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H. Mecheri - Offset correction when comparing 3D joint angles from two different motion capture systems

*Corresponding author. Email: hakim.mecheri@irsst.qc.ca 1

Offset correction when comparing 3D joint angles from

two different motion capture systems

H. Mecheri*, X. Robert-Lachaîne*, C. Larue* and A. Plamondon*

* Institut de recherche Robert Sauvé en santé et en sécurité du travail (IRSST),

505 Boul. De Maisonneuve Ouest, Montréal, Québec, Canada, H3A 3C2

Abstract

Inertial and magnetic wearable systems are becoming widely used as a Motion Capture Systems (MCS) in the

Biomechanical field. When comparing these systems to a golden standard system, for joint angles, the results are

affected by two errors: the first one is due to the system itself: how good the orientations of the segments are

estimated and the second is due to the misalignment between axes of local coordinate systems (LCS) of the

segments defined by the two MCS. The second error can be eliminated by choosing a protocol which allows us

to construct the same LCS for a segment in both MCSs. This solution is not always possible when using a

commercial system which uses its specific procedure for defining the LCS of the segments. The alternative

solution to eliminate the second error is to find this misalignment and correct it. The aim of this work is to

present a simple method for identifying the offset due to different definition of segments for two different

systems. In this study, two systems are compared: a full body inertial and magnetic system MVN (MVN; Xsens

Technologies BV, Enschede, The Netherlands) and an optoelectronic system Optotrak (Optotrak Northern

Digital, Waterloo, Canada). One subject was equipped with a full body system and Optotrak clusters. MVN

system includes seventeen sensors for seventeen segments. On each segment we fixed a cluster of four Optotrak

markers. For MVN, the segments are defined following its own calibration procedure. For Optotrak the segments

were constructed following the calibrated anatomical systems technique (CAST) protocol and the ISB

recommendations. The subject was asked to perform a trial of boxes handling of about 30 minutes. The Root

Mean Square Error (RMSE) and the Pearson correlation coefficient (r) were calculated for joint angles before

and after removing the misalignment bias. The RMSE dropped dramatically for some segments of the upper

body. For example, the RMSE for the right elbow longitudinal axis (Y) dropped from 25 to 3°, which is close to

a 90% improvement of the results. As a conclusion of this study, the introduced method was efficient for

removing the offset due to difference in anatomical segment calibration.

Keywords: Alignment, Local frames, Offset, Optotrak, Xsens.

1. Introduction

Inertial measurement units (IMUs) are becoming

widely used for motion analysis espcially in the

biomechanical field. Validation of these systems

are often performed against a golden standard

optoelectronic system (Plamondon et al., 2007). In

general, the comparison of two motion capture

systems (MCS) showed a good agreement in the

wave shape especially for the principal axis of the

movement but with a certain bias (Perez et al.,

2010). When comparing two MCS for joint angles,

the results are affected by two components: the first

one is due to the technological error i.e. how good

the orientations of the segments are estimated by

the MCS and the second is due to the misalignment

between axes of local coordinate systems (LCS) of

the segments defined by the two MCS. The second

component can be dealt with by choosing a protocol

allowing to construct the same LCS for a segment

in both MCS (Alberto et al., 2010; Kim and

Nussbaum, 2013). This solution is not always

possible when using a commercial system which

uses a specific procedure for defining the LCS of

the segments, like MVN (MVN; Xsens

Technologies BV, Enschede, The Netherlands). The

alternative solution to deal with the second

component is to find this misalignment and correct

it as described in previous studies (Koning et al.,

2012; Li and Zhang, 2014). The aim of this study

was to propose a simple method for identifying the

offset due to different definition of local coordinate

systems for two different motion capture systems

and isolate the technological error .

2. Materials and Methods

2.1. Subject

Two systems are compared: a full body IMU MVN

(MVN; Xsens Technologies BV, Enschede, The

Netherlands) and an optoelectronic system

including 8 cameras (Optotrak Northern Digital,

H. Mecheri - Offset correction when comparing 3D joint angles from two different motion capture systems

2

Waterloo ON, Canada). A subject is equipped with

a full body system and marker clusters (see Fig. 1).

