Journal of Biomechanics 33 (2000) 1751}1754
Technical note
A method to synchronise cameras using the direct linear
transformation technique夽
Philippe Pourcelot *, Fabrice AudigieH , Christophe Degueurce , Didier Geiger,
Jean Marie Denoix
UMR INRA-ENVA Biome& canique du Cheval, Ecole Nationale Ve& te& rinaire d+Alfort, 7 Av. du Gal de Gaulle, 94704 Maisons-Alfort Cedex, France
E.A. CNRS 7052, Laboratoire de Me& canique Physique, Universite& Paris XII 61, Av. du Gal de Gaulle, 94010 Cre& teil Cedex, France
Accepted 6 April 2000
Abstract
The aim of this paper is to present a method which enables the recordings of cameras that are not equipped with a synchronisation
system to be synchronised a posteriori. Using the Direct Linear Transformation technique, this method estimates the phase di!erence
between two cameras by minimising the reconstruction errors of a moving point. Once the phase di!erence value is known, one of the
recordings is chosen as a reference and the second one is synchronised to the "rst by cubic spline interpolation. 2000 Elsevier
Science Ltd. All rights reserved.
Keywords: Synchronisation; Camera; DLT; Kinematics; Genlock
1. Introduction
The Direct Linear Transformation (DLT) method (Abdel-Aziz and Karara, 1971; Marzan and Karara, 1975)
and its re"ned versions (Hatze, 1988; Gazzani, 1993)
allow the determination of the 3-D co-ordinates of
a point from two or more 2-D views of this point. These
methods are commonly used in kinematic analysis of
human and animal movement. This is due to the accuracy of the results obtained and the great #exibility in
camera set-up (Wood and Marshall, 1986; Hatze, 1988;
Challis and Kerwin, 1992; Chen et al., 1994; Hinrichs and
McLean, 1995). Another advantage of these methods is
that even though only two cameras are required, additional ones can be accommodated (Challis and Kerwin,
1992). Nevertheless, the di!erent cameras need to be perfectly synchronised to preserve the accuracy of the
results. Cameras with precise phase-locked synchronisation
* Corresponding author. Tel.:#33#1-43-96-70-49; fax: #33#143-96-31-62.
E-mail address: [email protected] (P. Pourcelot).
夽
Presented in part at the World Congress on Medical Physics and
Biomedical Engineering in Nice, France, 14}19 September 1997.
are 10 to 20 times more expensive than home video
cameras. It is tempting to use home video cameras to
increase the number of cameras at a low cost and to
develop a technique allowing the synchronisation of
these cameras. In previous studies, cameras' recordings
were synchronised by detecting a particular event recorded simultaneously by all the cameras. Miller et al.
(1980) synchronised their recordings by "ring a light
emitting diode, Degueurce et al. (1996) switched on
a light bulb. Such synchronisation methods do not take
into account for the relative time o!set between the
cameras, which may result in high inaccuracy of 3-D
kinematic data. Yeadon (1989, 1990) proposed two di!erent methods to synchronise cameras. The "rst one was
based on the digitised data of a ski jumper obtained at
take o! and landing and required to know the vertical
plane in which the ski jumper's centre of mass lay at take
o!. The second one used a timing device in view of each
camera. The present study describes a method that enables the synchronisation of multiple cameras by exploiting aspects of the DLT method. Firstly, the cameras are
approximately time matched by switching on a light
bulb. Secondly, a numerical method, presented in this
paper, is used to estimate the time o!set between the
cameras. This time o!set is then used to synchronise the
recordings of the cameras.
0021-9290/00/$ - see front matter 2000 Elsevier Science Ltd. All rights reserved.
PII: S 0 0 2 1 - 9 2 9 0 ( 0 0 ) 0 0 1 3 2 - 9
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P. Pourcelot et al. / Journal of Biomechanics 33 (2000) 1751}1754
2. Method
The Direct Linear Transformation equations are:
¸ X#¸ >#¸ Z#¸
,
x#dx" (1)
¸ X#¸ >#¸ Z#1
¸ X#¸ >#¸ Z#¸
(2)
y#dy" ¸ X#¸ >#¸ Z#1
in which (x, y) are the digitised co-ordinates of a point,
(dx,dy) are the errors associated with the co-ordinates,
henceforth referred to as DLT errors, (X, >, Z) are the
object's space co-ordinates, and (¸ , ¸ ,2, ¸ ) the
unknown DLT parameters of each camera.
