Instrumented Analysis of Human Movement


Shaw Bronner PT, MHS, EdM, OCS

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  Table of Contents


v    I.         Introduction

v    II.         Motion Systems

v    III.        Data Acquisition

v    IV.        Data Processing

v    V.         Data Analysis

v    VI.        Data Interpretation

v    VII.       Applications

v    VIII.      Definitions

v    IX.        References

v    X.         Questions and Comments



I. Introduction


            Modern studies of human motion can be traced to pioneering publications at the end of the 19th century by Muybridge (1887), Marey (1873), and Braune and Fisher (1895) (Cappozzo, 1975; Ladin, 1995) . Perhaps the most widely known is Eadweard Muybridge’s successive-exposure photography to study horse locomotion (1878) (Chronophotographical Projections, 2003; Eadweard Muybridge, 1998) . Components included 12 cameras, an electrically-controlled mechanism to operate the cameras' special shutters, and wires laid underground along a track at 21-inch intervals to release the shutter of each camera as the wheels of a horse carriage made contact. The 12 pictures, taken in a period of 0.5s, proved railroad baron and patron Leland Stanford’s theory that during a horse's running stride, there is a moment of suspension where no hooves are touching the ground (Figure 1). Photographic series such these were shown on a Zoopraxiscope, a primitive motion picture developed by Muybridge.


Figure 1. Muybridge’s galloping horse series.


            Early cinemagraphic motion analysis, generally limited to one plane, was extremely laborious and time consuming. Manual digitizing, frame by frame, provided information on change in position of limb segments. The development of powerful computer systems with high-speed photography in the late 20th century permitted faster routines for marker recognition, frame grabbing, and processing of three-dimensional (3-D) data. The ability to accurately determine temporal and spatial information from 3-D data, in turn, allowed more sophisticated analyses such as determination of the center of mass and forces through inverse dynamics calculations.

            The purpose of this review is to provide information on the instrumented analysis of human movement. This review will include an outline of the steps involved in conducting instrumented motion analysis research, the issues involved in acquiring good data, and describe what information quantitative motion analysis affords us. The major focus of this review will be on video imaging systems.

Why study human movement? The study of human movement allows us to understand how people move. We can gain insight into the effect of: maturation and development on motor learning (the child learning to walk), training on skill development (mastering a tennis serve); the effect of peripheral or central nervous system injury on activities of daily living (walking or rising from a chair following stroke); and whether our interventions are effective rehabilitation techniques (gait training for an individual with a below-knee leg amputation).

            Quantitative movement analysis falls within the domain of biomechanics (Figure 2), the science involving the study of biological systems from a mechanical perspective (Hall, 1999; Schombert, 2003) . [See section VIII. Definitions] Mechanics (the analysis of the actions of forces), in turn, encompasses statics (the study of systems that are in a state of constant motion (either at rest or moving at a constant velocity) and dynamics (the study of systems in which acceleration is present). In particular, movement analysis focuses on kinematics, which is the study of motion of bodies without reference to the forces that cause the motion. Kinematics describe the pattern and temporal aspects of motion such as positions, angles, velocities, and accelerations of body segments and joints during motion. Quantitative motion analysis also permits the calculation of kinetics, when the anthropometric characteristics of subjects are applied to inverse dynamic computations. Kinetics is the study of forces and moments acting on a body (which cause the motion of the body).


Figure 2. Biomechanics diagram.

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II. Motion Systems


In biomechanics, the human musculoskeletal system is viewed as a series of linked segments (Figure 3A), which are defined as rigid bodies (Ladin, 1995; Rash & Campbell, 2002) . We use two frames of reference in discussing human motion or kinematics. There is the Newtonian or global frame of reference, which divides the laboratory space into 3-planes (Figure 3B and C). Each body segment can be described as having up to 6-degrees of freedom (DOF), which can describe the location and orientation of that segment in space. In other words, we can discuss motion with respect to the global frame of reference, which includes moving forward or backward in the sagittal plane, side to side in the frontal plane, or inward or outward in the transverse plane.


A.                          B.  


Figure 3. A. Linked body segments, B. 3-D axes for global frame of reference, C. Planes of Motion: 1 = Frontal plane, 2 = Sagittal plane, 3 = Transverse plane.


            Figure 3A illustrates a body with 17 linked segments. Figure 3B demonstrates the X, Y, and Z axes which define the Newtonian or absolute frame of reference. In Figure 3C, the plane formed by YZ is the frontal plane (1); XZ is the sagittal plane (2); and XY is the transverse plane (3).

There is also a body-centered or local frame of reference, which can describes body segment with respect to another. By convention we discuss movement of the distal segment with respect to the proximal segment. For example, when angular displacement of the knee is reported, it may be described as the (distal) leg rotating with respect to the thigh (Figure 4).


Figure 4. Knee angular displacement: 120˚ flexion.


