taipei, Taiwan. He is
currently with MSI. II. T HEORETICAL F OUNDATION
C.-C. Wang is with the Department of Computer Science and
Information Engineering and the Graduate Institute of Networking
and Multimedia, National Taiwan University, Taipei, Taiwan e-mail: In this section, the theoretical foundation of monocular
bobwang@ntu.edu.tw SLAM with GO is described.

978-1-61284-385-8/11/$26.00 ©2011 IEEE 4060

A. Representation in Monocular SLAM with GO For generalized objects, the constant velocity model is
applied and the location of a generalized object at the next
Following the EKF-based SLAM framework, a state vector
frame can be calculated in a closed form:
χ in SLAM with GO consists of the pose and velocity of
the camera/robot and locations and velocities of generalized
objects. oi
k+1 = loc(oi ) + vk · ∆t
k
i
(7)
1 i
= ri + Gk + vk · ∆t
⊤ ⊤
χ = (x⊤ , o1 , o2 , . . . , on ⊤ )⊤ (1) ρk
k k k k
1
where xk composes of the camera position rW in the world = ri + Gk+1
ρk+1
coordinate system, the quaternion defining the camera orien-
where Gk and Gk+1 are the directional vectors.
tation qW in the world coordinate system, and the camera
In the observation update stage of EKF, generalized ob-
velocity vW in the world coordinate system and the camera
jects are transformed to the camera coordinate system and
angular velocity ω C in the camera coordinate system.
 W then projected on the camera image plane. Let Rc be the
k
r rotation matrix defined by the camera orientation qc . The
k
qW  points are transformed to the camera coordinate by:
xk =  W 
v  (2)
hoi
x
ωC hoi = hoi = h(oi , xk ) (8)
k y k
oi denotes the i-th generalized object which can be stationary hoi
z
k
or moving in the framework of SLAM with GO. The existing 1
= Rc ri +
k k Gk (θk , φk ) − rW
k (9)
parametrization for only stationary objects is insufficient ρk
to represent generalized objects. In [10], the inverse depth
The predicted measurements on the image plane are:
parametrization is added with 3-axis speeds in the world o
coordinate system to represent generalized objects. Each f hxi
u u0 − dx o
ho i
generalized object is coded with the 9-dimension state vector. zoi
k = = P roj(hoi )
k = z
hyi (10)
v v0 − f
oi
dy hz

⊤ ⊤
⊤ where P roj is the project function, (u0 , v0 ) is the camera
oi
k = oi
k
i
vk (3) center in pixels, f is the focal length, dx and dy represent
the pixel size. The monocular SLAM with GO state vector
⊤
is updated by the EKF algorithm.
ok = xk yk zk θk φk ρk (4)
C. Undelayed Initialization
where ok is the 3D location of a generalized object presented The location initialization of a new generalized object is
using the inverse depth parametrization. xk yk zk is the the same as the approach in [3]. To initialize the velocity
camera location when this object is first observed. of a generalized object, v0 is set to be 0 in this work. The
covariance value of the velocity estimate σv is designed to
vk = x
vk y
vk z
vk
⊤
(5) cover its 95% acceptance region [−|v|max , |v|max ].

where vk denotes the 3-axis velocities of the generalized |v|max
object in the world coordinate system. σv = (11)
2
The 3D location of a generalized object w.r.t. to the world
coordinate system can be computed as: |v|max is set to 3 m/sec in this work. A generalized
  object is augmented to the state vector of SLAM with GO
xk straightforwardly and the new covariance of the SLAM with
1
loc(oi ) =  yk  +
k × G(θk , φk ) (6) GO state is updated accordingly.
ρk
zk By using the modified inverse depth parametrization, a
where the direction vector G(θ, φ) defines the direction of new generalized object is augmented to the state vector at the
the ray and ρ is the inverse depth between the feature and first observed frame. Through this undelayed initialization,
camera optical center. the proposed monocular SLAM with GO system uses all
measurements to estimate both the camera pose and the
B. EKF-based SLAM with GO locations generalized objects.

