PDA

View Full Version : # of Cameras



Pete Stothart
11-05-1998, 01:24 AM
Hello Biomch-L Readers,

The following is a summary of responses to a question posted to the list
last week. Thank you to all who responded.
The original posting was:

I am requesting your help on an issue of accuracy in 3D kinematic data
analysis. We are conducting a project using 60 and 200 hz video cameras
to capture images of an activity in a field width of 1.5 - 3 metres.
We have determined that we can see our joint/segment markers
sufficientlywell with the 2 cameras but we are trying to decide whether
we need more than two cameras to achieve maximum accuracy. The research
literature
does not appear to clearly indicate whether greater accuracy can be
achieved with 3 or 4 cameras as opposed to 2 cameras. Is anyone out
there aware of studies that can help us with this question? Does anyone
have first hand experience with the issue? Thanks for any assistance you
can give us.


-Can't help you there, but I am curious if you have ever used a magnetic
tracking system. This would be a non-issue
since each sensor (or "marker") records all 6 degrees of freedom, xyz,
roll, pitch, yaw, automatically.
Let me know if you are interested in our biomechanic motion capture
systems.

Gregory S. Erdmann

-This is off the top of my head, so I can't document it, but when I did
some research with 4 cameras, I checked to see if accuracy improved. I
think 3 was better than 2, but 4 didn't add any accuracy. I think if
you have a good calibration and can see markers well from both cameras,
2 will be just as accurate as 4. I think the biggest key to accuracy is
to make sure the move is within/close to your control volume.

Martha Nichols-Ketchum


-I can say to you two things :
1/ the errors due to DLT can be really reduced with the use of 3
cameras (or more). Only 2 cameras are needed in order to determine 1
point in space. but with more cameras (better 4 +), the errors are
reduced by the leastsquare method. So the more you have cameras the
better are the results. But by experience the best number of cameras
depend on the field. Consequently what are your limit level of error ?
2/ 2 cameras cannot see every point because of complex movements.
So a greater number of cameras than 2 has to be used if you want to
cover correctly your field.I think that 4 cameras will be better in
anycase. I can't give you a lot of information today because of not
enough time. But remail me after 11/11/1998 for references.

Nicolas BELLUYE


- Of course it depends on what you are going to measure. If it is a
movement primarily in the x,y coordinate, 2 cameras are enough. If it is
a rotational movement and you need all the x,y,z coordinates, then 3 or
5 cameras will give you higher accuracy. From my experience, additional
3rd camera can increase the accuracy by as much as 5 percent. 4 Cameras
do not add much more. Check at:
http://www.arielweb.com/Topics/comparison/default.htm

Gideon Ariel


-I have not seen any specific study nor standard calculation of
accuracy. Especially with 2,3,or 4 cameras. At Motion Analysis we used
the following in investigations many years ago to determine 3D accuracy
and precision.
In determining accuracy, you are actually measuring the "Error" in the
system. Accuracy also starts with the camera / lens distortion mapping
and calibrations as well as your volume calibrations. In theory you can
calculate the average accuracy of 3D Measurements using the following:

Error = Measured Length -Known
Length Accuracy = Error / Field of View

For example: if you are using a rigid triangle for a dynamic test and
the distance between the lengths are as follows:

Sides Measured Known Error
Average Error = .467 Field of view = 3000 mm
Distance 1- 2 86.672 86.327 .345 mm
Distance 2-3 86.908 86.031 .949 mm Ave
Accuracy = .467 mm (Error) / 3000 mm (FOV)or
Distance 2-3 86.586 86.475 .111
mm .000155666 or 1:6424 parts

Therefore Accuracy is defined as the difference between the average
system measurement and the known measurement within your field of view.
Secondly, go one step further into precision defined as the standard
deviation of the length of measurement, usually expressed in relation to
the entire field of view.