            In order to record the dynamic motion of the joints and segments of the body for analysis, several types of equipment have been developed. These include:

1)    electrogoniometers,

2)    accelerometers and gyroscopes,

3)    electromagnetic systems, and

4)    imaging systems.


1. Electrogoniometers (Figure 5A) are electronic versions of the standard goniometers (Figure 5B) used in the clinic to measure joint range of motion or angular displacement. Available in unixial and biaxial form, the electrogoniometer consists of one or two potentiometers or strain gauges between two bars. Placed across the joint to be measured, the potentiometer produces a varying voltage output depending on the angle of motion. Advantages of electrogoniometry include ease of set up and processing, relatively low cost, and, with small data loggers, portability for collection in the workplace or other sites. These dataloggers permit the collection and storage of large quantities of data over a prolonged period such as a workday (Anderson & Lyons, 2001; Hansson, Asterland, & Kellerman, 2003) . Disadvantages include the lack of data with respect to the global reference system and 6-DOF, errors due to alignment of the axes of rotation, difficulty in monitoring joints surrounded by large amounts of soft tissue (such as the hip), and cross talk between potentiometers. Electrogoniometers are usually employed for inexpensive and approximate quantification of specific joint motion outside the lab (e.g. on the worksite for ergonomic analysis, etc). Currently, the most commonly used flexible-cable system is manufactured by Penny and Giles (Biometrics Ltd., Blackwood, Gwent, UK) (Ladin, 1995; Penny and Giles electrogoniometers, 2003; Rash & Campbell, 2002) .


A. B.

Figure 5. A. Electrogonimeter, B. Goniometer.

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2. Accelerometers and gyroscopes work on the principal of inertia. A single axis accelerometer (Figure 6) consists of a sensor comprised of a known mass suspended from a strain gauge in a housing. Deflection of the strain gauge with motion is translated into an electrical signal. The advent of piezoresistive devices has permitted miniaturization of the sensors and development of triaxial accelerometers measuring 3-D acceleration (Lugne, Alizon, Collange, & Van Praagh, 1999; Luinge, 2002) . Benefits of accelerometers include measurement of rotational segmental motion, broad frequency range (0– 1,000 Hz), small size, and relatively low cost. Disadvantages include signal “drift” which creates increasing artifact over time and the need to determine the following to accurately calculate a segment’s acceleration and velocity: the segment’s initial position and velocity values, the effects of gravity, and identification of the segment’s rotational DOF. Piezoresistive accelerometers include Entran (Entran Devices, Fairfield, NJ), ICSensors (ICSensors, Milpitas, CA) (Entran accelerometers, 2003; ICSensors, 2003) .


Figure 6. Accelerometer.

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Gyroscopes (Figure 7) are based on the principal of a vibrating mass undergoing an additional vibration caused by the coriolis effect (Luinge, 2002) . The Coriolis effect, described by Gustave-Gaspard Coriolis in 1835, is an inertial force related to the motion of the object, the motion of the Earth, and the latitude (Schombert, 2003) . The coriolis effect is the apparent deflection of the path of an object that moves within a rotating coordinate system (such as the earth). Gyroscope components include a mass and a piezoelectric element within a housing. Displacement caused by the coriolis force is proportional to the angular velocity and used as a measure of angular velocity. Similar to accelerometers, miniaturization has permitted the manufacture of triaxial gyroscopes. Benefits of gyroscopes include the direct measurement of rotational motion that is not influenced by gravity and small size. Disadvantages include increasing error of several degrees per second caused by gyroscope offset and noise. Small orientation errors lead to larger integration errors (calculation of angular displacement or position from angular velocity) over time. Therefore, gyroscopes have not been employed regularly for human movement measurement because they were not reliably accurate for periods longer than one second. Recent solid-state gyroscopes claim to have eliminated the drift by using a single crystal quartz element, producing long-term calibration stability. Solid-state gyroscope manufacturers include Motus (Motus Bioengineering, Inc, Benicia, CA) (Mayagoitia, Nene, & Veltink, 2002; Motus system, 2003) .


Figure 7. Gyroscope.

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3. Electromagnetic systems (Figure 8) are based on low-frequency magnetic coils that permit real time 6-DOF tracking of segments by sensors placed on the segments (Eckhouse, Penny, & Maulucci, 1996) . Limitations include cabling to connect sensors that can inhibit movement, slippage of the sensors, number of sensors that can be tracked at one time (usually up to four), and cost. Interference from metallic objects or other magnetic fields will degrade performance. Benefits include the elimination of marker dropout from the camera field of view (which can occur in videography), real time 6-DOF data, and accuracy. Electromagnetic systems include Liberty (Polhemus, Colchester, VT) and Flock of Birds (Ascension Tech. Corp., Burlington, VT) (Flock of birds electromagnetic tracking system, 2003; Polhemus Liberty electromagnetic tracking system, 2003) .


