ARIEL FILTER PROGRAM
INTRODUCTION
The ARIEL FILTER
software is used to remove small random digitizing errors or "noise"
from the transformed image sequence. In
addition, because the motion of each point is determined by a continuous smooth
function, the ARIEL FILTER software is able to compute point velocities
and point accelerations for each frame in the image sequence. Smoothing is always performed following
transformation and prior to the presentation phase.
It is not necessary to
understand the technical basis for smoothing in order to run the ARIEL FILTER
software and as such this section may be skipped. The Technical Aspects of Transformation and Smoothing section
presents the mathematical basis for the smoothing algorithms used by the ARIEL FILTER
software for those desiring a more technical discussion of smoothing theory.
The digitizing process
involves measuring the location of each body joint. As with any type of measurement, there is no correct value, only
an estimate to some known level of accuracy.
Therefore, each measurement consists of two parts: the actual or true
value, plus an error value due to the inability to perform exact
measurements. If there is only a single
measurement, it is impossible to separate the error value from the true value. However, if repeated measurements are made,
statistical theory allows the estimation and removal of the error, provided the
error is of a random nature.
Digitized joint locations
are a type of repeated measurement. For
a number of consecutive frames or time intervals, the location of each joint is
measured. These measurements consist of
the true joint location plus a random digitizing error due to the inability to
position the stylus or cursor to the exact joint location.
Two obvious questions are
"What is Optional Smoothing?” and "How does one determine the best
smoothing values for a given joint?”
The ARIEL FILTER software has been designed to allow visual
determination of optimal smoothing by viewing smoothed curves, as well as power
spectrum curves, on the graphic display.
Often, there is very little difference between the raw displacement
curves and the smoothed curves since digitizing errors tend to be small. It is necessary to highlight the differences
in these curves in order to tell how well a given smoothing value approximates
true joint motion.
One method would be to
greatly enlarge each curve to allow small variations to be easily viewed. The FILTER module allows for this
feature, but there is a better way.
In addition to the
displacement curves, the FILTER module can display velocity and
acceleration curves for each component.
Since the derivative of a curve is the slope or rate of change of the
values for that curve, taking successive derivatives has the effect of
emphasizing or highlighting the variations or "noise" in the data. Thus, by viewing the acceleration curves,
the extent of random error remaining in the data can more easily be
determined. Smoothing values can then
be adjusted accordingly.
WHAT’S NEW IN FILTER 1.0
A few of the new features
you will see in FILTER version 1.0
1. 1. Smooth Data Curves. Data curves are displayed for each of the X, Y, and Z components.
2. Power Spectrum Curves. Simultaneous display of Power Spectrum curve for each of the X, Y and Z components.
3. APAS Tool Bar. A toolbar has been added to allow the user to activate individual APAS modules from within the main programs.
4. Sliding Adjustment Bars. Sliding adjustment bars have been added to allow independent smoothing adjustments with real-time results.
5. Impact Points. Selected portions of the data curve can be designated as impact points to increase the closeness of fit.
SYSTEM REQUIREMENTS
The following table
provides the basic guidelines for minimum and recommended hardware to provide
the best possible performance. The
software requires Microsoft Windows 95/98/NT/2000 and APAS-2000 Revision 3.2 or
later.
Component Minimum Recommended
_____________________________________________________________________________________________________________________________________________________
Pentium
Computer Pentium 233 Pentium
III 333 MHz or higher
Video
Display S-VGA (256
Colors) High
Color Display (65,000 colors or more)
RAM
64 MB 128
MB or more
TO START THE FILTER PROGRAM
1. 1. Double-click the FILTER icon located in the APAS System window group. The main FILTER window will appear.
SCREEN LAYOUT
Prior to performing the FILTERING
process, you should take the time to familiarize yourself with the format and
contents of the various screens listed below:
THE APAS TOOL BAR
You can activate any of
the APAS software modules from within the current program by selecting the
icons located on the APAS tool bar. The
tool bar is toggled on/off using the APAS Toolbar command in the VIEW menu. A check mark in the left column of the menu
indicates that the toolbar is currently active. The toolbar can be re-located anywhere in the main program window
by dragging it with the mouse. The
following program modules can be activated by clicking the appropriate
icon. Icons are pictorial representations
of programs, commands or functions.
THE TOOL BAR
You can activate many
functions by selecting the icons located on the FILTER program tool
bar. The tool bar is located near the
top of the window. Icons are pictorial
representations of commands or functions.
You can access the following commands by clicking the appropriate icon.