MVN system includes seventeen sensors for

seventeen segments. On each sensor (segment) we

fixed a cluster of four Optotrak markers. For MVN,

the segments were defined following a Tpose

calibration procedure. For Optotrak the segments

were constructed following the CAST protocol

(Cappozzo et al., 1995) and following the ISB

recommendations (Wu et al., 2002; Wu et al.,

2005). The subject was asked to perform a trial of

boxes handling of about 30 minutes. Data were

recorded at 30 samples/s for the two systems. The

systems were synchronized using MVN Studio 3.5

with a trigger signal coming from the Optotrak

system. A commercial software, Matlab 2014a (The

MathWorks Inc., Natick, MA, USA) was used to

process the data.

Figure 1: The subject equiped with MVN and Optotrak

systems.

2.2. Systems alignment

The MVN system provides the angular velocity of

each segment 𝝎𝑺𝒆𝒈𝑴𝑽𝑵 in its global coordinate

system (SegMVN in the subscript stands for

segment defined within MVN system). Optotrak

system on the other hand provides the orientation of

each segment in its global coordinate system. The

angular velocity 𝝎𝑺𝒆𝒈𝑶𝑷𝑻 (SegOPT in the subscript

stands for segment defined within Optotrak system)

is estimated by the orientation’s derivative (Chou,

1992). Having the orientations and angular

velocities of each segment in the two global

systems, the angular velocities are transposed to the

LCS of each segment. The relative orientation of

the segments defined in the two systems and

presented by the quaternion 𝒒𝑺𝒆𝒈𝑴𝑽𝑵

𝑺𝒆𝒈𝑶𝑷𝑻 !is estimated

by a matching method using angular velocities (de

Vries et al., 2009).

Figure 2: Right Elbow Flexion angle given by: MVN,

Optotrak not corrected (OpOrig) and Optotrak after

correction (OpCorr).

2.3. Offset correction

For MVN, Joint angles are directly provided as an

output. For Optotrak, joint angles are calculated

from the relative orientation of the two adjacent

segments of the joint. If 𝒒𝑺𝒆𝒈𝑶𝑷𝑻_𝑷𝒓𝒐𝒙

𝑶𝑷𝑻 and

𝒒𝑺𝒆𝒈𝑶𝑷𝑻_𝑫𝒊𝒔𝒕

𝑶𝑷𝑻 !are the orientation quaternions of the

proximal and distal segments respectively in the

global frame of Optotrak, the relative orientation is

given by:

𝑞!"#$%&_!"#$

!"#$%&_!"#$= (𝑞!"#$%& _!"#$

!"# )*!𝑞!"#$%&_!"#$

!"#

(1)

Where 𝒒 is the quaternion conjugate of 𝒒. From this

relative orientation, the joint angles are extracted as

Euler angles in ZXY sequence for all joints, except

for the shoulders which is in XZY sequence to

match MVN standards.

The offset is compensated by using the orientation

of the MVN segments in Optotrak rather than the

Optotrak segments. The orientation of the MVN

segment in Optotrak is estimated by:

𝑞!"#$%&

!"# =𝑞!"#$%&

!"# ∗𝑞!"#$%&

!"#$%&

(2)

Equation (1) becomes:

𝑞!"#$%&_!"#$

!"#$%&_!"#$= (𝑞!"#$%$ _!"#$

!"# )*!!𝑞!"#$%&_!"#!

!"#

(3)

2.4. Error quantification

To quantify the effect of the bias correction

method, we compare the joint angle curves given

by MVN with the ones extracted with (Eq.1) which

are with bias, and with (Eq.3) which are without

H. Mecheri - Offset correction when comparing 3D joint angles from two different motion capture systems

3

bias. We used the root mean square error (RMSE)

and the Pearson’s linear correlation coefficient (r).

Figure 3: LCS of the right forearm defined by Optotrak

and MVN. The Optotrak LCS is considered as the one

wich matches the ISB recomandations

3. Results

A typical curve of a joint angle is shown in Fig. 2.