A. B.

Figure 8. Electromagnetic system with A. Large, and

B. Small sensors.

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4. Imaging systems are divided into cinematography, optoelectronics, and videography systems.


4.1 Cinematography, the earliest imaging system developed, provides a high quality image, but lacks automated systems for data reduction. Therefore, it is costly and time consuming.


4.2 Optoelectronic systems (Figure 9) employ active markers that are usually light emitting (infrared) diodes (LED’s) placed on the segments or joints (Ferrigno & Pedotti, 1985; Ladin, 1995) . The LED’s are triggered and pulsed sequentially by a computer, permitting automatic identification of each marker. Advantages include automated marker tracking hence no marker merging or misidentification. However, optoelectronic systems require wire connection to the LED’s, which makes measurement cumbersome and limits them to the laboratory environment. More than one unit may be required to obtain adequate marker coverage. Commercial systems include OptoTrak (Northern Digital, Inc., Waterloo, Ontario), CODA mpx30 (Charnwood Dynamics Ltd, Leicestershire, UK), and Selspot (Innovision Systems, Inc., Columbiaville, MO) (CODA, 2003; OptoTrak, 2003; Selspot) .


A. B. C.
Figure 9. Optoelectronic system. A. Position sensor, B. Active marker, C. Instrumented hand.
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4.3 Videography is the most frequently used type of motion analysis. These systems use one or more cameras to track passive reflective markers, which do not require wires (Gruen, 1997; Ladin, 1995; Richards, 1999) . Passive markers reflect either external ambient light or camera-projected light (frequently infrared). The markers then reflect the light back into the camera lens, and the digital signal is fed into a computer. A threshold is set to automatically discriminate the marker “pixels” which are the brightest objects in the laboratory. Because all markers are visible at any given time, potential merging of markers in various camera views places limitations on how close together markers may be placed with these systems (generally limited to 2mm) (Richards, 1999) . When markers are lost from view or their trajectories cross, they can lose their proper identification. If a marker is occluded, some systems supply the missing point by interpolation. Cameras may have either analog or digital output. Benefits include the ability to track large numbers of markers, faster cameras (50-250Hz), and the potential for high precision and accuracy (Cerveri, Pedotti, & Ferrigno, 2003; Eckhouse et al., 1996; Greaves, 1995; Gruen, 1997; Ladin, 1995) .

Video systems keep track of the horizontal and vertical coordinates of each marker from each camera. If only one camera is used (2-D), the assumption is that all motion is occurring in a plane perpendicular to the camera axis. This is seldom the case and any marker movement outside this plane will be distorted. As a result, 2-D systems are less accurate than 3-D systems, even if the researcher is only interested in one plane of motion. In 3-D systems, the computer software computes 3-D coordinates for each marker based upon the principle of optical triangulation. This includes the 2-D data from two or more cameras and the known location of all cameras. In practice, more than two cameras are necessary, as markers become obscured from camera views because of arm swings, subject rotation, or laboratory configuration. Many systems now employ 5 to 24 cameras (Figure 10). Commercial systems include the following: APAS (Ariel Dynamics, Inc., Trabuco Canyon, CA), ElitePlus (Bioengineering Technology Systems [BTS], Milano, Italy), HiRes (Motion Analysis Corporation, Santa Rosa, CA), Peak Motus (Peak Performance Technologies, Inc., Englewood, CO), ProReflex (Qualisys Medical AB, Gothenburg, Sweden), and Vicon (Vicon Motion systems Ltd, OMG Plc (formerly Oxford Metrics Ltd.), Oxford, UK) (APAS Ariel performance analysis system, 2003; ElitePlus motion analysis system, 2003; HiRes Motion Analysis system, 2003; Peak Motus motion capture system, 2003; ProReflex Qualisys Motion Capture System, 2003; Vicon motion analysis, 2003) .


A.  B. C.
Figure 10. Videography systems. A. Infrared camera, B. Instrumented videography gait lab, C. Passive marker set up for pitching study.

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The discussion of human movement analysis will henceforth use the example of videography motion systems using passive markers. When a human movement question is identified and a hypothesis generated, the biomechanics researcher moves to the laboratory to collect data appropriate to shed light on the question. Paramount is the collection of reliable and accurate data. Consideration must be made for potential sources of error and ways to minimize their effects. Issues include:

1)    laboratory configuration,

2)    ambient noise,

3)    marker placement,

4)    sampling,

5)    equipment synchronization,

6)    reconstruction,

7)    calibration, and

8)    software assumptions (modeling errors such as defining joint centers).

Each of these issues will be reviewed.


1.0 Laboratory Configuration. Laboratory configuration for video motion analysis usually ends up being a compromise between optimum camera placement and available space. To maximize data collection accuracy, several principles are advised (Allard, Blanchi, & Aissaoui, 1995; De Lisa, 1998) . These include:

  1. A dedicated laboratory to ensure subject and operator concentration and fewer interruptions.
  2. For 3-D motion capture, more than two cameras are advised to minimize marker dropout.
  3. Camera placement must ensure that a minimum of two cameras capture the markers during movement. Mapping of the amount of space required to perform the movement under analysis and pilot testing will ensure this (Figure 11).  


