View Full Version : Summary: Accuracy of 2D CR Methods

Julie Wilson Steege
04-26-1996, 01:22 AM
The following is a summary of responses to my posting about the accuracy of
various methods of approximating 2D joint centers of rotation from motion
analysis data. Thanks to all who responded; your suggestions were
extremely helpful.

Julie Wilson Steege
Research Engineer
Programs in Physical Therapy, Northwestern University

******************THE ORIGINAL POSTING********************


We are using an ELITE motion analysis system to collect whole-body, 3D
kinematic data, although we are performing 2D, sagittal plane analysis of
pulls made while standing. Because we study whole-body movements, we deal
with many joints including the ankle, knee, hip, lumbar spine, shoulder,
elbow, wrist, and neck. Currently, we palpate bony landmarks in order to
estimate the location of each joint's center of rotation and then place
reflective markers directly over these estimated joint centers. We are
concerned about the accuracy of this method, however, and are looking for a
more precise approach.

Recently, several questions have been posted to BIOMCH-L regarding the best
way of estimating specific joint center locations from anatomical landmarks.
It is clear from the responses to these postings, as well as from our search
of the literature, that there are several ways to approach the problem of 2D
joint center identification. These include:

(1) Putting markers directly on the estimated joint center locations;
(2) Putting markers on various anatomical landmarks and then using them to
infer a joint center location;
(3) Using an array (rigid or not) of at least 2 markers on each segment and
rigid body analysis to compute joint center locations from "calibration
movements", performed before the start of the experiment, that involve
substantial changes in joint angles;
(4) Using an array on each segment and rigid body analysis on the movements
in the experiment to determine the instantaneous center of rotation.

It seems that many labs use a combination of these methods due to the
limitations of the various techniques (solutions breaking down when changes
in joint angle are small, peculiarities of a particular joint, etc.).

While we realize that it is difficult to generalize across joints, we are
wondering if anyone has compared the errors in 2D joint center estimation
for these different techniques. We are aware of an article by Spiegelman
and Woo (1987) which compares a geometric (Reuleaux) approach with a rigid
body analysis approach and another by Crisco et al. (1994) who did a more
extensive error analysis of a similar rigid body method.

Crisco, J., Chen, X., Panjabi, M., Wolfe, S. (1994). Optimal marker
placement for calculating the instantaneous center of rotation. Journal of
Biomechanics 27(9): 1183-1187.
Spiegelman, J., Woo, S. (1987). A rigid-body method for finding centers of
rotation and angular displacements of planar joint motion. Journal of
Biomechanics 20(7): 715-721.

Please send any responses to jwsteege@merle.acns.nwu.edu and we will post a
summary of responses. Thanks in advance.

Wynne Lee, Ph.D.
Jim Patton, M.S.
Julie Steege, M.S.

Motor Control and Learning group
Programs in Physical Therapy
Northwestern University
Chicago, Illinois, USA

************************ RESPONSES **********************

FROM: Rebecca A. States, Ph.D. 276H Read Building
Dept. of Health & Kinesiology (409) 862-3229
Texas A & M University, M.S. 4243 (409) 847-8987 (fax)
College Station, Texas 77843 states@tam2000.tamu.edu

I would like to respond to your post about the accuracy of various
methods for estimating joint centers for 2D movements, in particular
about your question ...

> While we realize that it is difficult to generalize across joints, we are
> wondering if anyone has compared the errors in 2D joint center estimation
> for these different techniques. =20

Last fall, I presented a poster on this topic at the Society for=20
Neurosciences meeting, "Comparison of three methods for locating joint=20
centers during planar arm motion" (#174.15). The work was designed to=20
introduce a simple measure of the reliability of joint center estimates,
and to compare three methods for estimating the axes of rotation during
2D movements. A summary, written for a broad audience, follows. I will=20
also send you a copy of the poster by overground mail.

