A Dense Map Building Approach from Spherical RGBD Images
Tawsif Gokhool
1
, Maxime Meilland
2
, Patrick Rives
1
and Eduardo Fern´andez-Moral
3
1
INRIA, Sophia Antipolis, France
2
CNRS-I3S, University of Nice Sophia Antipolis, Nice, France
3
Mapir Group, Universidad de M´alaga, M´alaga, Spain
Keywords:
Visual Odometry, RGBD Dense Tracking, Spherical/Omnidirectional Vision, Optimisation, Pose Graph.
Abstract:
Visual mapping is a required capability for practical autonomous mobile robots where there exists a grow-
ing industry with applications ranging from the service to industrial sectors. Prior to map building, Visual
Odometry(VO) is an essential step required in the process of pose graph construction. In this work, we first
propose to tackle the pose estimation problem by using both photometric and geometric information in a direct
RGBD image registration method. Secondly, the mapping problem is tackled with a pose graph representation,
whereby, given a database of augmented visual spheres, a travelled trajectory with redundant information is
pruned out to a skeletal pose graph. Both methods are evaluated with data acquired with a recently proposed
omnidirectional RGBD sensor for indoor environments.
1 INTRODUCTION
This paper is focussed in the context of Visual Odom-
etry (VO), defined as the process of estimating the
relative motion of a mobile agent using vision sen-
sors. This incremental technique computes the pose
of a vehicle based on the movements induced by on-
board cameras. Over the years, VO has been useful
to compensate other similar techniques such as wheel
odometry which is highly affected by dead reckoning
in uneven terrains. On the other hand, global position-
ing system (GPS) has shown its limitation in aerial
and underwater applications (Fraundorfer and Scara-
muzza, 2012).
Odometry techniques in general require accurate
relative motion estimation to reduce trajectory drift.
Over the last decade, VO coupled with SLAM ap-
proaches have evolved in two main categories; fea-
ture based and dense techniques. Feature based meth-
ods rely on a preceeding identification and extraction
phase. Registration allows images which are further
apart , but are affected by outliers . Dense technique,
which uses the entire information content has become
increasingly popular recently as registration is per-
formed using a direct image alignment (Meilland and
Comport, 2013). The latter is generally more accurate
but is restricted by smaller interframe displacements.
An important attribute of a reliable mapping sys-
tem is scalability. Accumulation of frames over ex-
tended trajectories causes the issue of memory space
over time. In order to reduce data redundancy, main-
taining a sparse pose graph in a skeletal representation
is often desirable.Pose Graph pruning is therefore a
central issue as discussed in (Konolige and Agrawal,
2008).
This paper extends the results presented in (Meil-
land et al., 2011) in several ways. We introduce
a cost function combining both geometric and pho-
tometric constraints and use it in a direct image
registration method for pose estimation. Addition-
ally, the problem of pose graph optimization is ad-
dressed, whereby, given a database of augmented vi-
sual spheres, an explored trajectory with redundant
information is pruned out to a skeletal pose graph.
2 RELATED WORKS
2.1 Visual Odometry
After the well established theory of optical flow for
motion estimation using Intensity based images, the
communityhas nowturned to the fusion of both inten-
sity and depth information for registration and track-
ing. This trend is recurrent especially due to the
advent of consumer based RGB-D sensors such as
Microsoft’s Kinect or Asus’s Xtion Pro. A break-
656
Gokhool T., Meilland M., Rives P. and Fernández-Moral E..
A Dense Map Building Approach from Spherical RGBD Images.
DOI: 10.5220/0004745406560663
In Proceedings of the 9th International Conference on Computer Vision Theory and Applications (VISAPP-2014), pages 656-663
ISBN: 978-989-758-009-3
Copyright
c
2014 SCITEPRESS (Science and Technology Publications, Lda.)
through of this technique was devised by (Harville
et al., 1999), who were among the first to formalize
registration as a Brightness Change Constraint Equa-
tion (BCCE) and a Depth Change Constraint Equation
(DCCE). They argued that tracking is best achieved
with intelligent fusion of the two constraints men-
tioned above in order to reduce the effect of drift, oc-
clusions or illumination changes.
