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Dear colleagues on Biomch-L:
Dr. Guy Simoneau's posting reminded me of some other filtering related
issues.
In usual motion analysis of human movement, we deal with a lot of mechanical
quantities such as positions, velocities, accelerations, angular positions,
angular velocities, angular accelerations, linear and angular momenta,
forces and torques, etc. We are also dealing with many different objects
such as surface markers, joint centers, segmental and whole body CMs,
segments, segment groups, etc. You would all agree that these various
mechanical quantities of different objects are inter-related.
There are many different filtering methods available in these days, but it
seems to me that the digital filtering methods and the spline (cubic and
quintic) methods are the mainstream for the moment. There are many fancy and
beautiful algorithms to automatically take care of the filtering business.
(I recall the debate on Biomch-L sometime ago, saying that one algorithm is
better than others....) But it seems somehow we are missing the important
issues here.
We assume that the data obtained through motion analysis (but not limited to
motion analysis) are contaminated by the noises of random nature. The
filtering methods are employed during data reduction and processing to
discard these noises. Somehow we tend to focus only on the issue that which
method is better than others under which circumstance?
Now, here are the questions I'd like to ask to the Biomch-L readership.
1. Question 1: Which mechanical quantity is the primary candidate for
filtering?
Position of the surface markers or the joint centers? Or the accelerations
of the joint centers or the angular acceleration of the segments? The
general sequence of data processing in a motion analysis is position ->
velocity -> acceleration, so people usually filter the position data of the
surface markers or the joint centers first.
But is this reasonable? Human motion is basically the sum of all the joint
motions. In other words, the angular motions of the segments are the
essential components of human motion. Then should we filter the angular
accelerations of the segments first and then compute all the other
mechanical quantities from the conditioned angular accelerations through
integration, multiplication, etc?
On the other hand, the digitizing process (or marker tracking) is based on
the recorded image so that the position data are more susceptible to random
errors than the angular accelerations of the segments. So, does this justify
filtering of the position data rather than the angular acceleration data?
Then, the digitized coordinates of the markers from each camera or the
resultant 3-D coordinates? Given that the errors in the digitized
coordinates of the markers are random, then can we assume the errors in the
3-D coordinates of the markers to be also random?
2. Do we need to filter the data only once somewhere in data processing or
shall we do it several times?
Given that the primary candidate for filtering is the digitized coordinates
from each view (you know why), is it OK to filter the 3-D positions of the
markers or those of the joint centers, again? What about the CMs of the
segments and the segment groups?
The filtering does not remove all the noises perfectly. Everyone knows this
well. Then, does this justify repeated filtering of the position data at
different stages of data processing? Or should we assume that the noises
were well taken care by filtering the primary candidate.
This issue is certainly different from what Dr. Guy Simoneau raised
recently, though. Filtering off the high frequency signal components in the
velocities and accelerations is in a sense equivalent to distorting the
actual movement. The high frequency components from derivation is natural
and intrinsic to the movement, not something we can throw away that easily.
When we use the position data as the primary candidate for filtering, I feel
there is a possibility that we have to repeat filtering of other position
data as well. We normally treat each marker separately, and each coordinate
separately. This sometimes violates the 'constant segment length' rule. But
what about the angular quantities computed from the position data? Do we
need to filter the angular quantities also or just say the earlier filtering
with the position data was enough?
3. In case of multiple filtering, should we consider the relationships among
different mechanical quantities?
Suppose that we filtered the knee and ankle position data using a digital
filter with the cutoff freq. being f(knee) Hz and f(ankle) Hz, respectively.
What frequency should we use for the shank CM? Treat the shank CM
independent from its two end points? Or somehow consider the realtionship
between the shank CM position and the joint positions:
vector p(shank) = x * vector p(knee) + (1-x) * vector p(ankle) (Eq.
1)
where, x = inertial constant (0
Dr. Guy Simoneau's posting reminded me of some other filtering related
issues.
In usual motion analysis of human movement, we deal with a lot of mechanical
quantities such as positions, velocities, accelerations, angular positions,
angular velocities, angular accelerations, linear and angular momenta,
forces and torques, etc. We are also dealing with many different objects
such as surface markers, joint centers, segmental and whole body CMs,
segments, segment groups, etc. You would all agree that these various
mechanical quantities of different objects are inter-related.
There are many different filtering methods available in these days, but it
seems to me that the digital filtering methods and the spline (cubic and
quintic) methods are the mainstream for the moment. There are many fancy and
beautiful algorithms to automatically take care of the filtering business.
(I recall the debate on Biomch-L sometime ago, saying that one algorithm is
better than others....) But it seems somehow we are missing the important
issues here.
We assume that the data obtained through motion analysis (but not limited to
motion analysis) are contaminated by the noises of random nature. The
filtering methods are employed during data reduction and processing to
discard these noises. Somehow we tend to focus only on the issue that which
method is better than others under which circumstance?
Now, here are the questions I'd like to ask to the Biomch-L readership.
1. Question 1: Which mechanical quantity is the primary candidate for
filtering?
Position of the surface markers or the joint centers? Or the accelerations
of the joint centers or the angular acceleration of the segments? The
general sequence of data processing in a motion analysis is position ->
velocity -> acceleration, so people usually filter the position data of the
surface markers or the joint centers first.
But is this reasonable? Human motion is basically the sum of all the joint
motions. In other words, the angular motions of the segments are the
essential components of human motion. Then should we filter the angular
accelerations of the segments first and then compute all the other
mechanical quantities from the conditioned angular accelerations through
integration, multiplication, etc?
On the other hand, the digitizing process (or marker tracking) is based on
the recorded image so that the position data are more susceptible to random
errors than the angular accelerations of the segments. So, does this justify
filtering of the position data rather than the angular acceleration data?
Then, the digitized coordinates of the markers from each camera or the
resultant 3-D coordinates? Given that the errors in the digitized
coordinates of the markers are random, then can we assume the errors in the
3-D coordinates of the markers to be also random?
2. Do we need to filter the data only once somewhere in data processing or
shall we do it several times?
Given that the primary candidate for filtering is the digitized coordinates
from each view (you know why), is it OK to filter the 3-D positions of the
markers or those of the joint centers, again? What about the CMs of the
segments and the segment groups?
The filtering does not remove all the noises perfectly. Everyone knows this
well. Then, does this justify repeated filtering of the position data at
different stages of data processing? Or should we assume that the noises
were well taken care by filtering the primary candidate.
This issue is certainly different from what Dr. Guy Simoneau raised
recently, though. Filtering off the high frequency signal components in the
velocities and accelerations is in a sense equivalent to distorting the
actual movement. The high frequency components from derivation is natural
and intrinsic to the movement, not something we can throw away that easily.
When we use the position data as the primary candidate for filtering, I feel
there is a possibility that we have to repeat filtering of other position
data as well. We normally treat each marker separately, and each coordinate
separately. This sometimes violates the 'constant segment length' rule. But
what about the angular quantities computed from the position data? Do we
need to filter the angular quantities also or just say the earlier filtering
with the position data was enough?
3. In case of multiple filtering, should we consider the relationships among
different mechanical quantities?
Suppose that we filtered the knee and ankle position data using a digital
filter with the cutoff freq. being f(knee) Hz and f(ankle) Hz, respectively.
What frequency should we use for the shank CM? Treat the shank CM
independent from its two end points? Or somehow consider the realtionship
between the shank CM position and the joint positions:
vector p(shank) = x * vector p(knee) + (1-x) * vector p(ankle) (Eq.
1)
where, x = inertial constant (0