THE STATUS BAR
The status bar provides
useful information about the current status of the file during the Smoothing
process. The status bar is located at
the bottom of the FILTER window.
The far-left side of the status bar is divided into four separate
fields. The left field displays the total number of points in the selected
sequence. The DATA RATE field indicates
the data frequency. The third field
indicates the SMOOTH MODE. The right
field indicates whether the sequence is being smoothed Manually or
Automatically.
THE FILTER PARAMETERS BAR
You can activate most
smoothing functions by selecting the desired option located on the FILTER
Parameters bar.
Smoothing Values - The data curves show the smoothed and raw values
for each of the coordinate components, X, Y, Z for all frames in this
sequence. The FILTER module
automatically selects the default smoothing algorithm as well as the default
smoothing values. The degree of
smoothing for each coordinate joint is controlled by the smoothing values.
The smoothing value for the
spline algorithms is the average error allowance for each point on the curve in
user units. Thus, if the units for this
sequence are centimeters, the default smoothing value allows the smoothed
curves to vary from the raw curves by an average of one centimeter for each
point along the curves. The smoothing
value for the digital filter algorithm represents the “cut-off” frequency.
To change the degree of
smoothing for one or more of the coordinate curves, new smoothing values must
be entered. Smaller values allow less
error and thus fit the raw data more closely.
Larger values allow more error and thus produce smoother curves. New values are entered by either selecting
the desired X, Y and/or Z data field and typing the desired value, or by
adjusting the slider bar in the left and right directions.
When all changes have been
entered, the Re-Calc button is selected to display the new curves showing the
results of the new smoothing values.
Since smoothing is a repetitive process, this procedure may be repeated
several times for each joint.
Smoothing Algorithm - Smoothing algorithm is selected when the algorithm
or computational method used to smooth the data values is to be changed. The current algorithm is displayed in the
Algorithm field. After selecting the
desired algorithm, the Re-Calc button must be selected to graph the data curves
with the new algorithm.
Re-Calculate - The Re-Calc button is selected when the current
joint curves are to be re-smoothed using the algorithm and smoothing values
that appear in the Parameters bar. The
new curves will be displayed showing the results of the new parameters.
Current Joint - The Joint data field lists the current joint for
smoothing. This option can also be used
to smooth a joint out of the normal consecutive sequence of joints. For example, the Joint data field could be
used to return to a previously smoothed joint to check smoothing or to
re-smooth that data and them to proceed to the next joint to be smoothed. Another application might be to smooth a
specific joint or joints while skipping other joints. This would be the case if one wished to perform a partial
analysis, perhaps only considering the motion of certain body joints or
segments and ignoring others. In most
cases, it is recommended that all body joints be smoothed. Otherwise, certain joint and segment
velocities and accelerations would be missing when subsequent analysis
functions such as viewing, graphing and printing were performed.
SMOOTHING A SEQUENCE FILE (MANUAL)
Prior to performing the
smoothing procedure, make certain that the desired sequence has been completely
digitized and transformed. It is
possible to re-smooth a sequence at any time, as the original un-smoothed data
is always retained along with the current smoothed data values.
1. 1. Choose the OPEN command from the FILE menu. The OPEN File Dialog box will appear.
1. The OPEN File Dialog box looks for a particular type of file (files that have the extension of (*.3D). This file is automatically created when a Sequence file is transformed using either the ARIEL TRANSFORMATION software module. The OPEN File Dialog box can be used to specify the Drive, Directory, and Name of the sequence file to be retrieved. Select the sequence name to be smoothed and then select OPEN to proceed. When the desired sequence is opened, three smoothed data curves and corresponding power spectrum curves will appear on the graphic display. The smoothing values and algorithm for the first joint will be determined by the default settings.
1. 2. Select the desired algorithm from the Parameters bar at the top of the FILTER window.
2. 3. Specify the X, Y and Z smoothing values in the corresponding data fields from the Parameters bar at the top of the FILTER window. The slider bars can also be used to adjust the smoothing values and display the results in real-time.
3. Select the ReCalc button in the Parameters bar to smooth the data curve using the specified algorithm and smoothing values.
4. Select VIEW, GRAPH FWD to toggle between position, velocity, acceleration and 3rd derivative for viewing the desired "smoothed" curve.
5. Repeat steps 2 through 5 until the desired smoothing algorithm and values are achieved.
6. Select VIEW, NEXT JOINT to advance to the next sequential joint in the sequence.
7. Repeat steps 2 through 6 for each of joint in the selected sequence.
8. Select OPTIONS, SUMMARY to display a list of smoothed points, and the algorithms and smoothing values used.
9. Select FILE, EXIT to exit the FILTER program.
10.