In the prediction stage of the EKF algorithm, the constant D. Classification in SLAM with GO
velocity and constant angular velocity motion model [3] is In SLAM with GO, generalized objects are represented in-
applied for predicting the camera pose at the next time step stead of representing stationary and moving objects directly.
as the camera is the only sensor used to accomplish SLAM From a theoretical point of view, it could be unnecessary to
with GO in this work. have a stationary and moving object classification module in

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SLAM with GO. However, from a practical point of view,
stationary objects could further improve the accuracy and
convergence of the state estimates under the static object
model. After classification, generalized objects can be easily
simplified to stationary objects for reducing the size of the
state vector or can be maintained as moving objects using
the same parametrization of generalized objects. In addition,
stationary objects could contribute to loop detection more
than moving objects in most cases. Stationary and moving (a) Target 1 (a static object marked with green circle). The true velocity of
Target 1 is (0, 0, 0)
object classification still plays a key role in SLAM with GO.

III. S TATIONARY AND M OVING O BJECT C LASSIFICATION
USING V ELOCITY E STIMATES FROM MONOCULAR SLAM
WITH GO

Stationary and moving object classification from a moving
camera is a daunting task. In this section, the proposed clas-
sification approach using velocity estimates from monocular
SLAM with GO is described in detail. (b) Target 2 (a moving object marked with green circle). The true velocity of
Target 2 is (1, 0, 0)
A. Velocity Convergency
For using velocity estimates from SLAM with GO to clas-
sify stationary and moving objects, it should be demonstrated
that velocity estimates can be converged and are sufficient
to differentiate stationary and moving objects. A simulation
using the proposed monocular SLAM with GO is discussed
to show the feasibility of the proposed classification algo-
rithm. In this simulated scene, there were 40 static landmarks
and 2 moving landmarks. 39 static landmarks were added (c) Target 3 (a moving object marked with green circle). The true velocity of
to the state vector using the inverse depth parametrization Target 3 is (0, 0, 0.5)
as known features. One static landmark (Target 1) and two
Fig. 1. Velocity convergency of 3 targets under an observable condition.
moving landmarks (Target 2 and Target 3) were initialized The estimates using the modified inverse depth parametrization are con-
as generalized objects at the first observed frame using the verged to the true values.
modified inverse depth parametrization and were added to
the state vector. The camera trajectory was designed as a
helix. Fig. 1 shows the velocity estimates of Targets 1, 2 (0, 0, 0)⊤ . The score reveals the relative likelihood of the
and 3 after 150 EKF updates. velocity variable to occur at (0, 0, 0)⊤ .
In this simulation, the estimates using the modified inverse If a generalized object oi is static, its velocity vk is
k
i
⊤
depth parametrization are converged to the true values in expected to converge closed to (0, 0, 0) . This score would
terms of both locations and velocities whether the target thus increases and exceeds a threshold ts .
is moving or stationary. The simulation result shows that 2) Score function for detecting moving objects: Given
moving object classification using velocity estimates from a 3-dimension velocity distribution X = N (µ, Σ) of a
SLAM with GO should be feasible. generalized object, the score function is defined as:
2
B. Thresholding Classification Cm (X) = DX (0) = (0 − µ)⊤ Σ−1 (0 − µ) (13)
As velocity estimates directly show the motion properties where DX is the Mahalanobis distance function under dis-
of generalized objects, two simple score functions are defined tribution X. Mahalanobis distance is often used for data
i
here for thresholding classification. association and outlier detection. For a moving feature ok ,
i ⊤
1) Score function for detecting static objects: Given the its velocity vk is expected to converge away from (0, 0, 0) .
3-dimension velocity distribution X = N (µ, Σ) of a gener- The score would thus increases and exceeds threshold tm if
alized object, the score function is defined as: the generalized object is moving.
1
Cs (X) = fX (0) = 1 (12) C. Classification States in SLAM with GO
(2π)3/2 |Σ|1/2e− 2 (0−µ)⊤ Σ−1 (0−µ)
There are three classification states in SLAM with GO:
where fX is the probability density function of Gaussian unknown, stationary and moving. Each new feature is initial-
distribution X. This score function calculates the proba- ized at the first observed frame using the modified inverse
bility density function value of the velocity distribution at depth parametrization and the classification state is set to