Their work was further extended in (Rahimi et al.,
2001), where a Maximum Likelihood (ML) based
differential tracker was developed and the problem
of drift and loop closure were also addressed. To
improve the tracking performance, the measurement
model incorporated the fusion of multiple frames. A
similar formulation was proposed in (Wang et al.,
2006), but encapsulated in a Bayesian framework. A
2D-3D pose estimation along with an intensity cost
function helped to improve feature correspondence as
well as drift reduction.
Recent works of the same domain includes that
of (Newcombe et al., 2011) whereby a preliminary
frame to frame registration is fed to a surface re-
construction module which improves the perceived
model over time together with the estimated pose.
The RGB-D slam framework of (Henry et al., 2012)
used a variant of the Iterative Closest Point algorithm
(ICP) - direct alignment of 3D point clouds (Besl and
McKay, 1992), (Zhang, 1992), together with photom-
etry. Their work also included a surfel representa-
tion of the environment to have a more compact rep-
resentation of the information available. A robust
ICP flavour was experimented in (Lui et al., 2012)
using an inverse depth parameterisation. Other re-
lated works merging photometric and geometric in-
formation for Visual Odometry (VO) can be found in
(Tykk¨al¨a et al., 2011), (Tykk¨al¨a et al., 2013), (Kerl
et al., 2013).
2.2 Keyframe Selection
When exploring vast scale environments, many
frames sharing redundant information clutter the
memory space considerably. The idea to select
keyframes based on a predefined criteria happens to
be very useful in the conception of a sparse skeletal
pose graph. Furthermore, performing frame to frame
registration introduces drift in the trajectory due to un-
certainty in the estimated pose as pointed out in (Kerl
et al., 2013).
Therefore, in order to overcome this issue, frame
to keyframe odometry is rather desirable. Com-
mon techniques applied constitute of introducing
keyframes when two such frames share very few fea-
tures between them as defined by the view cluster-
ing criteria of (Konolige and Bowman, 2009), or a
threshold on the number of features shared between
a central frame and its corresponding adjacent frames
(Royer et al., 2007). Strasdat et al. (Strasdat et al.,
2010), introduce a new frame whenever a certain dis-
tance threshold between camera poses is exceeded.
Wang et al. (Wang et al., 2006) modeled a temporal
criteria to take into account the interpose frame dif-
ference as well as feature overlap among them. On
the other hand Meilland et al. (Meilland et al., 2011)
used a selection criteria based on the Median Abso-
lute Deviation (MAD) in intensity error between a
reference and a current frame to reinitialize on a pre-
defined threshold.
Recently, information theory (Kretzschmar et al.,
2010) was introduced to prune out nodes with a min-
imal expected information gain. On a similar note,
(Kim and Eustice, 2013) set up a salient keyframe
selection criteria based on the ratio between the co-
variance of the measurement and that of the innova-
tion to encode the entropy between two correspond-
ing nodes. However, this criteria is modeled based on
the probabilistic framework of iSAM where the co-
variances are easily extracted. On the other hand, we
found that the criteria based on a differential entropy
approach introduced by (Kerl et al., 2013) is more
suitable for our system of geo-referenced spheres
which will be discussed in section 4.3.
3 SPHERICAL SYSTEM
REPRESENTATION
A new sensor for a large field of view RGBD image
acquisition has been used in this paper. This device
integrates a set of Asus Xtion Pro Live (Asus XPL)
sensors and allows to build a spherical representation
as sketched in figure 1.
