Analog-to-Digital Converters
Analog-to-Digital Converters (ADC) convert voltage to a
digital value that represents the signal at the instant at
which it was sampled.
ADC integrate third-party devices for capturing analog data
into a Vicon system.
Analogue
devices
ADC
Vicon MX
controller
1
Signal type
Bipolar: (i.e. ±5.0V), full range output 10V
Unipolar: (i.e. between 0-10V)
Dynamic Range
Analog voltage signals digitized over a particular range
Input range
• i.e. min and max input voltage is defined over which the
quantization should occur.
• bipolar, i.e. range ±5V (full range 10V)
• unipolar, range from 0 to 10V
Many A-D converters have an actual range of 0 to 10 V, so
an input signal with a range of 0 to 50 mV needs to be
amplified by a gain of 200 before it can be converted.
Choose range that closely encompasses your signals, as
this will increase the resolution.
2
When sampling the voltage signal with an ADC, two
variables must be considered:
1. Sampling precision (resolution)
How many different gradations (quantization levels) are possible
when taking the sample.
2. Sampling rate
Samples per second
Resolution (quantization)
ADC have fixed number digits, described by binary
digits, or “bits” available for quantifying the voltage signal
detected at the input.
ADC resolution as a
function of bit length
Number of Bits
Range of n-bit ADC = 2n bits
• i.e. 12 bits describe 4096 values
Unique Values
2
4
4
16
8
256
12
4,096
14
16,384
16
65,536
ADC Resolution
Based on the number of steps the input range1 is divided
Many ADC’s have full range of 10 V (±5V),
if an input signal has a range of 50 mV, it needs to be
amplified2 by a gain of 200 before it can be converted.
1 Max
and min voltage that will be digitized.
increases the voltage signal to a level suitable for the ADC
2 Amplification
3
Resolution is expressed as Vresolution = Vrange / (2n)
For a 4 bit ADC with a range of ±10 Volts, (full range 20V)
Vresolution = 20V/(24)
=1.25 V
=1250mV
• Resolution for a ±10V range will be resolved to 1250mV,
• Resolution for a ±5V range will be resolved to 625mV.
Resolution increases when the input range is narrowed,
Steps from 0 to 15 scaled represent full input voltage range
(i.e. ±5 V)
Bits 0 to 7 represent the negative voltage range
Bits from 8 to 15 represent the positive voltage range.
±5.0 V ADC with 16-bit resolution
• 65,536 discreet samples mapped between 0 - 65,536 bits
• OFFSET is 32,767 for a symmetrical -5 to +5 V range
• equally mapped directly as signed integers in the range of –32,767
to + 32,767 OFFSET would be 0.
• If ANALOG:SCALE and OFFSET applied correctly, both
configurations return identical values for the -5 to +5V range.
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Typical input ranges for ADCs are ±5 and ±10 Volts.
• 16- bit ADC with an input range of ±5V has a precision of 153 μV.
• ADC specified for a range at ±10V would have a precision of 305
μV.
Note: no point in trying to resolve signals below the noise
level of the system: all you will get is unstable readings.
It is important to ensure that the ADC range encompasses
the full span of the voltage input while maintaining the
minimum resolution necessary.
Nyquist theorem
Sampling frequency should be at least 2X the highest
frequency contained in the signal.
fs ≥ 2fc
fs: sampling frequency (samples per unit of time)
fc: highest frequency contained in the signal.
Sine wave at a frequency of 1 Hz
Sampling @ 2 Hz capture
each peak
> 2X captures more variation
in the signal
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Aliasing (sampling errors)
< 2X sampling causes highfrequency components to be
aliased with genuine lowfrequency ones, resulting in
incorrectly reconstructed
waveforms during DAC.
Complex signals contain many frequency components.
• Fourier's theorem, continuous signals may be decomposed in terms
of a sum of sines and cosines at different frequencies.
• 1 Hz, 2 Hz, and 3 Hz sine wave added together.
Nyquist theorem is 2X the highest frequency, irrespective of how many
other frequency components.
fc = 3 Hz,
fs ≥ 2fc,
∴ fs ≥ 6 Hz
Digital representation of the original
signal
By increasing both the sampling rate and
the precision, you reduce sampling error .
both the rate and the precision have been
improved by a factor of 2
the rate and the precision have been
doubled again
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Motion Capture Systems & Analysis
Motion studies date back to the 19th century.
• Eadweard Muybridge (1878) most widely known.
Stanford and the gallop question
•
•
•
•
Successive-exposure photography
50 cameras along a track parallel to the horse
Shutters triggered by trip wire by the horse's hooves.