Figure 11. Laboratory mapping to ensure adequate camera coverage.


  1. Rule of thumb dictates that the angle between any two cameras should be greater than 60˚ for greater accuracy of marker coordinate determination. A recent report states that camera placement greater than 30˚ is sufficient for clinical testing (Thornton, Morrissey, & Coutts, 1998) .
  2. Camera placement should avoid shining their lights directly into another camera, and out of the way to minimize knocking after calibration (Thornton et al., 1998).
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2.0 Ambient noise. Efforts should be made to select a lab environment that minimizes ambient noise. Thus includes any external electromagnetic signal generation, floor vibration, or other factors that might interfere or be picked up by the laboratory equipment. Some systematic noise or error can be taken care of with filtering. In general, “white” noise added by equipment has a much higher bandwidth (Woltring, 1995) . 

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3.0 Marker placement. Customarily, passive markers are affixed to the skin of the subject with double-sided tape. For full body capture, 25mm markers are usually used. Marker placement is a large source of potential error. Researchers must have excellent palpation skills to orient markers to bony anatomy as well as good understanding of the principles of joint center estimation. Optimally, the same examiner sets up each subject to ensure consistent placement. The Standardization and Terminology Committee of the International Society of Biomechanics (STC-ISB) has defined a joint coordinate system for the reporting of ankle, hip, and spine motion in hopes that the biomechanics community will move to adopt common and acceptable standards of measurement and reporting (Wu et al., 2002) . Definition of the marker set prior to data collection will determine the number of markers used. The modified Helen Hayes marker set, probably the most widely employed marker set in gait analysis, uses 13 or 15 markers to define 7 body segments (Davis, Ounpuu, Tyburski, & Gage, 1991; Kadaba, Ramakrishnan, & Wootten, 1990) . The ADAM Center lab uses 31 markers to define an 11-segment model for dance research (Figure 12). Some but not all of the anatomical landmarks proposed by the STC-ISB are incorporated into the Helen Hayes and the ADAM Center’s marker sets.


A. B.
Figure 12. ADAM Center marker set.
A. Anterior view, B. Posterior view.


The 31 markers are placed bilaterally at the superior orbit, occiput, acromion process, anterior superior iliac spine (asis), posterior

superior iliac spine (psis), greater trochanter, lateral mid-femur, lateral knee joint line (knee), lateral mid-calf, lateral malleolus (ankle),

calcaneous (heel), dorsal first metatarsal-phalangeal joint (toe), dorsal fifth metatarsal-phalangeal joint (5th mtp), and dorsal second

metacarpal-phalangeal joint (finger); and unilaterally at the sternal notch, spinous process of the seventh cervical vertebra (C-7), and left

scapula to create a 11 segment model.

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4.0 Sampling. Data are either collected directly in digital form or are converted from analog to digital signals (Figure 13). It is important to know the characteristics of the signal in order to determine the frequency at which data should be collected. Signal characteristics include the amplitude and frequency as well as the phases of the frequency components (Hamill, Caldwell, & Derrick, 1997; Woltring, 1995) . Most signals are sampled at equal time intervals (d). The reciprocal of this time interval is the sampling rate (f), specified in samples/s or Hz. For a biological signal such as human movement (which is continuous), the Nyquist critical frequency is the basis of sampling theorem. This states that the original signal must be sampled at a rate greater than twice the highest frequency in order to obtain all the information found in the original signal. Some scientists advocate sampling at higher rates than the Nyquist theorem to improve the lower movement-related frequency estimates (Woltring, 1995) .



A. B.
C. D.
Figure 13. Signal sampling. A. Continuous analogue signal,
B. Digital sampled signal, C.  Spectrum of signal including amplitude and frequency, D. Spectrum of signal.

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5.0 Equipment synchronization. Synchronization of image capture from multiple cameras is either controlled by a master synchronization generator included in the hardware processor (which can also synchronize data from other systems such as force platforms or EMG) or through camera genlock to an external signal (Woltring, 1995) .

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6.0 Reconstruction. Reconstruction is the systematic integration of a flat image from each camera into a 3-D coordinate system. Reconstruction procedures are based on precise knowledge of both internal (lens and camera characteristics) and external (spatial orientation) camera parameters. With multiple cameras, reconstruction deals with multiple image pairs. The most frequently used reconstruction technique is called direct linear transformation (DLT) (Brewin & Kerwin, 2003; Cerveri et al., 2003; Chen, Armstrong, & Raftopoulos, 1994; Everaert, Spaepen, Wouters, Stappaerts, & Oostendorp, 1999; Wood & Marshall, 1986) . This method represents mathematical transformation between 3-D object space and 2-D image space. The full DLT 3-D algorithm contains up to 22 parameters (Allard et al., 1995; Gruen, 1997) . There are two principles for DLT to be optimized. These are the co-linearity condition (that a marker point forms a straight line that passes through the camera lens focal point) and the co-planarity condition (that a marker point and any two cameras’ focal points lie in a common plane). In order to determine all parameters for reconstruction procedures, calibration devices consisting of precisely measured marker points are used to determine any unknowns.