The DLT errors (dx,dy) presented above are the quanti"cation of the inconsistencies of location of a point in
two (or more) camera views. Once the object-space coordinates of a point are calculated, these DLT errors can
be computed, for each camera, using DLT equations (1)
and (2).
The use of non-synchronised cameras introduces an
additional error into these DLT errors. The phase di!erence between two cameras can be estimated by searching
for the phase di!erence value which minimises the mean
DLT errors (dx,dy) of a moving point. This mean DLT
error per frame and per camera can be calculated as follows:
H G,
(dx #dy
GH
GH
H
G
mean DLT error"
,
2NbF
(3)
where dx and dy are the DLT errors calculated at
GH
GH
frame i on camera j along the camera image x- and y-axis,
respectively, and NbF is the total number of frames
analysed.
The phase di!erence value giving the lowest mean
DLT error can be determined by successive approximations and then used to synchronise a posteriori both
recordings. To test di!erent phase di!erence values, and
"nally to synchronise both recordings, interpolated 2-D
co-ordinates of the points are calculated for one of the
two cameras from their digitised co-ordinates using an
interpolation method such as spline functions.
3. Experimental evaluation
A routine implementing this synchronisation method
was developed and added to a more general computer
program that tracks the markers on the 2-D video images, calibrates the cameras and calculates the 3-D coordinates of the markers.
3.1. Apparatus and recording procedure
In order to test the accuracy of the results obtained
with this method, the rotations (1.16 rps) of a 64 cm
Fig. 1. The motion of a wheel "tted with one marker was recorded by
four Hi 8 mm video cameras placed in such a way that each side of the
wheel was recorded by 2 cameras. To avoid temporary concealment of
the marker, the wheel's axis was suspended to a rigid body with nylon
yarns.
diameter wheel "tted with one marker was recorded in
outdoor conditions by four Hi 8 mm video cameras
(Sony FX 700, 50 Hz) (Fig. 1). These cameras imaged
a 6 m long "eld of view. Their shutter speed was set at
1/1000 s. While the wheel was recorded, a light bulb,
placed in the "eld of the 4 cameras, was switched on every
10 s. For each camera, the frame on which the "rst light of
the bulb appeared was selected to synchronise approximately the four recordings.
3.2. Film digitisation and marker detection
The image processing was conducted o!-line. The recordings were analysed for sequences of about 3 s (1.5 s
before and after the "ring of the light bulb). These sequences were digitised using a video card (VideoVision
Studio, Radius) with a resolution of 768 columns by 576
lines in 256 grey scale. The computer program determined automatically the positions of the marker.
3.3. Camera synchronisation
The numerical synchronisation of the cameras was
made for each digitised sequence. This synchronisation
was conducted as follows. One camera was chosen as
a reference, and the others were synchronised with it. To
synchronise one camera with the reference one (called
slave and master cameras, respectively), di!erent values
of phase di!erence between both cameras were considered and tested. The tests were performed by calculating, for the slave camera, interpolated 2-D locations of
the moving marker using cubic spline functions. For each
phase di!erence value considered, the mean DLT error
was computed for one entire rotation of the moving
marker using formula (3). The value of phase di!erence
corresponding to the lowest mean DLT error was
P. Pourcelot et al. / Journal of Biomechanics 33 (2000) 1751}1754
1753
Fig. 2. Mean DLT error versus phase di!erence between two cameras.
The phase di!erence value corresponding to the minimal value gives an
estimation of the phase di!erence value between the cameras (arrow).
determined using an iterative method (Fig. 2). This phase
di!erence value was then used to synchronise both recordings by calculating, for the slave camera, interpolated 2-D co-ordinates of the marker using cubic spline
functions.
