arXiv:1707.04444v2  [cs.CV]  19 Jul 2017
Monocular Visual Odometry for an Unmanned Sea-Surface Vehicle
George Terzakis1, Riccardo Polvara2, Sanjay Sharma2, Phil Culverhouse2 and Robert Sutton2
Abstract— We tackle the problem of localizing an au-
tonomous sea-surface vehicle in river estuarine areas using
monocular camera and angular velocity input from an inertial
sensor. Our method is challenged by two prominent drawbacks
associated with the environment, which are typically not present
in standard visual simultaneous localization and mapping
(SLAM) applications on land (or air): a) Scene depth varies
significantly (from a few meters to several kilometers) and, b) In
conjunction to the latter, there exists no ground plane to provide
features with enough disparity based on which to reliably detect
motion. To that end, we use the IMU orientation feedback
in order to re-cast the problem of visual localization without
the mapping component, although the map can be implicitly
obtained from the camera pose estimates. We find that our
method produces reliable odometry estimates for trajectories
several hundred meters long in the water. To compare the
visual odometry estimates with GPS based ground truth, we
interpolate the trajectory with splines on a common parameter
and obtain position error in meters recovering an optimal affine
transformation between the two splines.
I. INTRODUCTION
Outdoor visual SLAM is a problem under constant
scrutiny in the robotics research community [1], [2], [3],
[4]. However, to the best of our knowledge, there have
been not many cases in which the SLAM algorithm targets
sequences of estuarine and possibly, natural scenes from the
vantage point of a surface vehicle. Perhaps the only known
recorded case is the work of [5] on lakeshore monitoring
which makes use of visual SLAM to localize the vehicle on
the surface of the lake. The approach of Griffith et al. relies
on the same tools as the method described in this paper.
The idea is to detect a sparse set of Harris corners [6] in
an image and thereafter compute camera pose by tracking
these features using the pyramidal Lucas
Kanade tracker
[7], [8]. Of course, the primary objective of Griffiths work
is the registration of shore images and vehicle localization is
simply a subsidiary operation used to confine the search for
an image within a subset of images taken in a region close
to the estimated position of the boat. It follows that multiple
poses can be refined without time limitations in large-scale
bundle adjustment runs.
The work in this paper is motivated by the scenario of a
surface vehicle [9] cruising autonomously on GPS feedback
which may be interrupted; therefore visual odometry on
lakeshore images is used as an auxiliary localization system
for the vehicle during periods in which GPS reception is
1George Terzakis is with the University of Portsmouth, PO1 3HF, UK.
Email: george.terzakis@port.ac.uk
2Riccardo
Polvara,
Sanjay
Sharma,
Phil
Culverhouse
and
Robert
Sutton
are
with
Plymouth
University,
PL4
8AA,
UK.
Emails:
{riccardo.polvara, sanjay.sharma,
p.culverhouse, r.sutton}@plymouth.ac.uk
disabled. Thus, in contrast with Griffith et al., this is an ex-
clusively real-time visual SLAM problem and the exact same
approach cannot be employed due to the inherent limitations
in computational resources. There are however time-efficient
alternatives which employ non-linear optimization over only
a small pool of poses and images in a sliding time-window,
such as local bundle adjustment [10] and generally provide
satisfactory pose estimates on demand.
One other significant limitation in our application has
to do with extreme depth variations in the shore sequence
(1). Although there are ways to assess the nature of the
photogrammetric degeneracies in the geometry of two views
[11], [12], [13], [14], these methods require Monte-Carlo
based model selection and would impose a significant over-
head if applied on a regular basis. One remedy would be to
include ground-plane features in the field of view [3], [15],
[16] and allow motion estimation to be affected primarily
by these features. Unfortunately, this is generally not an
option when the camera is on-board a surface vehicle due to
the presence of the water-surface instead of the ground. It
therefore becomes necessary to infer camera motion solely
based on the features in the background beyond the sea-
surface.
Fig. 1: Extreme opposites in estuarine sequences. On the left,
only very distant features over the horizon can be tracked,
while on the right, scene depth is very small. In the first
case, disparity is very small and only a few carefully selected
correspondences can determine motion; in the second case,
the disparity is sufficient to determine motion from the
majority of features.