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25

25
1 1
20
misclassified ratio[moving object] misclassified ratio[moving object]
20 0.9 misclassified ratio[static object] 0.9 misclassified ratio[static object]
15
wrongly classified [static object] wrongly classified [static object]
15 0.8 0.8
Z[m]

10

Z[m]
10
5 0.7 0.7
5
0 0.6 0.6

error ratio

error ratio
0
−5 0.5 0.5
5 −5
5
0.4 0.4
0
0
0.3 0.3
−5
−5
25 Y[m] 0.2 0.2
25
20
20
15 15 0.1 0.1
10 10
X[m] 5 X[m] 5
0 0
0 0 0 0.5 1 1.5 2 2.5 3 3.5 4 0 0.5 1 1.5 2 2.5 3 3.5 4
−5 −5 t t
s s

(a) Observable scenario (b) Unobservable scenario (a) Misclassified ratio in the observ- (b) Misclassified ratio in the unob-
able scenario servable scenario
Fig. 2. The simulation scenarios to evaluate the effects of different
thresholds on the classification results. Grey dots denote stationary objects Fig. 3. Effects of the different ts on the classification results. tm is fixed
and black dots with lines denote moving objects and their trajectories. at 3.5830.

unknown. In each of the following observed frames, the two error are accordingly defined:
score functions are computed based on the estimated velocity Wrongly Classified Error: If a feature is classified as
distribution for determining if the feature is stationary or a different type as it should be, this feature is wrongly
moving. classified. For instance, a static feature is classified as moving
1) From Unknown to Stationary: If the score value Cs (X) or a moving feature is classified as stationary.
of a new feature exceeds the predetermined threshold ts at Misclassified Error: If a feature is wrongly classified or
a certain frame, this new feature is immediately classified as not be classified as either static or moving, this feature is
stationary. The velocity distribution of this feature is adjusted misclassified.
to satisfy the property of a static object in which the velocity
a) Effects of ts : Fig. 3(a) and Fig. 3(b) show the effects
is set to (0, 0, 0)⊤ and the corresponding covariance is also
of ts under an observable and an unobservable condition,
set to 0. There will be no motion prediction at the prediction
respectively. In both scenarios, the misclassified ratio of
stage to ensure the velocity of this object fixed at (0, 0, 0)⊤ .
stationary features increases when the threshold ts increases,
2) From Unknown to Moving: If the score value Cm (X)
while the misclassified ratio of moving features decreases.
of a new feature exceeds the predetermined threshold tm
at a certain frame, this feature is immediately classified as The misclassified ratio of moving features is decreasing
moving. As the feature has been initialized with the modified when ts is increasing under the observable situation. Mean-
inverse depth parametrization and both the position and the while, the misclassified ratio of moving features is decreasing
velocity are already being estimated, there is no need to when ts is increasing under the unobservable situation.
adjust the state distribution and the motion model. These results satisfy the expectation that a larger threshold
ts would result in less features classified as static. Thus,
D. Simulation Results when a larger threshold ts is chosen, the misclassified ratio
The proposed classification approach is first evaluated of static features would increase and misclassified ratio of
using Monte Carlo simulations with the perfect ground truth moving features would decrease. The trade-off between these
in this section. The effects of different thresholds and moving two misclassified ratios could be considered according to the
object speeds on classification are shown and discussed. usage of the monocular SLAM with GO system.
1) Effect of Different Thresholds under Observable and Furthermore, the classification performance is better under
Unobservable Conditions: While the observability issues observable situations than under unobservable conditions by
of SLAM and bearings-only tracking are well understood, comparing Fig. 3(a) and Fig.3(b). The observable situations
SLAM with GO also inherits the observability issues of could be critical to achieve better classification performance
SLAM and bearings-only tracking. In other words, velocity based on the proposed approach.
estimates of generalized or moving objects may not be b) Effects of tm : Fig. 4(a) and Fig. 4(b) show the effects
converged in unobservable conditions. Two scenarios, one of tm . In both scenarios, the misclassified ratio of static
is under an observable condition and the other is under an features decreases when the threshold tm increases, while the
unobservable condition, were designed as depicted in Fig. misclassified ratio of moving features increases. This finding
2(a) and Fig. 2(b). In Fig. 2(a), the camera moved at a non- satisfies our expectation that a larger threshold tm would
constant speed on a circle to avoid unobservable situations. result in less features classified as moving. Accordingly,
In Fig. 2(b), the camera moved at a constant speed on four when a larger threshold tm is chosen, the misclassified ratio
connected lines to test the classification performance under of static features would decrease and misclassified ratio of
an observable situation. 300 static landmarks and 288 moving moving features would increase. However, it should be noted
landmarks with different speed were randomly located in a that only a small portion of misclassified features are caused
3D cube with a width of 30 meters in each scenario. Each by wrongly classification. This means that the proposed
scenario has 50 Monte Carlo simulations. classification algorithm does not provide incorrect results.
As there are three possible states (unknown, static and The situations should be more about insufficient data for
moving), the wrongly classified error and the misclassified classification.