For single camera 2-D analysis, reconstruction generally entails a scaling procedure, based on a known camera distance and videotaping of a calibration device with markers spaced at a precisely measured distance. However, any movement outside the plane perpendicular to the camera axis will be distorted. DLT reconstruction is preferred to scaling because it is more accurate, providing that the motion under analysis stays within the volume of space described by the calibration (Brewin & Kerwin, 2003) .

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7.0 Calibration. In any motion analysis system, systematic errors may occur due to effects such as lens distortion, lack of flatness of the imaging plane, warm-up effects, unequal pixel spacing (Gruen, 1997; Ladin, 1995) . Calibration procedures have been developed to minimize these effects. For 2-D analysis, most systems require four or more non-colinear points with known spatial coordinates. The calibration points must be placed precisely in the plane of motion at a known distance from the camera lens, otherwise the scaling will be incorrect. It is also important for 2-D analysis that the camera is positioned perpendicular to the plane of motion and level to the horizontal plane.

3-D motion analysis systems customarily use manufacturer provided calibration cubes and/or calibration wands (Figure 14) (Gruen, 1997; Ladin, 1995) . The cubes consist of 8 or more marker points positioned in 3-D space at known coordinates. The cube is leveled with respect to the horizontal plane, as well as the sagittal and frontal axes. The cameras are not required to be leveled. The calibration device is videotaped and marker coordinates are determined. In a second step, a wand (also with markers at precisely determined distances) is used to define the 3-D spatial area that will be used for data collection. Once the calibration procedures have been completed, parameters are stored for transformation of image coordinates into 3-D marker coordinates. Therefore it is crucial that camera positions remain untitleered throughout the data collection.


Figure 14. Calibration frame (centered on force platform) and wand.


Performance comparisons of various videography systems have been made by several researchers (Figure 15) (Ehara et al., 1997; Everaert et al., 1999; Richards, 1999) . These comparisons include analysis of accuracy of static and/or dynamic points, distances, and/or angles. Generally error ranges between 1.0 – 5.0mm and 1.0 – 5.0deg; but reported errors values do not always use the same definition of error. A summary of 6-motion analysis systems is included below.





# markers


# cameras






up to 6






up to 16/box


Motion Analysis




up to 16


Peak Performance




6 to 12






up to 16






up to 24




Sampling freq

Accuracy (mm)

RMS error (mm)

RMS error (deg)











Motion Analysis





Peak Performance
















Figure 15. Characteristics of videography systems.
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8.0 Software assumptions. As mentioned earlier, the most commonly used biomechanical model represents the human body as a series of linked rigid segments. This model assumes that the rigid segments are connected by smooth, spherical joints and does not allow for tissue deformation, other joint shapes, or joint translations. To obtain 3-D motions, each body segment must be defined by at least three markers (which create a plane passing through the segment), joint centers must be defined, and either Euler or Lagrange (the most frequently used equations) angles computed (Andrews, 1995) . Certain assumptions are made in the use of kinematic modeling to determine joint centers, some of which follow.

In earlier 2-D motion analysis applications, the trajectories measured by motion analysis systems relied upon the skin-fixed markers. With the advent of more complex 3-D systems, improved estimations of joint centers became necessary for accurate kinematic and kinetic calculations. Confounding the development of improved estimations of joint centers is the problem that in some joints, such as the knee, there is no fixed center of rotation (Frigo & Rabuffetti, 1998) .

Some numerical models incorporate specific morphologic measures such as knee and ankle width for each subject. Others are based on formulas derived from cadaver or radiograph measures of selected populations. Selection of accurate joint center estimations is particularly critical when forces and moments are calculated via inverse dynamics or muscle models. For example, a 2.0cm superior displacement of the hip joint center results in decreased estimated abduction force (44%), and a 2.0cm inferior displacement results in increased estimated abduction force (20%) (Delp & Maloney, 1993) . Several estimations for the hip joint center (Figure 16) have been compared to the ‘gold standard’ of radiographs Errors of various estimations range from an rms distance of 13.0 to 38.0mm (Bell, Pedersen, & Brand, 1990; Frigo & Rabuffetti, 1998; Leardini et al., 1999) .


Figure 16. Pelvis-hip anatomy and surface markers differ from the hip joint center.

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III. Data Processing


            Data or signal processing refers to the filtering (smoothing) and differentiation procedures that take place following data collection. Usually, prior to processing, each marker must be identified once in order to run the model. After the model is run, a stick figure is generated (Figure 17). Viewing the stick figure as it performs the movement, assists in checking for any errors in marker identification prior to running any processing procedures.