1
The chosen configuration offers the advantage of
creating full 360
◦
RGBD images of the scene iso-
metrically, i.e. the same solid angle is assigned to
each pixel. This permits to apply directly some oper-
ations, like point cloud reconstruction, photo consis-
tency alignment or image subsampling. To build the
images, the sphere S
2
is sampled according to the res-
olution of our device, so that the equator (θ direction)
contains 1920 samples in the range [0,2π], while the
meridian (φ direction) is sampled with the same spac-
ing, containing 960 samples in the range [−π/2,π/2].
For spherical warping, a virtual sphere with the
1
The conception of this sensor system is out of scope
of this paper and details are omitted due to ongoing patent
consideration.
ADenseMapBuildingApproachfromSphericalRGBDImages
657
C
1
C
2
C
3
C
4
C
5
C
6
Figure 1: Multi RGBD acquisition system.
θ
φ
x
y z
p
q
Frame
i
[R|t]
K[R|t]
Figure 2: Spherical image construction.
above sampling and radius ρ = 1 is used to project
the sample points into image coordinates (u,v), (see
figure 2). For that, the extrinsic calibration of each
sensor is taken into account. Thus, a point p in S
2
is
parameterized in R
3
with
x
y
z
=
ρ cos(φ) sin(θ)
ρ sin(φ)
ρ cos(φ) cos(θ)
(1)
where ρ in this case equals 1 (unit sphere). This
point q = (u,v) on image coordinates is found by ap-
plying perspective projection to p, through the ho-
mogeneous matrix M = K[R|t] where K ∈ R
3×3
is
the camera projection model and [R|t] ∈ SE(3) is the
relative position of the camera (extrinsic calibration).
Nearest neighbor interpolation is used to assign the
intensity and depth values to the respective spherical
images.
The point cloud from the spherical representation
(figure 3) is obtained by applying equation (1), sub-
stituting ρ by the measured depth and the values of θ
and φ by its corresponding image location.
Figure 3: Point cloud obtained from the spherical RGBD
acquisition system.
4 SPHERICAL RGBD
REGISTRATION
To accurately recover the position of the RGBD
spheres with respect to one-another, a 6 dof pose es-
timation method is proposed based on accurate dense
localization. Considering an RGBD sphere S(I,ρ) as
defined in Section 3, the objective is now to compute
a pose between a reference sphere and the next one.
The localisation problem is then to estimate the rela-
tive pose
b
T between the two consecutive spheres.
Inter-frame incremental displacement is defined as
an element of the Lie groups applied on the smooth
differential manifold of SE(3) (Blanco, 2010),
also known as the group of direct affine isome-
tries. Motion is parametrized as a twist (a ve-
locity screw motion around an axis in space), de-
noted as x = {[ω,υ]|υ ∈ R
3
,
ˆ
ω ∈ so(3)} ∈ se(3):
ω =
ω
x
ω
y
ω
z
, υ =
υ
x
υ
y
υ
z
, with so(3) =
{
ˆ
ω ∈ R
3×3
|
ˆ
ω = −
ˆ
ω
T
), where ω and υ are the angular
and linear velocities respectively . The reconstruction
of a group action
b
T ∈ SE(3) from the twist consists
of applying the exponential map using Rodriguez for-
mula (Ma et al., 2004). Thereon,
b
T is denoted as the
transformation (pose) recovered between the current
frame I
c
∈ R
m×n
observed at time t and the reference
frame I
∗
∈ R
m×n
.
4.1 Cost Function Formulation
In (Meilland et al., 2011), the pose estimation was
tackled as an image registration problem whose ob-
VISAPP2014-InternationalConferenceonComputerVisionTheoryandApplications
658
jective was to perform a direct image alignment by
minimizing a cost based on the image intensity only:
F
I
=
1
2
k
∑
i
η
HUB
I
w(
b
TT(x);P
∗
i
)
−I
∗
w(I;P
∗
i
)
2
,
(2)
where w(.) is the warping function that projects a 3-D
point P
i
, given the pose T, onto the sphere and η
HUB
is a robust weighting function on the error given by
Huber’s M-estimator (Huber, 1981). The latter plays
an important role in reducing the effect of outliers by
measuring the similarity between two corresponding
pixels. Hence the weight computed accommodates
partially the uncertainty associated to each pairing be-
tween a reference and a current frame.