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1 1
estimation error of the camera
misclassified ratio[moving object] misclassified ratio[moving object] 2
0.9 misclassified ratio[static object] 0.9 misclassified ratio[static object]
wrongly classified [static object] wrongly classified [static object]
0.8 0.8
1.8
0.7 0.7

0.6 0.6 1.6
error ratio

error ratio
0.5 0.5

camera estimation error [m]
0.4 0.4 1.4
0.3 0.3
1.2
0.2 0.2

0.1 0.1
1
0 0
1 1.5 2 2.5 3 3.5 4 1 1.5 2 2.5 3 3.5 4
t t
m m
0.8
(a) Misclassified ratio in the observ- (b) Misclassified ratio in the unob-
0.6
able scenario servable scenario
0.4
Fig. 4. Effect of different tm on the classification results. ts is fixed at
1.6. 0.2

0
1 30 60 120 180 240 300 360 420 480 540 600
0.9
misclassified ratio
wrongly classified ratio
frame
0.8 25
(a) The estimate errors of the camera pose. Exploring: Frame
0.7
1 to Frame 450), Revisiting: Frame 450 to Frame 600.
classification steps

0.6 20
error ratio

estimation error of the static objects estimation error of the moving objects
0.5
12 12
0.4 15

0.3

moving object estimation error [m]
10 10

static object estimation error [m]
0.2 10
8 8
0.1

0 5
0 0.5 1 1.5 2 0 0.5 1 1.5 2 6 6
moving speed moving speed

4 4
(a) Classification performance on (b) Number of frame needed for
moving objects with different speeds classification 2 2

0 0
6 12 18 24 30 36 42 48 54 60 6 12 18 24 30 36 42 48 54 60
Fig. 5. Effects of speed variation of moving objects on classification. frame frame