A.      B.
Figure 17. Stick figures generated after running the model for a postural task protocol. A. Bipedal starting position, and B. Ending position in a unipedal balance posture.


            A movie of an arabesque sequence demonstrating the dancer performing the movement and the stick figure generated by the model is seen in Figure 18.


Figure 18. Arabesque movie. A. Dancer video, and B. Stick figure.

1.0 Filtering. Despite the most meticulous preparation, calibration, and collection, sampled data is contaminated with noise (Figure 19). The noise content must be minimized prior to differentiation (calculation of displacement derivatives such as velocity, acceleration, etc.) because differentiation magnifies the signal and hence the noise. Following satisfactory data collection, additional measures can still be taken to minimize random error (Challis, 1999; Fioretti, 1996; Vint & Hinrichs, 1996; Woltring, 1995) . Random noise is usually “white noise,” characterized by a high frequency content. The movement signal is generally limited to a band of low frequencies. It is, therefore, customary to use a low-pass filter to remove the high frequency components and retain those of the low frequency, the movement signal. Systematic noise (such as the change in position of skin-fixed markers due to tissue deformation which is not accounted for in the rigid segment model) is a greater problem. Systematic noise may include both high and low frequency components. However, only the high frequency components will be filtered out by a low-pass filter. No algorithms or filters can distinguish between a low-frequency systematic error signal and the movement signal if nothing is known about the nature of the error signal except that it is not random.


A. B.
Figure 19. Raw and filtered data.


There are many types of filters and several methods to determine the “optimal” cut-off frequency. Types of filters include the classic Butterworth, Fourier series, Kalman, cubic and quintic spline (Woltring), and finite impulse response (FIR) filters (Winter, 1990; Woltring, 1995; Yu, Gabriel, Noble, & An, 1999) . Filter equations, such as in the Butterworth filter, are frequently recursive. Current values depend on the previous values, which introduces a phase lag into the signal. These filters are, therefore, applied in both forward and reverse directions in order to remove the phase lag (resulting in accurate temporal measures). This doubles the application of the filter; so that a filter applied once in the forward and once in the reverse direction is termed a second order Butterworth filter.

“Optimal” refers to obtaining the best approximation to the “true” signal. Visual comparison of filtered data using various cut-off frequencies to the raw data is the oldest method and usually continues to be included along with more objective methods. Residual analysis plots (Figure 20), of the raw data filtered at several cut-off frequencies to determine when the residual is a linear function of the cut-off frequency, may be used as a guideline (Winter, 1990; Woltring, 1995; Yu et al., 1999) . By utilizing this method, the characteristics of the filter in the transition period are reflected in the decision process.



Figure 20: Residual analysis plot to determine cut-off frequency.


Figure 20 illustrates a representative subject’s Residual Analysis plot for a knee displacement signal, and shows residual (y axis) versus cut-off frequency (x axis). The optimum cutoff frequency is determined by regressing the linear portion of R-Fc curve (dashed line, which represents the best estimation of the noise residual) back to the residual axis. The intersection on this axis can then be projected to the original R-Fc curve, and the cutoff frequency read from the x (Fc) axis. Pilot data produced cutoff frequencies between the 5 and 6 Hz. The mean of these (5.5 Hz) was chosen for filtering of all pilot data; this was verified by inspection to ensure correct attenuation of the raw signal.

There are also algorithms with set cut-off frequencies and other automatic cut-off techniques. Several common automatic cut-off techniques are the optimally regularized Fourier series and the generalized cross-validated spline (Woltring, 1995; Yu et al., 1999) . Finally, researchers may select previously published cut-offs for similar movements.

(Return to Data Processing)


2.0 Differentiation. In most motion analysis systems, velocity and acceleration are not directly available. Instead they must be estimated from the position data through differentiation. The problem with the application of filter and differentiation equations is resolving the order in which they occur. Most of the research on filters and cut-off selection focuses on displacement data. Winter (1990) reported that 99.7% of gait signal was contained below 6 Hz based upon displacement data (Winter, 1990) . But more recently, scientists have demonstrated that the frequency characteristics of higher derivatives differ from that of displacement data (Giakas & Btitlezopoulos, 1997; Woltring, 1995) . Analysis of best fit cut-offs for displacement, velocity, and acceleration ranged between 3.0 and 10.0 Hz (Giakas & Btitlezopoulos, 1997) . The recommendation was made to calculate derivatives first and filter each output separately to achieve optimal results.

            At the ADAM Center, we conducted an experiment in which the movement of professional dancers following anterior cruciate ligament reconstruction (ACL) was compared to that of uninjured dancers (Bronner, Kaminski, & Gordon, 2002) .  We examined the passé movement (Figure 21), which is a common transitional dance movement.



A B.

Figure 21. Passé sequence. A. Dancer performing passé en pointe. B. Dancer wearing reflective markers for data collection.