Becky States

Reliability of Three Methods for Measuring Joint Angles

College of Education Seed Grant
3/1/95 - 12/31/95

Rebecca A. States
Department of Health & Kinesiology
College of Education
Texas A & M University

In many studies that measure joint motion, video or=20
other optical systems are used to track the positions of=20
markers attached to the body as they move about in 3-D=20
space. Several problems limit the reliability of this=20
approach. Markers are generally placed on or near bony=20
landmarks so one can judge their location relative to the=20
positions of the underlying bones, and relative to the=20
center of joint rotation. Locating the center of joint=20
rotation is crucial for measuring joint angles and forces=20
that act on the joint. Judging the center of rotation from=20
bony landmarks is not easily accomplished however, since the=20
shapes and sizes of individuals' bones differ. An=20
additional problem arises in that skin and soft tissue=20
motion may cause the markers to move in relation to the=20
bones, further distorting estimates of the center of joint=20
This study seeks to improve reliability of systems that=20
use surface markers to measure joint angles in humans by=20
introducing a new method for evaluating the reliability with=20
which joint centers are located. Segment length=20
variability is suggested for this purpose since under ideal=20
measurement conditions, an individual's segment lengths=20
should remain precisely constant within and between=20
measurement sessions. A clear advantage of this technique=20
is that segment length variability can be easily assessed=20
from data collected during the experimental procedures. =20
Hence, it can provide an indicator of measurement problems,=20
such as particular types of soft tissue motion, that only=20
occur during the experimental procedures. Moreover, this=20
technique is ideally suited to the many studies where=20
multiple joints are measured. For example, in studies that=20
record motion of the arm, one might place markers at the=20
shoulder, elbow, wrist and tip of the index finger. =20
Comparing the variability in segment lengths for the hand,=20
forearm and upper arm can help pinpoint measurement errors=20
linked to one of the joints. If the marker over the elbow=20
were out of place, then the variabilities for the forearm=20
and upper arm segments would be especially large.=20
This study also compared two methods for making post-
hoc adjustments to data from surface markers to see if=20
either one improved reliability beyond that seen in the raw=20
data. Both of these methods are limited to situations where=20
motion stays predominantly within a single plane. In those=20
circumstances, the joint is said to have one and only one=20
axis of rotation (AoR). Hence, the rest of this write-up is=20
concerned only with planar arm movements. =20
Data from planar arm movements that go through a large=20
range of motion can be used to mathematically estimate the=20
location of the true AoR relative to the positions of=20
surface markers. If the calculated AoR differs from the=20
position of the marker which is supposed to track that=20
joint, an adjustment factor can be determined and applied to=20
subsequent data. The adjusted data can then give a better=20
estimate of the AoR. Reliability studies on such post-hoc=20
methods have generally been performed using an ideal=20
mechanism like a mechanical hinge joint (Walter & Panjabi,=20
1988; Fioretti et al., 1990; Bell et al., 1990; Hart et al.,=20
1991) so they can verify the effectiveness of the adjustment=20
method. This study takes a different approach by testing=20
two post-hoc methods in a real-world setting where soft=20
tissue motion and small amounts of out-of-plane motion may=20
occur. This more ecologically valid approach is only=20
possible given the novel technique introduced above for=20
measuring reliability.
Four subjects performed a series of single and multi-
joint movements. This series was repeated five times during=20
each of five sessions. Joint motion was measured during=20
these movements by collecting 3-D position data from 18=20
active markers using an Optotrak 3020 infrared measurement=20
system running at 100 Hz. Markers were placed at the=20
apparent axes of joint rotation for the right wrist, elbow,=20
and shoulder, as well as for the left shoulder. In=20
addition, markers were placed on splints which were attached=20
to the hand, forearm, upper arm, and on a harness attached=20
to the torso. The splints were designed to track the motion=20
of the limb segments rather than to restrict joint motion. =20
Data from the single-joint elbow movement trials were used=20
to find post-hoc adjustment factors for the elbow using two=20
methods - Speigelman & Woo's (1987) 2D method, and a novel=20
3D method described in States (1995). The adjustment=20
factors were applied post-hoc to data from the multi-joint=20
movement trials, a procedure which increases the rigor of=20
the reliability test. Results showed that both post-hoc=20
methods improved within-session reliability, reducing=20
segment length standard deviations by about 50% compared to=20
the raw data. This verifies the usefulness of post-hoc=20
adjustment procedures even under conditions where there may=20
have been significant soft tissue or out-of-plane motion. =20
These results also demonstrate that the reliability of 2-D=20
data can be equivalent to 3-D data, at least for the=20
movements tested. Neither post-hoc method was found to=20
improve between-session reliability, supporting the common=20
practice of making critical comparisons within a single=20
testing session.
This study also examined a related problem, that=20
markers sometimes can not be placed near the apparent AoRs=20
since doing so would occlude them from the view of the=20
camera or other sensing device. In those circumstances,=20
markers are placed at a distance from the joint, and some=20
type of post-hoc adjustment procedure is used to calculate=20
AoR. The abilities of the two post-hoc procedures=20
investigated here to cope with this problem were examined. =20
Each post-hoc procedure was used to locate the AoR for the=20
shoulder joint from markers placed on a shoulder harness.=20
Variability in upper arm and torso segment lengths were=20
compared to those obtained for data from an observational=20
condition where markers were placed directly over the joints=20
for those same trials. Both post-hoc methods were found to=20
be as reliable as the unadjusted raw data from the=20
observational condition, though they were not as reliable as=20
data from the observational condition after it had been=20
adjusted. These results show the post-hoc methods can be=20
used to successfully accommodate for situations where=20
markers must be placed at a distance from the joint, even=20
when there is soft-tissue or limited out-of-plane motion.=20
The methods described here will be applied in future=20
studies investigating joint coordination during skilled=20
movement tasks which are planned by the PI. This study was=20
presented as a poster (#174.15) at the 25th Annual Meeting=20
of the Society for Neuroscience in San Diego, CA, November,=20