(b) The estimate errors of the static (c) The estimate errors of the mov-
objects ing objects
2) Effects of Speed Variation of Moving Objects: In this Fig. 6. Convergency of the proposed SLAM with GO algorithm shown
simulation, the effects of speed variation of moving objects with boxplot. The lower quartile, median, and upper quartile values of each
are evaluated. Fig. 5(a) shows that the classification error box shows the distribution of the estimate errors of all the objects in each
observed frame.
decreases when the speeds of moving objects increase under
the setting of ts = 1.6 and tm = 3.5830. Regarding
stationary objects, the error ratio is near 0 which means that
A. Unobservable Situations
almost all stationary objects are correctly detected.
Fig. 5(b) shows the number of frames needed for classi- As shown in the previous section, the proposed clas-
fication. Recall that the number of frames for classification sification approach could be less reliable in unobservable
is data-driven and not fixed in the proposed approach. The situations than in observable situations. A simulation was
result shows that the number of frames needed decreases designed to analyze the effects of unobservable situations.
when the speeds of moving objects increase. The scenario here is the same as the scenario in Fig. 1 except
These two findings satisfy the expectation that moving that the camera moves at a constant velocity. Fig. 7 shows
objects at higher speed can be detected within fewer frames the velocity distribution of these 3 targets using the modified
and the classification results are more accurate. inverse depth parametrization after 150 EKF steps.
3) Convergency of our SLAM algorithm: The conver- The results show that the estimate uncertainties of these
gency of the proposed monocular SLAM with GO algorithm targets could be too large to reliably determine if these targets
in the observable scenario is checked. The estimate errors of are static or moving. In addition, the observations of Target
the camera, static features and moving features of 50 Monte 1 are the same as Target 3 under this camera trajectory
Carlo simulation results are shown in Fig. 6. The errors of the even though Target 1 is static and Target 3 is moving. It
camera pose estimates increase when the robot is exploring is impossible to correctly classify Target 1 and Target 3
the environment from Frame 1 to Frame 450. The camera using the observations from a camera moving at a constant
starts to close loop from Frame 450 and the errors decrease velocity. This means that we can find a corresponding
which is depicted in Fig. 6(a). Fig. 6(b) and Fig. 6(c) show moving object whose observations are the same as a specific
that the estimate errors of static features and moving features stationary object in unobservable situations. Note that such
decrease when the number of the frames increases. corresponding moving objects must moves parallelly to the
camera and at some specific speeds.
IV. C LASSIFICATION FAILURE IN U NOBSERVABLE However, the velocity distribution of Target 2 reveals
S ITUATIONS another fact. The 95% confidence region of the velocity
In this section, we discuss the failures of the proposed estimate of Target 2 does not cover the origin point (0, 0, 0)⊤ .
stationary and moving object classification in unobservable This means that Target 2 can be correctly classified as
situations. moving using the proposed approach even in unobservable

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(a) Target 1 (static object marked with green circle). The true velocity of Target Fig. 8. The NTU-PAL7 robot.
1 is (0, 0, 0)

all classified correctly as static, and 12 moving features are
also classified correctly as moving.
classification state
static moving unknown
Static 107 0 0
Moving 0 12 0
(b) Target 2 (moving object marked with green circle). The true velocity of TABLE I
Target 2 is (1, 0, 0) T OTAL CLASSIFICATION RESULT OF REAL
EXPERIMENT

Fig. 9 shows some of the input images and corresponding
SLAM with GO results. At the beginning of the experiment,
the checkerboard with known sizes was used for estimating
the scale. It is demonstrated that the camera poses are prop-
erly estimated, the 3D feature-based map is constructed using
the proposed monocular SLAM with GO algorithm, and
(c) Target 3 (moving object marked with green circle). The true velocity of moving features are correctly detected using the proposed
Target 3 is (0, 0, 0.5) velocity estimate-based classification approach.
Fig. 7. Velocity convergency of 3 targets in an unobservable condition. VI. CONCLUSION AND FUTURE WORK
We proposed a simple yet effective static and moving
situations. We argue that no static object would have the same object classification method using the velocity estimates
projection as the non-parallelly moving objects. Therefore, directly from monocular SLAM with GO. The promising
it is feasible to determine thresholds to correctly classify results of Monte Carlo simulations and real experiments
non-parallelly moving objects as moving under unobservable have demonstrated the feasibility of the proposed approach.
situations. The modified inverse depth parametrization and the proposed
classification method achieves undelayed initialization in
monocular SLAM with GO. We also showed the interesting
V. E XPERIMENTAL R ESULTS
issues of classification in unobservable situations.
Fig. 8 shows the robotic platform, NTU-PAL7, in which The constant acceleration model and other more advanced
a Point Grey Dragonfly2 wide-angle camera was used to motion models should be applied for tracking moving objects
collect image data with 13 frames per second, and a SICK with high-degree motion patterns. Evaluating the tracking
LMS-100 laser scanner was used for ground truthing. The performance of moving objects with more complicated mo-
field of view of the camera is 79.48 degree. The resolution of tion pattern using SLAM with GO is of our interest. In
the images is 640 × 480. The experiment was conducted in addition, solutions to move-stop-move maneuvers should be
the basement of our department. 1793 images were collected developed.
for evaluating the overall performance of monocular SLAM
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Fig. 9. (a)-(d) show the examples of input images and the results of feature extraction and data assoication. (e)-(f) are the top views of the corresponding
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