With the aim of robustifying the above cost func-
tion, a geometric point to plane constraint (Chen and
Medioni, 1992) is added to the equation (2) as fol-
lows:
F
S
=
1
2
ke
I
k
2
D
I
+
λ
2
2
ke
ρ
k
2
D
D
, (3)
which can be written in its explicit form:
F
S
=
1
2
k
∑
i
η
HUB
I
w(
b
TT(x);P
∗
i
)
− I
∗
w(I;P
∗
i
)
2
+
λ
2
2
k
∑
i
η
HUB
n
T
P
i
−
b
TT(x)P
∗
i
2
,
(4)
such that P ∈ (X,Y,Z) −→ (θ,φ,ρ) and λ is a tun-
ing parameter to effectively balance the two cost func-
tions. n
T
is the normal map computed from the cross
product of adjacent points on the grid structured depth
map.
Since the unknown x is common in both parts of
equation (4), the error function is stacked in a single
vector computed simultaneously as shown:
e(x)
S
=
η
HUB
I
w(
b
TT(x);P
∗
)
− I
∗
(P
∗
)
λη
HUB
n
T
P −
b
TT(x)P
∗
(5)
The Jacobian matrix J
S
is the total Jacobian relative
to the augmented cost function defined above and is
given as:
J
S
=
J
I
∗
J
w
J
T
λn
T
J
D
, (6)
Where, respectively, J
I
∗
is the jacobian w.r.t. the in-
tensity, and J
w
is the jacobian w.r.t. the warping func-
tion, J
T
is the jacobian w.r.t. the pose and J
D
is the
jacobian w.r.t. the depth.
Similarly, the weighting function for each part of
cost function is stacked in a block diagonal matrix
where D
I
,D
D
∈ R
mn×mn
are the confidence level in
illumination and depth respectively for each corre-
sponding feature pair:
D
S
=
D
I
0
0 D
D
(7)
Linearization of the above cost function leads to
a classic closed form solution given by an Iterative
Least Mean Squares (ILMS) and the incremental mo-
tion x is given by the following expression:
x = −(J
T
S
D
S
J
S
)
−1
J
T
S
D
S
e(x)
S
(8)
Using an iterative optimization scheme, the es-
timate is updated at each step by an homogeneous
transformation:
b
T ←−
b
TT(x), (9)
where
b
T = [R t] is the current pose estimate with
respect to the reference available from the previous
iteration.
This method, requires an initial guess of the pose
and it happens that an initial solution does not give
an optimum of x depending on how far the initializa-
tion has been made with respect to the reference. To
be able to recover a pose close to the solution, equa-
tions (5) to (9) are evaluated iteratively until a toler-
ated threshold in kxk < ε is reached. This leads us to
the term Iterative Re-weighted Least Squares (IRLS)
where the Gauss-Newton algorithm is well adapted
for these genres of non linear unconstrained optimiza-
tion problem.
4.2 Information Selection
In order to estimate displacement between two
frames, a set of correspondences between them has
to be found to constrain the motion model (R,t) effi-
ciently. This is a vital step in visual odometry as bad
feature matches lead to pronounced deviation from
the real motion. In literature, two mainstreams are
identified: the first one based on feature extraction
while the second one uses dense (correspondence-
free) methods (Fraundorfer and Scaramuzza, 2012).
Both approaches exhibit their advantages and in-
conveniences. The former, based on point feature de-
tection needs to undergo an identification phase where
primitives such as blobs, corners, lines or edges are
usual candidates. Good features are characterized in
terms of several properties such as stability, computa-
tional efficiency, distinctiveness or invariance to geo-
metric and photometric changes.