Bell, A.L., Pedersen, D.R. & Brand, R.A. (1990). A=20
comparison of the accuracy of several hip center=20
location prediction methods. J. Biomechanics, 23, 617-
Fioretti, S., Jetto, L. & Leo, T. (1990). Reliable in vivo=20
estimation of the instantaneous helical axis in human=20
segmental movements. IEEE Trans. on Biomedical=20
Engineering, 37, 398-409.
Hart, R.A., Mote, C.D.Jr. & Skinner, H.B. (1991). A finite=20
helical axis as a landmark for kinematic reference of=20
the knee. J. Biomedical Engineering, 113, 215-222.
Spiegelman, J.J. & Woo, S.L.-Y. (1987). A rigid-body method=20
for finding centers of rotation and angular=20
displacements of planar joint motion. J. Biomechanics,=20
20, 715-721.
Walter, S.D. & Panjabi, M.M. (1988). Experimental errors in=20
the observation of body joint kinematics. =20
Technometrics, 30, 71-78.

FROM: Cheng Cao (chengcao@engin.umich.edu)
Biomechanics Research Laboratories
Department of Mechanical Engineering and Applied Mechanics
The University of Michigan
Ann Arbor, MI 48109
(313) 936 0367

I have used the 2D rigid body method in calculating the COR for thorax=20
flexion/extension relative to pelvis. I used it in a slightly different=20
way than Spielgman and Woo by considering both pelvis and thorax were=20
moving. As a check (will not be published), I compared the results from=20
the rigid body method and from the traditional graphical method, no=20
significant difference was obtained, execept for the rigid body method=20
was easier to program and less sensative to the time interval size. We=20
have a draft paper available on the topic if you need.

FROM: H=E5kan Lanshammar (hl@frej.teknikum.uu.se)
H=E5kan Lanshammar Systems and Control Group
hl@SysCon.uu.se Uppsala University
Tel: +46-18-18 30 33 P.O. Box 27
Fax: +46-18-50 36 11 S-751 03 Uppsala, SWEDEN

Concerning the problem of finding 2D joint centers, we have done some=20
investigations concerning the hip joint. Results are published in:

Lanshammar H, Persson T, Medved V
Comparison between a marker-based and a marker-free method to estimate=20
centre of rotation using video image analysis. Abstract Volume II, Second=20
World Congress of Biomechanics, Amsterdam, (ed: Blankevoort L, Kooloos J), p=
375, July 10-15, 1994.

Lanshammar, H, Persson T, Medved V
A marker-free method to estimate hip joint centre of rotation, compared with=
radiological determination. World Congress on Medical Physics and Biomedical=
Engineering, Rio de Janeiro, p 111, August 21-26, 1994.

Persson, T, Lanshammar, H, Medved, V
A marker-free method to estimate joint centre of rotation by video image=20
processing. Computer Methods and Programs in Biomedicine, 46, pp 217-224,=

Good luck!

FROM: Alberto Leardini
Oxford Orthopaedic Engineering Centre
Nuffield Orthopaedic Centre
Windmill Road, Headington, Oxford OX3 7LD ENGLAND
tel: ++ (0)1865 227688
fax: ++ (0)1865 742348 email:=

Can I add one more way to estimate 3D joint center?
(5) Using an array (rigid or not) of at least 3 markers on the segment of=20
interest in order to estimate its 6 DoF during exercises, and than collect=
local position of relevant anatomical landmarks from which anatomical=20
center of rotation might be estimated.