We can visualize the effect of the bias correction on

the right elbow flexion angle. Table 1, presents the

curve similarity parameters for the 3 axes of the

right joints between the MVN joint angles and the

original Optotrak angles (with the bias = 1) and the

corrected Optotrak angles (without bias = 0). We

have similar results for the left joints. The

misalignment between the two LCS of the right

forearm constructed with MVN and Optotrak can

be visualized in Fig. 3. This misalignment produces

the bias shown in the graphics of Fig. 2 and the

results of Table 1.

Figure 4: LCS of the right leg defined by Optotrak and

MVN. The Optotrak LCS is considered as the one wich

matches the ISB recomandations

4. Discussion

A LCS of a segment constructed in two different

environments should be considered as two different

segments. In fact, even if we are tracking the same

segment with two different systems, we are not

tracking the same LCS. If we have one MCS but

two definitions of LCS of the same segment, than

we will have a constant bias. This bias can be

removed if we know the relation between the two

LCSs. The same idea is used when using two

different MCS. The method presented in this work

try to find the relation between two LCS of the

same segment constructed in two different MCS.

When the bias is correctly calculated and removed,

the only error between the two joint angle curves

should be attributed to the performance of

orientation estimation. For example, if we look at

the flexion angle of the right wrist in Table 1, the

RMS error drops from 11 to 4°. The first value

includes both the technological error and the

misalignment of the LCS of the right hand and right

forearm. The second value (4°) corresponds only to

the technological error.

Table 1: Curves similarity parameters with and without

Bias removing: Axe is the 3 axis of rotation, Bias is 1

when using the original data and is 0 when the bias is

removed.

Joint

Axe

Bias

r

RMSE

Right Wrist

Z

1

0.78

11

Right Wrist

Z

0

0.92

4

Right Wrist

X

1

-0.14

12

Right Wrist

X

0

0.87

3

Right Wrist

Y

1

0.77

5

Right Wrist

Y

0

0.81

4

Right Elbow

Z

1

0.99

5

Right Elbow

Z

0

0.99

3

Right Elbow

X

1

0.01

25

Right Elbow

X

0

0.97

3

Right Elbow

Y

1

0.56

18

Right Elbow

Y

0

0.97

4

Right Shoulder

Z

1

0.91

20

Right Shoulder

Z

0

0.99

5

Right Shoulder

X

1

0.75

35

Right Shoulder

X

0

0.98

4

Right Shoulder

Y

1

0.42

27

Right Shoulder

Y

0

0.99

7

Right Ankle

Z

1

0.91

7

Right Ankle

Z

0

0.91

5

Right Ankle

X

1

0.87

5

Right Ankle

X

0

0.87

5

Right Ankle

Y

1

0.56

8

Right Ankle

Y

0

0.56

8

Right Knee

Z

1

0.98

4

Right Knee

Z

0

0.98

3

Right Knee

X

1

0.77

4

Right Knee

X

0

0.93

3

Right Knee

Y

1

0.95

4

Right Knee

Y

0

0.96

4

Right Hip

Z

1

0.99

9

Right Hip

Z

0

0.99

3

Right Hip

X

1

0.96

4

Right Hip

X

0

0.98

2

Right Hip

Y

1

0.92

4

Right Hip

Y

0

0.93

3

4

Also, shown in Table 1, the bias is more important

for the segments of the upper body than for those of

the lower body. As an example, Fig. 4 shows the

LCSs of the right lower leg defined by Optotrak

and MVN systems. The two LCSs are close to each

other comparatively to the LCSs of the right

forearm (see Fig. 3), which lead to a smaller bias

between the two LCS.

Some minor aspects are needed prior to the

instrumentation and during the data collection.

Once the Optotrak clusters are fixed to the IMUs, a

short trial of functional movements must be

executed. This trial requires that the segments are

moved several times around their three axes and

last approximately less than a minute. An alignment

between the two LCS is obtained by matching the

angular velocities (de Vries et al., 2009).

Afterwards, the observed difference between the

two systems is attributable to: the technological

error (how good the inertial system estimates 3D

orientations or the performance of the Kalman

filter), to the LCSs misalignment between the

clusters and the sensors and to the anatomical

calibration approach (misalignment between the

LCSs of the segments defined in Optotrak and

MVN environment). Optoelectronic systems use

anatomical landmarks to found the segment LCS.