Another significant problem that arises from extreme depth
variation is the fact that the map can be potentially harmful
for pose prediction, due to tracking noise induction with large
depth. The problem of reconstructing points with very small
disparity is that tracking noise is augmented proportionally
to depth as shown in Figure 2. And since having exclusively
distant points in the map is a very likely case as illustrated
on the left of Figure 1, it will be difficult to assess the quality
of the position estimates in order to choose inliers for pose
estimation with a Perspective-n-Pose (PnP) algorithm. In
short, the map points obtained from scenes with large scene
depth can jeopardize SLAM if used for pose prediction.
Fig. 2: Uncertainty induction with depth. The size of the
blue shaded rhombic region surrounding the triangulated map
point is representative of its uncertainty. A similar sketch can
be found in Multiple View Geometry in Computer Vision
(Hartley and Zisserman 2003).
II. PROBLEM SETUP
A. Overview
The method proposed herein aims at estimating the pose of
a sea-surface vehicle in the context of GPS-denied scenario
using an on-board camera with view of the shore. In particu-
lar, in the case of GPS signal loss, the vehicle should be able
to continue cruising autonomously based solely on visual
feedback until GPS becomes available again. We focus on
river estuarine environments where the primary assumption
of shore visibility is met. The camera is mounted on the side
of the vehicle as shown in Figure 3.
Fig. 3: The unmanned surface vehicle. The camera (circled
in red) is mounted on the left hull, pointing sideways.
B. Apparatus
All video sequences were obtained using a Pointgrey Flea3
USB3 camera, typically at a resolution of 800600 pixels.
We addressed camera calibration with Zhangs chessboard
method [17], [18] as implemented in OpenCV computer
vision library [19]. For the rest of this paper, it is assumed
that the camera is calibrated and all formulas involving
projections are given in normalized Euclidean coordinates.
Fig. 4: Flea3 and SiIMU02 (right). The SiIMU02 coordinate
frame (left) is shown with the 3 axes labelled 1+, 2+ and
3+ and M denotes the transformation which transforms the
sampled angular velocity vectors with the camera frame
(shown in red).
Inertial data were sampled using a Goodrich SiIMU02
(Figure 4) at a rate of 150 Hz. It should be noted that
the SiIMU02 coordinate frame does not represent a right
handed coordinate system and therefore it is necessary to
apply a transformation M to the samples in order to obtain
the angular velocities x, y, z about the axes x, y, z of the
local camera frame. Thus, the rotation matrix representing
the change in IMU orientation is:
R = I3 + sin∥ω∥
∥ω∥
[ω]× + 1 −cos∥ω∥
∥ω∥2
[ω]2
×
(1)
where ω =
ωx
ωy
ωz
T is the sampled angular velocity
vector. We addressed the problem of minor misalignments
between the camera the IMU using the recovered camera
calibration extrinsic parameters as described in camera-aided
robot calibration [20].
III. METHOD
Our method loosely follows the standard SLAM pipeline
of pose prediction and refinement with measurements over
a sliding window of no more than 5 frames. The idea is to
detect new features in each frame and track them for up to 5
frames in the sequence. However, pose is estimated directly
on the pairs of corresponding Euclidean projections instead
of using the reconstructed map-points. In effect, this is a
version of SLAM in which the map can only be inferred
from camera pose in conjunction with the measurements and
is not directly involved in pose prediction. Figure 5 illustrates
our adaptation of the SLAM paradigm in the form of a Bayes
network. The pose at time instance-t (time is discrete) is a
vector xt =
st
ψt
T containing the position of the camera st
and its orientation parameter vector ψt. We also denote the
IMU angular velocity sample with ωt and the normalized
Euclidean projections of the tracked features with mt.
In the SLAM adaptation of Figure 5, each tracked feature
location at time t is regarded as a function of its projected
location and camera pose in the view in which it was
Fig. 5: A Bayes network depiction of the SLAM paradigm
adaptation of our method. The dashed-line rectangle indi-
cates a 3-frame sliding window from time t to time t + 2.
originally detected; and since we are using a sliding window
of length 3, it follows that it can only be associated with
times t −1 or t −2, hence the factor between mt, xt−1, xt−2,
mt−1, mt−2 in the network. The measurement model is simply
the pinhole projective relationship between the ith feature
measurement m(i)
t
at time t and its corresponding image in
the view of original detection (henceforth called the home
view) at time h:
m(i)
t
=
RhiRT t