SMOOTHING A SEQUENCE FILE (AUTOMATIC)
This mode smoothes all the
remaining joints in this sequence with the current default smoothing algorithm
and values. It is the equivalent of
selecting the NEXT JOINT command once for each joint after the current one. Automatic smoothing is used when completing
the smoothing process as rapidly as possible and without additional human
interaction is the concern and not obtaining optimal smoothing for each joint.
The curves for each joint
will still be displayed as smoothing is performed, however, re-smoothing of
joints is not allowed during the automatic process. At the end of the process, individual joints may be re-smoothed
if desired.
Typically, the first joint
is smoothed manually and the default smoothing algorithm and values are then
adjusted accordingly before selecting the Automatic option. In general, the best smoothing is performed
manually rather than in automatic mode.
1. 1. Choose the OPEN command from the FILE menu. The OPEN File Dialog box will appear.
1. The OPEN File Dialog box looks for a particular type of file (files that have the extension of (*.3D). This file is automatically created when a Sequence file is transformed using the TRANSFORMATION software module. The OPEN File Dialog box can be used to specify the Drive, Directory, and Name of the sequence file to be retrieved. Select the sequence name to be smoothed and then select OPEN to proceed. When the desired sequence is opened, three smoothed data curves and corresponding power spectrum curves will appear on the graphic display. The smoothing values and algorithm for the first joint will be determined by the default settings.
2. Select OPTIONS, ALGORITHM to set the Default Algorithm and Default Smoothing values for the specified algorithm. These parameters are best determined by manually smoothing the first joint.
3. Select AUTOMATIC, BEGIN (or the GO icon in the Toolbar) to begin the automatic smoothing function.
4. Select OPTIONS, SUMMARY to display a list of smoothed points, and the algorithms and smoothing values used.
5. Select FILE, EXIT to exit the FILTER program.
IMPACT POINTS
A special function
included with the ARIEL FILTER software is the ability to specify
“impact” points. The name of this
function is derived from its most common application - instances of impact or
abrupt applications of external force in the sequence being analyzed. Impact is selected when you wish to have the
smoothed curves more closely fit the raw data curves over a small interval of
the sequence (to increase the closeness of fit over a large interval or the
entire sequence, the smoothing values should be used). A typical application for impact points would
be to accommodate sudden accelerations, such as when a club or racket strikes a
ball - a situation requiring a “tighter” fit.
When impact occurs, the
acceleration of one or more joints will change significantly over a period of
only a few milliseconds. All smoothing
algorithms have the effect of removing high frequency variations in the data,
and as a result, the change associated with an impact point is “spread” over a
longer interval in the smoothed curve.
The “Impact” option
provides a way of specifying that for a given data interval higher frequency
variations in values are to be permitted.
This will result in smoothed curves that more closely fit an abrupt
change in the raw data curves. When
this option is selected, the user will be asked to specify the impact region
using the mouse. These points will be
marked on the display with arrows to indicate where the impact function will be
applied. This can be repeated up to 3
times for any point with each additional time causing a tighter fit at the
point. This will be indicated by the arrow
having a longer tail. It is suggested
that when re-applying the impact option, the interval over which it is applied
should be reduced by one or two points in order to produce a smooth transition
on the smoothed curve. Each time the
impact option is applied, the allowed “error” over that interval is reduced to
about one third of the previous value.
Thus, two applications of impact reduce the allowed error by an order of
magnitude.
A word of caution about
the use of the impact option: Try to
keep the intervals small and the number of re-applications to a minimum. When the frequency of the allowed data
variations increase, the amount of “noise” that will be present in the smoothed
data is also increased. A point of
diminishing returns is rapidly reached.
That is, there will be little or no additional information that can be
extracted from the raw data curves by increasing the closeness of fit.
NOTE: This option
may only be selected for the Cubic and Quintic Spline algorithms, it is not
supported for the digital filter or polynomial algorithms.
ADDING
IMPACT POINTS
1. Use the Advance/Reverse commands to display the desired joint for the impact option to be implemented.
2.
Select the ADD command from the IMPACT
menu (or select the ADD IMPACT icon).
A dialog menu appears instruction the user to click at the start of the
impact region and then drag to the end.
When the mouse is released, a down arrow appears over the points in the impact
range. This can be repeated up to 3
times for any point with each additional time causing a tighter fit at the
point. This will be indicated by the
arrow having a longer tail.