Hooves leave the ground at the moment when all the
hooves are tucked under the horse.
Developed methods to capture human motion
• Pioneer in the Science of Biomechanics and the
mechanics of human movement.
Biomechanics Yellow Pages
http://isbweb.org/c/isb/pub/files/orig_website/~byp/Category_List.html
Animazoo
Intelitek
Qualisys AB
Ariel Dynamics, Inc.
JC Labs
Redlake
Biogesta
Kine ehf.
Robotic Systems Ltd
Biomechanical Solutions
Mechanical Dynamics Inc.
Silicon COACH Ltd
BTS SpA - Bioengineering
Medical Imaging Systems
Charnwood Dynamics Ltd
Motion Imaging Corporation
Skill Technologies, Inc.
Computerized Function Testing Corporation
Mikromak
Spica Technology Corporation, Inc.
CONTEMPLAS GmbH
Motion Analysis Corporation
Sport and Physical Education Technology Ltd.
Darras Software Development
NAC Image Technology
STT Engineering and Systems
Digital motion analysis
Northern Digital
True Tape, LLC.
Electronic Imaging Systems
OsteoKinetics Corporation
Vaquita Software
eMotion
Peak Performance Technologies, Inc.
Vicon Motion Systems
SIMI Reality Motion Systems GmbH
GaitMat II
PhoeniX Technologies
Webbsoft Solutions
Image Diagnostics Ltd
Photo-Sonics
welch-e technologies
Innovative Sports Training, Inc.
Photron
Zebris GmbH
Innovision Systems, Inc.
Pixoft Diagnostics Imaging Ltd
zFlo, Inc.
Electrogoniometers
Biometrics Ltd.
Inexpensive & approximate measure of
joint angle.
Placed across the joint,
One or two or potientimeters between two
bars.
• Uniaxial: rotations in one plane
• Biaxial: simultaneous measure of two rotations
Potentiometer produces change in
electrical output depending on angle
Data logger accommodates EMG,
electrogoniometers, accelerometers.
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Advantages
• portability for collection in the workplace or other
sites
• ease of set up and processing
• relatively low cost
• permit collection and storage of large data sets
over a prolonged period
Disadvantages
• 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 cross talk between
potentiometers.
Electromagnetic tracking systems
Flock of Birds, Polhemus
Transmitter
• (low-frequency magnetic coils) emit an
electromagnetic field.
• reference frame for sensor measurement.
Receiver
• small lightweight cube
• enclosed are electromagnetic coils that detect
magnetic fields.
• position & orientation are precisely measured
as it is moved.
• are completely passive devices, having no
voltage applied to it.
Advantage
• Elimination of marker dropout from camera FOV (which can occur
in videography),
• real time 6-DOF data,
• Accuracy
Limitations
•
•
•
•
Cable connecting sensors can inhibit movement,
sensors slippage,
Limited number of sensors can be tracked at one time and cost.
Interference from metallic objects or other magnetic fields degrade
performance.
• distortion effects normally seen with long range electromagnetic
systems.
• Cost
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Optoelectronic systems
OptoTrak, CODA,Selspot
Active markers
• infrared emitting diodes (LED’s) placed on the
segments or joints.
• LED’s triggered and pulsed sequentially by a
computer, permitting automatic identification of
each marker.
• Position Sensor detects horizontal and vertical
movement of each active marker.
• Independent marker frequencies enables you
to capture data at even higher speeds.
Advantages
• automated marker tracking, no marker
merging or misidentification.
Limitations
•
•
•
•
•
LED’s require wire connection,
Cost
Measurement cumbersome
Limited to the laboratory
More than one camera bank may
be required to obtain adequate
marker coverage.
Videography
APAS, ElitePlus, Motion Analysis, ProReflex, Vicon
Most frequently used.
1 or more cameras track passive reflective
markers.
• Passive markers reflect either external ambient light or
camera-projected light (infrared).
• 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.
Track horizontal and vertical coordinates of each
marker from each camera.
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2D systems
• one camera
• Assumption: all motion is occurring perpendicular to the camera
axis.
• Seldom, marker movement outside this plane will be distorted.
• 2D systems are less accurate than 3-D systems
3D systems
• 3D coordinates computed using 2D data and the known location
from each camera using the principle of optical triangulation.
• Many systems now employ >6
Advantages
•
•
•
•
Track large numbers of markers
High sampling rates (>1000Hz)
the potential for high precision and accuracy
Unencumbered movement
Limitations
• Potential marker merge from various camera views.