Zhim(i)
hi −Rh
st −shi


1Tz RhiRTt

Zhim(i)
hi −Rhi
st −Shi


(2)
where Rt is the rotation matrix corresponding to the camera
frame orientation at time t (direction vectors are stored
column-wise), st is the position of the camera at time t in
world coordinates, hi is the time index of the home view
(i.e., original detection) if the ith feature, Zt is the depth of the
map-point at time t and 1z =

0
0
1
T. As will be shown,
provided that orientation is known, it is possible to eliminate
Zh from eq. 2 and replace it with an expression that contains
st, sh, Rt, Rh and the measurements. Thus, the corresponding
conditional distribution of mt depends only on previous
measurements and poses and it can be loosely regarded as the
marginal of the standard visual SLAM measurement model
over the map.
A. Predicting camera pose
Our method makes use of a technique that loosely draws
inspiration from the work of Kneip et al. [21]. In particular,
knowing the rotation matrix between two key-frames, we
are able to do camera resectioning directly from image
correspondences, thereby circumventing the potentially noisy
distant map-points. To lighten notation in the derivations
that follow, we isolate two views from the sequence in
both of which a feature is measured and assume, without
constraining generality, that the first camera is at the origin
and its orientation is the identity. The relationship of eq. 3
can now be re-written as follows:
m2 =
RT(Z1m1 −b)
1T
ZRT(Z1m1 −b)
(3)
where m2 and m1 are the measured normalized Euclidean
coordinates of the feature in the current and previous (home)
view, Z1 is the depth of the feature in the previous (home)
view, b is the baseline vector in the coordinate frame of
the previous camera and R is the relative orientation ma-
trix (containing the current camera frame in column-wise
arrangement).
Fig. 6: Removing rotational effect from the projections in the
second view. The rotation matrix R transforms the first cam-
era frame triad (x1,y1,z1) at O1 into the second, (x2,y2,z2)
attached to the camera center O2. The homography H = R is
applied to the normalized Euclidean projection m2 in order to
obtain its ”unrotated” version, m′
2 in the virtual view (shown
with dashed outline).
Now, provided reliable prior information on relative orien-
tation between two camera frames, it is possible to remove
the effects of rotational motion from the image projections
in the current view by creating a new, virtual view in which
all projections are, the result of pure translational motion.
This way, motion equations become linear in the translation
components and standard least squares optimization can
be applied. Figure 6 illustrates this concept of unrotating
projections in order to produce a virtual view that shares the
same baseline with the original, but without the rotational
portion of projective distortion. Specifically, if a pure rotation
RT is applied to the second camera frame, then it will align
with the first. It follows that the normalized projections in
the unrotated view will simply transform by a homography
H = R:
m′
2 =
Rm2
1Tz Rm2
(4)
where ∝denotes equality up-to-scale. Eq. 3 can now be
re-written without the rotation matrix using the unrotated
projection m′
2:
m′
2 =
Z1m1 −b
1Tz (Z1m1 −b)
(5)
Equation 5 decomposes in the following two equations
corresponding to the projections in x and y axes:
(x′
2 −x1)Z1
=
x′
2bz −bx
(6)
(y′
2 −y1)Z1
=
y′
2bz −by
(7)
where m′
2 =
x′
2
y′
2
1T, m1 =
x1
y1
1T and b =