ADenseMapBuildingApproachfromSphericalRGBDImages
659
On the other hand, dense methods make use of the
entire photometric and geometric information content
for tracking. Along that streamline, (Dellaert and
Collins, 1999) argued that instead of using all the in-
formation content which is computation intensive, se-
lection of a subset of good pixels that yield enough in-
formation about the 6 degrees of freedom (DOF) state
vector could considerably reduce computational cost
as well as data redundancy without compromising on
the accuracy of the estimation.
Recently, a similar approach was independently
devised in (Meilland et al., 2010) which relies on find-
ing the most informative pixel subset based on the
decomposition of the Jacobian matrix obtained from
equation (2). We hereby outline the backbone of the
algorithm which has been implemented in the system
and is also illustrated in figure 4:
• Decomposition of the Jacobian J gives in itself a
saliency map pertaining to each DOF of x
• Columnwise, J is sorted out for the best pixel
which is indexedin decreasing order of magnitude
• Each DOF is then looked-up for the best ranked
pixel i in ascending order and the i
th
line is lifted
to a new table as shown in figure 4
• In case a particular pixel gives the best indexing in
more than one DOF and given that it has already
been selected, we proceed to the second best pixel
and so on.
• The selection process is performed iteratively un-
til all the pixels have been successfully sorted out
• The final result is a table of best ranked pixels with
respect to their response to a particular DOF
Therefore, instead of using all the pixels from the
intensity and depth map, a wise selection of the top
10-20% of the pixels are used for registration.
Figure 4: Saliency map.
4.3 Salient Frames Criterion
We define the differential entropy of a random vari-
able x with dimensions n such that x ∼ N (µ, Σ) as:
H(x) =
n
2
1+ ln(2π)
+
1
2
ln(|Σ|), (10)
where, Σ is the covariance matrix of the estimate x
which is obtained by the inverse of the Fisher Infor-
mation matrix computed from the normal equations
(8):
Σ =
J
T
S
D
S
J
S
−1
(11)
The entropy ratio between a motion estimate
x
k:k+ j
from a reference frame k to a current frame k+ j
is obtained by the following deduction:
α =
H(x
k:k+ j
)
H(x
k:k+1
)
, (12)
where the denominator is just the entropy relative to
the consecutive of the k
th
frame in question. The
greater the gap between the reference and the current
frame, the smaller the value of α. Hence a preset on
the value of α is used to decide whenever a keyframe
needs to be inserted or not.
5 RESULTS
5.1 Simulated Data
Our first fold of experiments have been performed on
a synthetic dataset available along with the provided
ground truth. Our algorithms have been thoroughly
tested on this dataset of around 600 images in order
Figure 5: Example of spherical views obtained from the
Synthetic dataset.
VISAPP2014-InternationalConferenceonComputerVisionTheoryandApplications
660
−10 −5 0 5 10
0
5
10
15
20
X (meters)
Z (meters)
Trajectory Z/m vs X/m
Curr. Traj.
Ref. Traj.
Grnd Truth
Figure 6: Trajectory comparison between ground truth and
that of the Intensity with Geometric cost function with the
keyframe criteria based on the differential entropy approach
to validate the convergence of the various cost func-
tions discussed in the paper before moving on to real
data. Figure 6 shows the trajectory plot obtained from
the augmented cost function (4). As illustrated, we
observe a small but noticeable offset between ground
truth and the computed trajectory using the proposed
approach. This is accountable for the fact that VO is
prone to drift phenomena.
5.2 Real Data
Our experimentations are performed on a dataset of
around 170 intensity and depth images within an of-
fice environmentconstituted of several rooms and cor-
ridors. Figure 7 illustrates the different types of places
observed along the trajectory.
Figure 7: Example of spherical views from the Office
dataset.
Figure 8(a) shows the trajectory obtained using the
cost functions of equations (2) and (4) respectively.