            After collecting the data and running the model, a stick figure was generated (Figure 22A). Figure 22B top illustrates the displacement data stream for the toe marker. The toe velocity data stream (derivative of displacement) is illustrated in the Figure 22B bottom.                

A. B. 

Figure 22. Passé sequence. A. Stick figure. B. Top: Toe displacement, and Bottom: Toe velocity.

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IV. Data Analysis


            The successful processing of the data produces smooth data streams or trajectories of displacement and its derivatives. With the incorporation of force platforms into data collection and processing, the model can also calculate kinetics such as forces and moments acting at the various segments and joints, but is beyond the scope of this discussion.

            When a human movement question is formulated and a hypothesis generated, various parameters are identified. These may include temporal parameters such as reaction time to movement onset, initiating segment of movement onset, segment sequencing order and timing, total movement time, etc. Spatial parameters may include peak amplitude of displacement (how far) and velocity (how fast). Ratio of deceleration to acceleration timing may give insight into control. Order and timing sequencing of segments may give insight into coordination.

            Generally subjects are asked to perform the same movement a series of times because there is variability inherent in human movement. The variable under analysis, for example – amplitude, is determined for each of the trials. Averages (means) are then calculated for each subject. Statistical analyses are performed on the data.

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V. Data Interpretation


            Using the example of our study on the effect of ACL reconstruction on the passé movement, the interpretation of several parameters is illustrated below. The abstract is included to give an overview of the experiment (Bronner et al., 2002) .


Effect of anterior cruciate ligament reconstruction on the passé movement in elite dancers

Shaw Bronner, Terry R. Kaminski, Andrew M. Gordon


Semitendinosus-gracilis (STG) and patella tendon bone (PTB) are frequently selected grafts for ACL reconstruction in dancers. While STG and PTB ACL reconstruction outcomes appear to be similar in restoring acceptable mechanical joint stability, it is not known whether there are titleerations in the kinematics of dance movements following these procedures. The present study examined two-dimensional kinematics of trunk-lower extremity coordination in 18 adult professional dancers: six dancers with STG, six with PTB ACL reconstruction, and six healthy Controls. All dancers with ACL reconstruction had returned to full dancing and performance activities with no visible asymmetries in their dancing. We examined whether temporal organization and peak velocity of the gesture limb differs in STG and PTB ACL reconstruction dancers compared to Controls when performing the passé. Hip and knee peak angular velocities were slower on the involved limb of STG and PTB dancers compared to Controls. Adaptations were seen bilaterally in delayed movement times, shorter deceleration times, and greater number of movement units in the ACL reconstruction groups. These findings suggest that injury to a single joint can affect kinematics throughout the involved and uninvolved lower extremities. The titleered movement patterns found in dancers with both types of ACL reconstruction suggest that their control of complex movements may be adaptive in nature. Journal of Dance, Medicine and Science, 6(4):110-118.


We predicted that the postural adjustments associated with the onset of trunk movement and the initiation and completion of toe movement would be less tightly coupled following ACL reconstruction. To examine the coupling between gesture limb and pelvis, we determined movement onset and completion timing (Figure 23).


A. B.


Figure 23. Sequencing of movement initiation and completion. A. Profile of a representative subject. Top: Resultant displacement curves of the gesture side asis and toe markers; Bottom: Angular displacement curve of the gesture knee, for the same trial of this subject. Movement initiation and termination of the gesture side markers are indicated by the vertical lines labeled T0-5. Trunk translation (T0 = asis/green) preceded gesture limb marker onset. Gesture limb movement followed a proximal to distal order at movement onset (T1 = knee/red, T2 = toe/blue), and a distal to proximal order at movement termination (T3 = toe, T4 = knee). Trunk translation (T5 = asis) followed gesture limb marker termination to complete the sequence (returning to first position). [Note: anterior superior iliac spine (asis)]. B. Group mean (SD) displacement onset and termination times (relative to the marker which began or ceased moving first) of the non-preferred limb in Control (green) and involved limb in STG (blue) and PTB (pink) groups. B) Mean (± SE) displacement onset and termination times of the preferred limb in Control and uninvolved limb in STG and PTB groups.


        The trunk was the first segment to move and the last to stop when performing the passé. This movement pattern was similar to that observed in other voluntary movements which begin and end with a postural adjustment. However, ACL reconstructed subjects displayed bilateral delays in initiation of movement at the distal extremity (toe) (P<0.05), and delays in completion of movement at more proximal segments (knee and asis) (P<0.01), supporting our hypothesis of less tightly coupled trunk and limb movement. Delays were, in some instances, quite substantial (up to 110ms), considering that both the passé ascent and descent phases were only 600ms in length. These delays were greatest on the uninvolved gesture limb in the STG group. Perhaps this was due to a more cautious­ control strategy on the part of STG subjects of weight shift and acceptance, particularly onto the operated stance limb. Movement onset and termination temporal coupling on both limbs of PTB subjects more closely resembled that of controls. Whether this ‘cautious’ control strategy existed prior to or was a result of the ACL injury and surgery is unknown.