bx
by
bz
T. The depth can be eliminated if we simply
multiply eq. 6 by (y′
2 −y1) and eq. 7 by (x′
2 −x1) and then,
subtract eq. 7 from eq. 6:
−
y′
2 −y1


bx+
x′
2 −x1


by+
y′
2 −y1


x′
2 −
x′
2 −x1


y′
2


bz = 0
(8)
We therefore obtain a linear equation in the components of
b which can be used to formulate an overdetermined linear
system that can be solved in ordinary least squares fashion.
It should be stressed here that eq. 8 is tolerant to points with
very low disparity as it is quite evident that, if both terms
(x′
2 −x1) and (y′
2 −y1) vanish, then the equation becomes
trivial (0b = 0) and subsequently has little or no effect on the
least squares estimate. We may now formally ”repackage”
eq. 8 for the ith feature in a new camera view at time t using
a determinant:
det
h
Rhi
st −shi



m(i)
t
′
−m(i)
hi

m(i)
t
′i
= 0
(9)
where hi is the time index of the camera view in which
the ith feature was originally detected, st and shi are the
position of the camera at times t and hi in world coordinates,
Rhi is the orientation matrix of the camera at time hi, m(i)
hi
is the normalized Euclidean projection of the feature in its
home camera view and

m(i)
t
′
is the unrotated normalized
Euclidean projection in the camera view captured at time t.
In the initializing pair of views (i.e., for hi = 0 and
t = 1), the overdetermined linear system will obviously be
homogeneous and therefore the solution will be the direction
of the baseline between the respective camera frames. In this
case, of multiple camera views, the solution will be sign-
ambiguous and therefore it will be necessary to reconstruct
the scene and vote for the best reconstruction (i.e., the one
with fewer negative/vanishing depths). However, in the case
of more than two camera views, the system becomes a
standard least squares formulation with a unique scale-aware
solution in which scale is infused by the known positions of
previous camera frames.
B. Outlier rejection
To eliminate outliers we employ a robust random sample
consensus [22] scheme called MLESAC proposed by Torr
and Zisserman [23]. For each new camera view, we compute
the baseline using eq. 9 over randomly picked minimal
subsets of at least 3 points. Then, for the recovered camera
position we obtain a robust epipolar score on the misalign-
ment of epipolar planes between camera views. Unlike the
case of Sampson error [24], our epipolar misalignment error
works directly on the relative pose without the need to use
an essential matrix and it is generally easy to compute.
Consider the two corresponding normalized Euclidean
projections m1 and m2 (again, superscripts are dropped for
Fig. 7: Measuring misalignment of epipolar planes ε1 and ε2
on a plane π, orthogonal to the baseline b.The misalignment
angle cosine will be the inner-product of the normalized
projections of m1 and Rm2 on the plane π.
simplicity) in two camera views indexed by 1 and 2. Then,
if the correspondences are noisy, the two epipolar planes
defined by m1, m2 and the baseline will not coincide as
shown in Figure 7 and will subsequently form an angle
between them. Since the baseline vector b is common for
both planes, one way of obtaining the angle between the two
misaligned planes is to project the two correspondences onto
the orthogonal space of the baseline, which is essentially a
plane π through the origin O1 and to which normal is the
baseline. The (projector) matrix P that projects a vector onto
the space orthogonal to b is:
P = I3 −bbT
(10)
Thus, the projection of m1 would be:
p1 = Pm1 = (I3 −bbT)m1
(11)
The projection of m2, accounting for the difference in the
orientation of camera frames, is:
p2 = PRm2 = (I3 −bbT)Rm2
(12)
where R is the relative orientation matrix. The cosine of the
angle between the two planes ε1 =< m1,b > and ε2 =<
Rm2,b > will be the following inner-product:
cosφ =
pT
1 p2
∥p1∥∥p2∥
=
mT
2 RT I3 −bbT