You might find some interesting considerations in=20
Cappozzo, A., Catani, F., Della Croce, U. and
Leardini, A.(1995) Position and orientation of bones
during movement:anatomical frame definition and
determination. Cl. Biom. 10(4):171-178.

Good luck

FROM: ariel1@ix.netcom.com (Gideon Ariel )

Surf the web at URL:

FROM: Anita Vasavada (anitav@merle.acns.nwu.edu)
Northwestern University

I just thought I'd add to your responses on 2D joint centers.

First, there is an "ICR Topic" file, on the biomch-l archives, that you may
already know about. This is a compilation of discussions on joint centers
and axes of rotation.

Next, some other papers on rigid body kinematics (though you are probably
aware of most of them, and I don't think any of them include comparisons of
the methods you are discussing):

Spoor and Veldpaus (1980). Rigid body motion calculated from spatial
co-ordinates of markers. J Biomech, 13:391-393.

Veldpaus, Woltring, and Dortmans (1988). A least-squares algorithm for the
equiform transformation from spatial marker co-ordinates. J Biomech,

Panjabi (1979). Centers and angles of rotation of body joints: a study of
errors and optimization. J Biomech, 12:911-920.

Woltring, Long, Osterbauer and Fuhr (1994). Instantaneous helical axis
estimation from 3-D video data in neck kinematics for whiplash diagnostics.
J Biomech, 27:12:1415-1432.

Amevo, Worth, Bogduk (1991). Instantaneous axes of rotation of the typical
cervical motion segments: a study in normal volunteers. Clin Biomech,

I am hoping to look at how the ICR between the head and trunk relates to
the intervertebral centers of rotation, using the model and some kinematic
analysis with optotrak.

Good luck!!


FROM: Dimitrios Tsirakos (ad432@dial.pipex.com)
The Manchester Metropolitan University
Crewe + Alsager Faculty
Biomechanics research group
Emberton Bungalow, Hassall Road,
Alsager ST7 2HL

I am writing to you for he enquiry you made in Biomech-L, as far as the
estimation of the center of rotation in 2-D is concerned. Currently I made a
comparison study between the different techniques that were introduced in
the literature. I am working with the elbow joint and in this comparison
study I used all the techniques that I could found. (currently I am writing
this chapter-paper of my PhD).

Specifically I compared the techniques introduced by the next papers:

Crisco, J., Chen, X., Panjabi, M. and Wolfe, S. (1994). Optimal marker
placement for calculating the instantaneous centre of rotation.
Journal of
Biomechanics, 27, 1183-1187.=20
Walter, S.D. and Panjabi, M.M. (1988). Experimental errors in the
observation of the body joint kinematics. Technometrics, 30, 71-78.
Spiegelman, J. and Woo, S. (1987). A rigid-body method for finding centres
of rotation and angular displacement of planar joint motion. Journal=
Biomechanics, 20, 715-721.
Panjabi, M. (1979). Centres and angles of rotation of body joints: A study
of errors and optimization. Journal of Biomechanics, 12, 911-920.
Reuleaux, F. (1875). The Kinematics of Machinery: Outline Of A Theory Of
Machines (translated by Kennedy, A. B. W.) pp. 56-70. Dover: New=

In my experimental design I used also the ELITE system and a mechanical arm
that was rotating around a hinge joint, assuming rigid body movements. To
get an accurate information of the position of the center of rotation I
used a reflective marker on the pin of the hinge joint. To calculate the
theoretical position of the center of rotation I used each method described
in the above papers and also the classical method of axis intersection.=20

According to my experimental design and the results I obtained, comparing
the X and Y co-ordinates of the actual centre of rotation (non movable
reflective marker co-ordinates) and the estimated (from the applied
techniques), it was concluded: i) That mainly the Releaux, and the rigid
body methods have problems when the angle of rotation is very small, ii)The
axis intersection and the technique that is described by Crisco gave the
more accurate results (RMS error at about 5mm ).=20

Practically, the axis intersection technique is not possible to be used
reliably, as the limb axis orientation using two markers is an assumption,
plus that you need four markers to describe the orientation of the axis
(more markers than the other method). Thus, in my knowledge, the use of the
technique that is described by Crisco, et al. seems that is a very good

I would be very glad to send you some of the results when I finish the
paper. Please let me know if you have any other questions or suggestions.

************************************************** ********************
Julie Wilson Steege, Research Engineer
Programs in Physical Therapy=20
Northwestern University
Ph. (312)908-6785