3. The actual smoothed curves will not change until the RECALC button is selected.
REMOVING
IMPACT POINTS
1. Use the Advance/Reverse commands to display the joint with the impact option applied.
2. Select the ERASE command from the IMPACT menu (or select the ERASE IMPACT icon).
OPTIONS
The ARIEL FILTER software
contains many options designed to enhance the smoothing process. Selecting the OPTIONS menu accesses these
options. Available options allow for
selecting the default algorithm and smoothing values, changing the smoothing
mode and providing a summary of smoothing values used for the current
sequence.
SMOOTHING ALGORITHMS
The Algorithm
command is selected from the OPTIONS menu when the algorithm or
computational method used to smooth the data values is to be changed. When this command is selected, the Algorithm
Defaults menu will be displayed listing the smoothing algorithm that is
currently set as the default algorithm.
CUBIC SPLINE ALGORITHM
The Cubic Spline
algorithm is based on traditional spline function theory and has been enhanced
to allow approximate fitting rather than the traditional exact fitting to the
data points. The
"closeness-of-fit" can be adjusted using the smoothing values. Smaller smoothing values result in a closer
fit to the original data while larger values result in smoother curves. A cubic spline is constructed of piecewise
third-order Polynomials that pass through a set of control points. When this
algorithm is utilized, the user should be aware that the second derivative
(acceleration curve) of each Polynomial is forced to zero at the end points
regardless of the actual data. The
Cubic and Quintic splines are the most sophisticated of the smoothing
algorithms and give the best results in approximating complex data curves. Select the Cubic tab to enter the Default
smoothing values and slider limits for the Cubic Spline algorithm.
QUINTIC SPLINE ALGORITHM
The Quintic Spline
algorithm, like the Cubic Spline, is based on traditional spline function
theory and has been enhanced to allow approximate fitting rather than the
traditional exact fitting to the data points.
The "closeness-of-fit" can be adjusted using the smoothing values. Smaller smoothing values result in a closer
fit to the original data while larger values result in smoother curves. A Quintic spline is constructed of piecewise
fifth-order Polynomials that pass through a set of control points. Quintic
spline smoothing proves extremely useful for cyclical type motion such as
pedaling a bicycle. The Cubic and
Quintic splines are the most sophisticated of the smoothing algorithms and give
the best results in approximating complex data curves. Select the Quintic tab to enter the Default
smoothing values and slider limits for the Quintic Spline algorithm.
DIGITAL FILTER ALGORITHM
The Digital Filter,
algorithm smoothes the data points by removing or attenuating "noise"
above the selected cutoff frequency while retaining the lower frequency
data. Larger values produce a closer
fit while smaller values produce smoother curves. This is just the opposite of spline smoothing. Select the Filter tab to enter the Default
smoothing values and slider limits for the Digital Filter algorithm.
1.
MODE
The Mode command is
selected from the OPTIONS menu when the smoothing mode used to smooth
the data values is to be changed. When
this command is selected, the Enter Smoothing Mode menu will be displayed
listing the smoothing mode that is currently selected.
EXAMINE MODE
The Examine Mode is
selected when all un-smoothed joints are to be smoothed using the current
default smoothing values, but only the current smoothing values for joints
already smoothed are to be displayed. This
is the default mode for smoothing, as it allows the user to return to previous
joints to inspect smoothing without inadvertently changing the smoothing
values. Previously smoothed joints may
be re-smoothed by specifying new X, Y and/or Z values and selecting the ReCalc
button.
RESMOOTH MODE
The Resmooth Mode
is selected when every joint is to be smoothed with the current default XYZ
smoothing values. Joints that have been
previously smoothed will be re-smoothed with these default values. This mode should be used when a previously
smoothed sequence is to be re-smoothed.
FROM FILE MODE
The File Mode is
selected when the smoothing values from the corresponding joint in a previously
smoothed sequence is to be used as the default smoothing values for the current
sequence. Corresponding joints are
matched by joint ordinal (i.e. 1st, 2nd, 3rd, etc.) not be joint name. This option is frequently used when
smoothing a number of sequences of the same activity that were digitized by the
same person and is also frequently used in conjunction with the automatic
mode. When this option is selected, an
additional menu will be displayed for selecting a previously smoothed sequence.
SUMMARY
The Summary option can be selected from the OPTIONS menu to present a table summary of the smoothing performed on the current sequence. This table shows, for each joint, if smoothing has been performed and the smoothing values and algorithm used. The summary option is helpful for quickly checki