m1
q
∥m1∥2 −
mT
1 b

2q
∥m2∥2 −
mT
2 RTb

2
(13)
Clearly, the measure of eq. 13 is a score that increases with
the accuracy of the correspondence and therefore we seek to
maximize it. Nominal values used for the MLESAC cutoff
bound were in the range of cos7◦to cos3◦. It should be
stressed here that the score of eq. 13 penalizes angles above
90◦(i.e., correspondences with negative depth in exactly one
view), whereas the classic epipolar constraint does not (due
to the minimization requirement). Most importantly, it is a
score that is independent of the type of camera motion and
fitted model (homography or essential matrix), including the
case of pure rotational camera motion, in which case the
two projection directions should be collinear and the formula
reduces to a simple inner-product which yields the cosine of
the angle between m1 and Rm2.
C. Iterative refinement
Pose estimates are iteratively refined with the Gauss-
Newton method over a few (usually 3) recent views. Instead
of the traditional reprojection error [24], we employ an
epipolar alignment score, similar to the one of eq. 13. In par-
ticular, instead of considering the misalignment of epipolar
planes, this time, we focus the angle between the direction of
the second correspondence and the normal of the first plane.
This way, a minimization problem is obtained, suitable to
apply the Gauss-Newton method. Suppose a sliding window
of n camera views is used. We construct the following cost
function C over this window:
C =
t+n−1
∑
k=t ∑
i∈Vt

mtRT
t

st −shi

× Rhimhi
2
(14)
where Vt is the set of visible points in the window com-
mencing at time t, hi is the time index of the ”home” view
(i.e., first detection) of the ith feature, m(i)
t
is the normalized
Euclidean projection of the ith feature in the camera view
at time t and Rk, sk are the orientation matrix and position
vector (in world coordinates) of the camera at time t = k.
The cost function of eq. 14 is a sum of epipolar constraints
over the camera poses in the sliding window. The latter
suggests that the Gauss-Newton normal equations scale only
with camera poses, as opposed to the larger system sizes
we typically obtain with sparse bundle adjustment. For a
window of size n = 2, the cost function is scale unaware and
becomes theessential matrix least squares formulation [25].
For n > 2, at least one camera pose is taken as constant and
the optimization problem becomes scale aware owed to the
presence of measurements in more than two camera views.
IV. EXPERIMENTS
We executed our method on video sequences of the river
shore recorded on a cruising vehicle averaging 5-7 knots
speed. Each sequence is accompanied by IMU samples at
150 Hz and GPS readings at approximately 1Hz (standard
refresh rate of USB dongle). Both IMU and GPS data are
time-stamped with a video frame index. The GPS readings
are used as our main measure of ”ground truth”.
A. Ground truth
Due to the limitations imposed primarily by the environ-
ment, GPS was the only reliable means of a ground truth
estimate. Although the GPS position reading is known to
have approximately 1.5 meters variance, it however is highly
reliable in long routes, simply because it does not accumulate
error. The routes corresponding to the recorded sequences are
longer than 30 meters and therefore, in this context, the GPS
routes are accurate representations of ground truth.
The scale of the vision-based estimated trajectory is de-
fined by the last reading of speed over ground from the
GPS, before the visual odometer takes over. Since this is
a fairly noisy estimate and scale errors accumulate during
SLAM, direct comparisons between the GPS trajectory and
the respective SLAM-generated estimate would be biased,
regardless of whether this estimate is adequate to safely
localize the vehicle while cruising. Thus, in order to perform
unbiased comparisons, both trajectories are interpolated with
a Catmull
Rom spline [26] and parametrized relative to
their length; using the common parameter, we estimate the
optimal (in the least squares sense) affine transformation that
minimizes the distances between the two splines for common
parameter values. The choice of interpolating spline can be
arbitrary, but Catmull-Rom curves are more convenient to
construct locally with only four points at a time. It should
be stressed that in order to obtain corresponding parameters
values between the GPS and vision based trajectories, it
is necessary to re-parametrize the curves by means of arc
length. The general concept is illustrated in Figure 8.
Fig. 8: Parameter correspondence between the GPS (blue)
and visual odometry (red) interpolated curves irrespectively
of scale. Synchronization is achieved using the GPS-frame
index log.
Suppose we fit two splines g(tg) and v(tv) where tg,tv ∈
[0,1] to both GPS and vision based odometry points using
a common parameter u ∈[0,1]. It is necessary for this
parameter to reflect percentage of overall arc-length in either
curve. Thus, the warping functions for tg (u) and tv (u) can
be computed from the following differential equations:
sg (u)
=
Z tg(u)
0
g(t) dt
(15)
sv (u)
=
Z tv(u)
0
v(t) dt
(16)
where sg and sv are the arc-lengths of g and h respectively.
Having obtained the reparametrized splines in terms of u,
it is now a matter of ordinary least squares to fit a 2D
affine transformation A that minimizes the distance between
a number of sampled points in g and v for common values
of u:
ˆA = argmin
A
(
n−1
∑
k=0