Since IMUs rely on orientation estimation and not

position, the calibration is based on specific posture

or motion. The calibration approach creates an

offset between the two LCS. The proposed method

can help to correct this offset and provide more

similar joint angles between the two systems.

5. Conclusion

A simple method is proposed to remove the bias

caused by two different definitions of the same

segment. For validation studies this method will be

helpful to isolate the error caused by the system

itself (technological error). This method is based on

matching the estimated or measured angular

velocities by the two different MCSs of the same

individual segment in order to find the anatomical

calibration difference between LCSs of this

segment. The limitation of the method is to have

movements with angular velocities above 0.5 rad/s

for all segments, to avoid the noise level. These

movements should also be around three more or

less orthogonal axes in order to have enough data

on the three axes of the LCS of the segment.

Acknowledgement

The authors are grateful to the Institut de Recherche

Robert Sauvé en Santé et en Sécurité du Travail

(IRSST) for their financial support of the study

through grant #2012-0040 and the postdoctoral

scholarship program.

References

Alberto, F., Andrea, G.C., Pietro, G., Michele, R.,

Monique, H., Angelo, C., Angelo, D., 2010. First in

vivo assessment of ‘‘Outwalk’’: a novel protocol

for clinical gait analysis based on inertial and

magnetic sensors. Medical & biological engineering

& computing 48, 1-15.

Cappozzo, A., Catani, F., Della Croce, U., Leardini,

A., 1995. Position and orientation in space of bones

during movement: anatomical frame definition and

determination Clinical Biomechanics 10, 171-178.

Chou, J.C.K., 1992. Quaternion Kinematic and

Dynamic Differential Equations. IEEE Transactions

on Robotics and Automation 8, 53-64.

de Vries, W.H., Veeger, H.E., Baten, C.T., van der

Helm, F.C., 2009. Magnetic distortion in motion

labs, implications for validating inertial magnetic

sensors. Gait Posture 29, 535-541.

Kim, S., Nussbaum, M.A., 2013. Performance

evaluation of a wearable inertial motion capture

system for capturing physical exposures during

manual material handling tasks. Ergonomics 56,

314-326.

Koning, B.H.W., van der Krogt, M.M., Baten ,

C.T.M., Koopman, H.F.J.M., 2012. Three

dimensional rotation offset correction, XII

International Symposium on 3D Analysis of Human

Movement, Bologna, Italy, pp. 223-226.

Li, Q., Zhang, J.T., 2014. Post-trial anatomical

frame alignment procedure for comparison of 3D

joint angle measurement from magnetic/inertial

measurement units and camera-based systems.

Physiological measurement 35, 2255-2268.

Perez, R., Costa, U., Torrent, M., Solana, J.,

Opisso, E., Caceres, C., Tormos, J.M., Medina, J.,

Gomez, E.J., 2010. Upper limb portable motion

analysis system based on inertial technology for

neurorehabilitation purposes. Sensors 10, 10733-

10751.

Plamondon, A., Delisle, A., Larue, C., Brouillette,

D., McFadden, D., Desjardins, P., Lariviere, C.,

2007. Evaluation of a hybrid system for three-

dimensional measurement of trunk posture in

motion. Appl Ergon 38, 697-712.

Wu, G., Siegler, S., Allard, P., Kirtley, C., Leardini,

A., Rosenbaum, D., Whittle, M., D'Lima, D.,

Cristofolini, L., Witte, H., Schmid, O., Stokes, I.,

2002. ISB recommendation on definitions of joint

coordinate system of various joints for the reporting

of human joint motion—part I: ankle, hip, and

spine. Journal of biomechanics 35, 543-548.

Wu, G., van der Helm, F.C.T., Veeger, H.E.J.,

Makhsous, M., Van Roy, P., Anglin, C., Nagels, J.,

Karduna, A.R., McQuade, K., Wang, X., Werner,

F.W., Buchholz, B., 2005. ISB recommendation on

definitions of joint coordinate systems of various

joints for the reporting of human joint motion—Part

II: shoulder, elbow, wrist and hand. Journal of

biomechanics 38, 981-992.