3.4. 3-D reconstruction of the marker
To evaluate the e!ects of this synchronisation method
on the kinematic data, four di!erent reconstructions of
the marker were carried out: two left reconstructions
using cameras 1 and 2, and two right reconstructions
using cameras 3 and 4. In both cases, the "rst reconstruction was performed with numerical synchronisation of
the cameras and the second without. For each of these
two cases, the distance between the left and right reconstructions of the marker was calculated. The two distances were then compared. Moreover, the consistency of
the phase di!erences between cameras 1 and 2, 1 and 3,
1 and 4, 2 and 3, 2 and 4, and 3 and 4 were studied.
4. Results
4.1. Distances between the left and right reconstructions
of the marker
The distances calculated with and without synchronisation between the left and right reconstructions of
the marker are shown in Fig. 3. This "gure was obtained
by superimposition of 3 rotations of the wheel. The start
of the rotation (t"0 s) corresponded to a position of the
marker at 3 o'clock. The phase di!erence values calculated between the left (1 and 2) and right (3 and 4)
cameras were !36 and !5% of the time interval between two frames, respectively. In other words, as the
recording frequency of the cameras used in this study was
Fig. 3. Distances calculated with and without synchronisation between
the left and right reconstructions of a marker (superimposition of
3 rotations). The highest distances were observed with non-synchronised cameras when the marker was at 6 and 12 o'clock.
50 frames per second, the time interval between two
consecutive frames was 0.02 s and consequently, the position of the marker was recorded by the second camera
0.0072 s before the "rst one (as indicated by the negative
value of the phase di!erence). The mean distances obtained with and without synchronisation were
0.68$0.20 and 1.81$0.75 cm, respectively.
4.2. Consistency of the phase diwerences between cameras
The phase di!erences values between cameras 1 and 2,
1 and 3, 1 and 4, 2 and 3, 2 and 4, and 3 and 4 were !36,
!23, !27, #15, #6 and !5% of the time interval
between two frames, respectively. The consistency of
these phase di!erence values was high but not perfect. As
an example, the phase di!erence value between cameras
1 and 2 (!36%) was not perfectly equal to the sum of
the phase di!erences between cameras 1 and 3, and
cameras 3 and 2 (!23 !15"!38%). The highest
inconsistencies were less than 5% of the time interval
between two frames.
5. Discussion
The distance between the left and right reconstructions
of the marker obtained for non-synchronised cameras
presented two maxima for each rotation of the wheel
(Fig. 3). The "rst one occurred approximately when the
marker was at 6 o'clock and the second one at 12. These
high distances were mainly due to di!erences between the
transversal co-ordinates (Y-axis) of the left and right
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P. Pourcelot et al. / Journal of Biomechanics 33 (2000) 1751}1754
make it impossible the cabling between cameras. In practice this synchronisation method can be performed using
the digitised data of landmarks or markers on the body
of interest.
Acknowledgements
This study was supported by the Institut National de
la Recherche Agronomique and the Service des Haras et
de L'Equitation.
References
Fig. 4. In this example, the marker has been recorded at time t by the
camera 1 and at time t#dt by the camera 2. At 12 o'clock the 3-D
co-ordinates of the marker were greatly translated along Y-axis but the
DLT errors calculated were very small because of the almost perfect
intersection of the marker's rays. At 9 o'clock, opposite results were
found, no signi"cant translation along the Y-axis occurred but large
DLT errors were observed due to the high distances which separated
the marker's rays at the point where they were the closest.
reconstructions. This phenomenon is due to the phase
di!erences between the cameras and to the position of
these cameras with respect to the wheel. At 6 and 12
o'clock, the marker's location (the point for which the
marker's rays are the closest) obtained with the left reconstruction was not in the main plane of the wheel but
greatly translated along the Y-axis (Fig. 4). This phenomenon occurred to a lesser degree for the right reconstruction of the marker because of the small phase di!erence
value between both right cameras. In contrast, the DLT
errors calculated at 6 and 12 o'clock were very small
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was very high. With synchronised cameras, the high
distances observed at 6 and 12 o'clock disappeared so
that the mean distance between the left and right reconstructions of the marker was equal to the one calculated
when the marker was static.
This synchronisation technique allows the use of
cameras which cannot be synchronised either because
they are devoid of a genlock or the recording conditions
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