Av

tv

k
n −1

−g

tg

k
n −1





2)
(17)
where n is the number of uniform samples in [0,1].
B. Odometry estimates
Figures 9 and 10 illustrate odometry estimates and GPS
ground truth superimposed on satellite imagery for two
indicative sequences. Overall data was recorded in the Tamar
river, Devon, UK. The trajectories are generally long (several
hundred meters); unfortunately, the vehicle had to follow
specific routes in order to avoid shallow waters and this many
times resulted in trajectories without many twists. It should
be noted however that transient rotational and linear motion
is generally rich as shown in the actual footage, yet it is not
reflected in the GPS based trajectory for obvious reasons.
Fig. 9: GPS ground truth spline (blue) and estimated visual
odometry spline (red) overlaid in satellite imagery. Approx-
imate distances along the x and y axes are given to indicate
scale.
Fig. 10: GPS ground truth spline (blue) and estimated
visual odometry spline (red) overlaid in satellite imagery.
Approximate distances along the x and y axes are given to
indicate scale.
We evaluated the quality of localization in a total of 8
trajectories, averaging approximately 350m total distance
0
5
10
15
20
25
Error (m)
0
0.002
0.004
0.006
0.008
0.01
0.012
Normalised frequency
Error Distribution
Fig. 11: Position error distribution obtained from 8 routes in
the river.
covered on the water. The position error was evaluated in
meters using the method described in Section IV-A. On
average, the maximum position error is typically in the range
of 8-10m with the exception of occasional occurrences in
the 20m range, such as in the 400m long trajectory of
Figure 15. The position error distribution obtained from all
8 sequences is depicted in Figure 11. Interestingly, the plot
is very reminiscent of the χ2 distribution, which empirically
indicates consistency with normally distributed relative pose
squared error.
Figures 12, 13, 15, 14 illustrate plots generated from 4
selected sequences, illustrating comparison of visual odom-
etry with ground truth, position error distribution and its
progression with distance traveled by the vehicle.
V. CONCLUSION
We have presented a method to obtain reliable visual
odometry estimates for an unmanned sea-surface vehicle
using imagery of the shore, in order to accommodate au-
tonomous cruise when GPS feedback becomes unavailable.
To the best of our knowledge, this is the first time that
a sea-surface vehicle location is obtained exclusively with
standard Visual SLAM techniques. Except for the typical
shortcomings of outdoor visual SLAM (brightness, shading,
motion blur, environmental conditions, etc.), the application
at hand presents us with additional challenges associated
with the absence of a ground plane and extreme scene-depth
variation. Typically, the ground plane endows the imagery
with features that correspond to near-by world points based
on which, camera motion can be reliably estimated. In
contrast, for imagery obtained on a cruising boat, there is no
ground plane and motion must be estimated from features
in the background which may or may not be near, as depth
varies significantly.
To cope with depth variation in the useful portion of the
background, we advocate the use of structure-less visual
SLAM with the aid of orientation priors from an IMU.
With this information, we are able to cast the relative pose
-350
-300
-250
-200
-150
-100
-50
0
x - axis (m)
-5
0
5
10
15
20
25
30
y - axis (m)
GPS trajectory and Vision based estimated trajectory
GPS trajectory
Estimated trajectory
(a) Visual odometry vs GPS trajectory.