• Limit on how close markers may be placed (> 2mm)
• Marker label loss resulting from marker occlusion, dropout or
trajectories crossing
– Missing points filled by interpolation.
• Loss of resolution with high sampling rates
Vicon
Camera performs 2 functions;
• Illuminates capture volume with infrared strobe light.
• Reflections from surface markers seen by each camera.
Pixel resolution and sampling inversely related
• Higher resolution, the lower your sampling rate.
• 2352x1728 pixel images up to 160 Hz
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Marker centroid derived using edge
detection or 10-bit grayscale precision.
More pixel resolution from the markers,
greater accuracy calculating relative 2D
marker position in the 2D FOV.
Vicon: Sampling rate and resolution
MX40 full resolution is over 4 million pixels (2352 H x 1728 V)
≥ 160Hz, decreased camera resolution reduce (vertical windowing).
≥ 500Hz, cameras resolution is 2MP.
Max sampling rate up to 1000Hz.
Turn cameras on side for greater vertical resolution during
high speed capture.
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Purpose of Calibration
Assist in reconstructing 3D positions of captured markers
from 2D camera images
• To establish an absolute reference of origin and orientation
Earlier calibration and reconstruction methods
• Direct Linear Transformation (DLT)Abdel-Aziz YI and Karara HM (1971)
DLT 3-D algorithm contains up to 22 parameters.
to determine all parameters for reconstruction procedures, calibration
devices consisting of precisely measured marker points are used to
determine any unknowns.
• Non-Linear Transformation (NLT) Dapena J, Harman EA, and Miller JA (1982)
Direct Linear Transformation (DLT)
Cameras calibrated using control
points fixed to a rigid calibration
frame.
Accuracy determined by the precision
of the coordinates for the control
points and digitizing errors.
Measurement volume limited by the
size of the calibration frame
• accuracy increased as control points
increased
• Best accuracy achieved with even
distribution
• Accuracy decreased as distance from
control region increased Chen 1994
Static & Dynamic Calibration
y
Static calibration
Establish absolute spatial reference
Utilizes L-frame with two axes
•
•
•
•
x
Establishes origin of lab space
Combines with the first axis to establish the 2nd axis
Resultant cross product is the third axis
Origin specified in CRO file
Dynamic calibration
• Determines relative camera position & orientation
• Linearization
– optical distortion from camera lenses measured
– correction matrix calculated
– corrections applied to each camera
for every frame during MoCap
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Algorithm uses known distance between markers to
establish the scale of the measurement volume.
Additional cameras initiate optimization algorithm to
determine best fit.
This distance constant is specified in the Calibration
Reference Object (CRO) file.
Reconstruction
Mathematical transformation of 2D images from each
camera into a 3-D coordinate system.
Based on precise knowledge of both internal (lens and
camera characteristics) and external (spatial orientation)
camera parameters.
Camera residual
A measure of the accuracy of one camera relative to all
other cameras
Derived from reconstructed wand marker positions from all
cameras.
• Camera in question does not contribute to its own 3D
reconstruction residual
The distance between the reconstructed markers image
and the camera’s own image averaged across all available
samples
– High camera residual = 2D contribution that tends to be less
accurate than the other cameras
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Mean Residual – average of individual residuals
Residual Range – the highest and lowest residuals
Wand Visibility – the average percentage of the wand wave
that contributed to each camera’s calibration
Static Reproducibility – a measure of the accuracy of the
reconstructed positions of the L-frame markers compared
to the CRO file
Common reasons for failed calibrations
Inappropriate wand wave
• Too fast (low frequency)
• Solution: slow wand wave
Poor camera positioning
• Inadequate overlap
• Solution:
– adjust cameras
– May need to customize wand wave
Background static noise
• Reposition cameras
• Adjust camera sensitivities (can be turned up after calibration)
Wand wave tips:
• Avoid breaking cameras’ views with one’s body.
• Position body so the wand can be seen by as many cameras as
possible.
• Move around the entire volume to give all cameras an equal
opportunity to see the wand wave.
• No need to collect more than 1000 samples
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Definitions
Residuals –indicate the quality of calibration
Linearization –process of correcting for lens distortion
Bundle Adjustment – an algorithm that performs the
linearization process by optimizing the camera parameters
to give the best re-projection error
• In signal processing,
• sampling is the reduction of a continuous signal to a discrete signal.
i.e. conversion of a sound wave (a continuous-time signal) to a
sequence of samples (a discrete-time signal).
• Exact reconstruction of a continuous-time baseband signal
from its samples is possible if the signal is bandlimited and the
sampling frequency is greater than twice the signal bandwidth.
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