We observe that the algorithm using vision-only per-
forms poorly in low-textured regions such as corri-
dors or in the presence of reflections from window
panes. Such circumstances lead to erroneous esti-
mated poses coming from poor convergenceof the al-
gorithm. On the other hand, the photometry + geom-
etry cost function takes care of these discrepancies by
relying more on the depth information available. This
is justified by the overall faster convergence of the al-
gorithm as profiled in figure 8(b). The high spikes of
the figure capped at 200 iterations are due to the non-
convergence of the intensity cost function while the
new approach still manage to converge at lower itera-
tions. Finally, figures 8(c) and 8(d), depicts the error
norm of each frame at convergence.
Figure 9 focusses on the keyframe criteria dis-
cussed in section 4.3 for the same dataset: MAD
(method 1) and Entropy ratio (method 2). Over here,
we fix the photometry + geometry approach with the
keyframe criteria as the only variants. While the
MAD acts on the residual warping error after conver-
gence, the entropy ratio α abstracts the uncertainty in
the estimated pose along the trajectory. The number
of spheres initialized for method 1 is around 50 while
method 2 revealed 27 re-initializations. However, we
believe that greater reduction is achievable with lesser
inter frame acquisition so that the pose estimation al-
gorithm is better initialized leading to a faster and
more accurate convergence. A heuristic threshold of
15 was chosen for the case of the MAD and 0.96 for
that of α.
6 CONCLUSIONS
In this paper, a spherical RGBD registration method
has been proposed and we have demonstrated that
both photometry and geometry can co-exist within
the same framework. The idea is to implement a ro-
bust registration process that compensates mutually
for poorly conditioned photometric images as well as
depth maps. Furthermore, we have compared two dif-
ferent criteria for keyframe selection and have shown
an improvement by using a criterion based on differ-
ential entropy. Results have been presented with syn-
thetic and real data. For the latter, a novel sensor was
used to acquire an indoor dataset at the INRIA Sophia
Antipolis offices.
Our future works will be directed towards the
exploitation of our new spherical mapping system
on board of a mobile robot platform for simultane-
ous localisation and mapping (SLAM) as well as au-
tonomous navigation.
ADenseMapBuildingApproachfromSphericalRGBDImages
661
0
4
8
12
16
0 4 8 12
Z /m
X /m
(a) Trajectory Plot
0
40
80
120
160
200
0 40 80 120 160
Iterations
Frame Nos.
(b) Graph of Iterations vs Frame Nos.
0
0.05
0.1
0.15
0 40 80 120 160
kek
N
Frame Nos.
(c) Error norm vs Frame Nos.
0
0.5
1
1.5
0 40 80 120 160
kek
N
× 10
−3
Frame Nos.
(d) Error norm vs Frame Nos.
Int +D
Int
Int + D
Int
Figure 8: Performance comparison between Intensity only and Intensity and Depth cost functions.
0
10
20
30
40
0 5 10 15 20 25
MAD
Distance/m
(a) Graph of MAD vs Distance Travelled/m
0
4
8
12
16
0 4 8 12 16
Z /m
X /m
(b) Trajectory Plot
0.9
0.925
0.95
0.975
1
0 4 8 12 16 20 24
α
Distance/m
(c) Entropy ratio vs Distance Travelled/m
0
4
8
12
16
0 4 8 12 16
Z /m
X /m
(d) Trajectory Plot
Current
Reference
Figure 9: Comparison between MAD vs entropy ratio α using the same augmented photometry + geometry cost function.
ACKNOWLEDGEMENTS
This work has been developed at INRIA Sophia-
Antipolis and extends a previous collaboration with
the I3S/CNRS team. It is funded by EADS/Astrium
under the contract N. 7128 and by the “European Re-
gional Development Fund ERDF” through the
Spanish Government under the contract DPI2011-
25483.
VISAPP2014-InternationalConferenceonComputerVisionTheoryandApplications
662
Figure 10: Top view of real trajectory with fusion of inten-
sity and depth with entropy ratio α.
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