0
50
100
150
200
250
300
350
Distance travelled (m)
0
0.5
1
1.5
2
2.5
Error (m)
Error vs distance
(b) Position error vs Distance travelled.
0
0.5
1
1.5
2
2.5
Error (m)
0
1
2
3
4
5
6
Normalised frequency
10 -3
Error Distribution
(c) Error distribution.
Fig. 12: An approximately 340m long route along the Tamar river, near Halton Quay, Devon, UK.
0
50
100
150
200
250
x - axis (m)
0
50
100
150
200
250
y - axis (m)
GPS trajectory and Vision based estimated trajectory
GPS trajectory
Estimated trajectory
(a) Visual odometry vs GPS trajectory.
0
50
100
150
200
250
300
350
Distance travelled (m)
0
1
2
3
4
5
6
7
8
9
10
Error (m)
Error vs distance
(b) Position error vs Distance travelled.
0
2
4
6
8
10
Error (m)
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Normalised frequency
10 -3
Error Distribution
(c) Error distribution.
Fig. 13: An approximately 285m long route along the Tamar river, in Bohetherick, Devon, UK.
-50
0
50
100
150
200
x - axis (m)
-180
-160
-140
-120
-100
-80
-60
-40
-20
0
y - axis (m)
GPS trajectory and Vision based estimated trajectory
GPS trajectory
Estimated trajectory
(a) Visual odometry vs GPS trajectory.
0
50
100
150
200
250
300
350
Distance travelled (m)
0
5
10
15
20
25
Error (m)
Error vs distance
(b) Position error vs Distance travelled.
0
5
10
15
20
25
Error (m)
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
Normalised frequency
Error Distribution
(c) Error distribution.
Fig. 14: An approximately 400m long route along the Tamar river, in Calstock, Devon, UK.
0
50
100
150
200
250
300
350
400
x - axis (m)
0
20
40
60
80
100
120
140
160
180
y - axis (m)
GPS trajectory and Vision based estimated trajectory
GPS trajectory
Estimated trajectory
(a) Visual odometry vs GPS trajectory.
0
50
100
150
200
250
300
350
400
450
Distance travelled (m)
0
1
2
3
4
5
6
7
8
9
Error (m)
Error vs distance
(b) Position error vs Distance travelled.
0
1
2
3
4
5
6
7
8
9
Error (m)
0
1
2
3
4
5
6
7
Normalised frequency
10 -3
Error Distribution
(c) Error distribution.
Fig. 15: An approx6imately 450m long route along the Tamar river, near Cotehele, Devon, UK.
problem directly in terms of image projections, thereby
circumventing the map which may contain a number of
noisy reconstructions. Our relative pose equations do not
discard distant points, but they simple ignore them when
their disparity is not large enough to provide additional mo-
tion information. However, regardless of depth, a point can
always be an outlier, so in order to combine our model with
RANSAC, we propose a robust error reflecting epipoplar
plane misalignment. The error is valid for any type of
degenerate configuration, including pure rotational motion.
To avoid having to use the map during error (reprojection)
refinement, we employ a cost function which is formed by
the sum of standard epipolar constraints.
The specifics of the application described herein, naturally
do not exactly match the conditions in available datasets.
We therefore recorded our own sequences and timestamped
inertial data and GPS readings with frame indexes in each
sequence. To obtain unbiased comparisons with ground truth,
it was necessary to compare the GPS-generated trajectory
with visual odometry using a common parameter that reflects
equal proportions of arc-length with respect to the origin in
both curves. To do so, we interpolate both curves using a
spline and thereafter, reparametrize resulting curves in terms
of their arc-length in the interval [0,1]. The use of a common
arc-length parameter allows for actual-scale comparisons
with the GPS trajectory.
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