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            By combining motion analysis with force platforms and surface electromyography (sEMG), biomechanics laboratories have allowed clinicians to gain greater insight into the effects of pathology (both central and peripheral), maturation and development, and skill acquisition on selected human movements.

            The assessment of gait in patients with cerebral palsy assists in the determination of appropriate surgical or orthotics intervention as well as determination of outcomes following such interventions. Analysis of the effects of neuromuscular disorders such as Parkinson’s disease on gross and fine motor movements can provide baselines from which to determine disease progression and the effectiveness of medications.

Comparisons of pre-and post-operative movement patterns in orthopaedic patients provides understanding of both the effectiveness and limitations of surgical and rehabilitation techniques and outcomes. Particularly well studied over the last decade, is the effect of anterior cruciate ligament (ACL) deficiency and reconstruction on locomotion (walking, running, pivoting, cutting, stairs, etc.). Post ACL reconstruction, subjects have similar gait kinematics compared to uninjured subjects, but continue to display titleered kinetics (forces and moments) on their involved limb. Furthermore, they demonstrate bilateral balance deficits compared to uninjured subject (Henriksson, Ledin, & Good, 2001) . The loss of afferent information due to ACL injury may result in modifications of the central nervous system in patients with ACL deficiency, resulting in titleered neuromuscular function bilaterally. This change may persist despite ACL reconstruction (Valeriani et al., 1999) .

The majority of movement analyses on subjects following ACL reconstruction have focused on the weightbearing limb. For dancers, the “gesture limb” is a focal point of movement expression. Comparison of the movement of professional dancers without injury and following ACL reconstruction (semitendinosus-gracilis and patella tendon-bone) found kinematic titleerations in gesture limb control on both the involved and uninvolved limbs of the ACL reconstructed groups

Patients with chronic low back pain display titleerations in muscle firing patterns and hence protective mechanisms during reaching and other movements (Hodges, 2001) . This titleeration is also present in acute experimentally induced low back pain (Hodges, Moseley, Gabrielsson, & Gandevia, 2003) .

            In addition to the use of motion analysis for scientific purposes, the technology has been applied to animation, choreography, and game development. The film “The Matrix Reloaded” employed motion analysis systems with passive markers to capture human martial arts movements. These were, in turn, animated for the special effects fight scenes (Matrix Reloaded, 2003) . The Life Forms software package has been extensively used by choreographer Merce Cunningham to choreograph prior to setting the movement on his dancers (Current Research: Life Forms, Human Animation, Telelearning and ... 2003; Life Forms Dance, 2001; Schiphorst, 2003) . Choreographer Bill T. Jones collaborated with digital artists Shelley Eshkar and Paul Kaiser to create an abstraction of his dancing using motion analysis technology in a piece called "Ghostcatching". (Jones, Eshkar, & Kaiser, 1999) .  

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Definitions of some common biomechanics terms are included below.


Acceleration – the rate of change in velocity with respect to time. Acceleration is also a vector. The metric unit is meters/seconds/second (m/s2).

Angular displacement – The amount of rotation of one segment moving around another. Angular displacement is a vector because both magnitude and direction (clockwise or counterclockwise) must be specified. By convention, counterclockwise is positive and clockwise is negative. The unit for angular displacement is degrees or, in the metric system, radians.

Angular velocity – The rate of change in angular displacement with respect to time. This is also a vector and reported in units of degrees/s or radians/s.

Biomechanics – the science involving the study of biological systems from a mechanical perspective.

Body segments – are considered to be rigid bodies for the purposes of describing the motion of the body. They include the foot, shank or leg, thigh, pelvis, thorax, hand, forearm, upper-arm and head.

Displacement – the change in position in space of a point or object. Displacement is a vector because it both magnitude and direction must be specified. The metric unit is the meter (m).

Dynamics – study of systems in which acceleration is present.

Kinematics – the study of motion of bodies without reference to the forces that cause the motion. Kinematics describe the pattern and temporal aspects of motion such as positions, angles, velocities, and accelerations of body segments and joints during motion.

Kinetics – the study of forces and moments acting on a body (which cause the motion of the body).

Mechanics – the branch of physics involving analysis of the actions of forces.

Position – describes the location of a body segment or joint in space.

Scalar: – a quantity that has only magnitude. Scalar quantities include temperature, height, and speed.

Statics – study of systems that are in a state of constant motion (either at rest or moving at a constant velocity).

Vector – a quantity, which has both magnitude and direction. Force and velocity are both vectors.

Velocity – the rate of change in position with respect to time. Velocity is a vector quantity with both magnitude and direction. This may be either linear or angular. The metric unit for linear velocity is meters/second (m/s). Customarily, velocity is derived from displacement data through the process of differentiation.

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