For example
Sides Measured Stnd Dev
Average = 1.02 mm
Distance 1- 2 86.672 .93 mm
Distance 2-3 86.908 1.01 mm Average
Precision = 1.02 mm (Ave S.D) / 3000 mm (F.O.V)
Distance 2-3 86.586 1.12
mm or 1:2941

Finally, you can do the same calculation to determine Angular error
which is derived from the above precision and accuracy measures.
The Dynamic Triangle measures the following:

Error Mean SD
Known Angular error = .247 degrees
Angle 1,2,3 (.233 degrees) 59.945 .87 59.712
Angle 1,3,2 (.371 degrees) 59,843 .85
60.214 Average Angular Error = .247 degrees / 3000 mm
Angle 2,1,3 (.138 degrees) 60.212 .80 60.074

Daniel India


-I am assuming that you are using the DLT procedure to get the 3-D
coordinates. The basic requirement of the DLT procedure regarding the
number of cameras is that each marker has to be captured by at least two
cameras at any
moment during the movement. There is no evidence that increasing number
of cameras will improve the accuracy. As far as I understand, the main
purpose of using more than two cameras is to make sure that the basic
requirement of the
DLT procedure is satatisfied for every marker, not to improve the
accuracy of the estimated 3-D coordinates. When using more than two
cameras and a marker was captured by all cameras, it is not necessary to
use the digitized data from
all cameras to estimate the 3-D coordinates. Idealy, only the data from
the two cameras with the optimum optical axis angle (about 90 degrees)
should be used. That may give you the best accuracy. Adding a camera
with a poor optical axis angle (less than 45 degrees) with other cameras
may actually cause extra error in the estimated 3-D coordinates. In
adding an extra camera will increase your digitizing time. With all
these considerations, I suggest you use only two cameras as long as the
basic requirement of the DLT procedure is satistied for every marker.
Good luck.

Bing Yu


-The following journal article may be of benefit: Ehara Y et al. 1995
Technical note: comparison of the performance of 3D
camera systems. Gait and Posture, Vol. 3, 166-169. This article compares
the accuracy of eight motion analysis systems.
Could you send me a summary of your replies? I am presently completing a
doctorate that requires subjects to be filmed as they approach (10 m
approach) a raised surface. I am trying to determine how many cameras I
need to film the approach. At present, it appears that I may only be
able to use a camera field of approx. 2.5 m width and 2 m high.
Therefore 4 cameras may be required. Have you considered panning? The
new Motus Peak system can accomodate
panned film, but I have no idea of the accuracy.

Noel Lythgo


-As you mentioned correctly, 2 cameras are sufficient to collect 3D
data.Basically, the correct statement should read: you need at least 2
cameras that can "see" you markers all the time. Depending on the
movement you
are considering, this might ask for at least 2, but may be 3, 4 or even
6 cameras. There is one big however, though, and that is normally never
mentioned by the analysis equipment manufacturers. Any camera has its
own accuracy and off set. During calibration, these camera parameters
are determined. When calculating 3D data the camera parameters of the
camera combination that "see" the marker are used. In case of 2 cameras,
there is no problem, because the DLT is unique. When 3 or more cameras
"see" the marker, usually a certain averaging is applied so that the
data of all cameras are effectively used in determining the 3D data.
This is claimed to improve the accuracy of the 3D data. Basically a
statement that is true. Now the "however". Suppose you have a situation
where 3 cameras see the marker, and 1 camera loses the view. From that
moment onwards only 2 cameras must be used to calculated the data from.
Inevitably, there will be a (small) jump in calculated 3D data because
the camera parameters of all 3 cameras are not identical. Basically, a
(minimal) jump in 3D data will occur any time there is a change in
number of cameras that see a marker. Is this jump a problem? Usually not
in determining normal 3D position data. However, when you want to
calculate position derivatives, such as velocity, or even worse,
acceleration, these jumps might seriously interfere with accurate and
reliable data (understatement!). Keep in mind, that data smoothing might
be effective in getting rid of these jumps, but not
necessarily in all cases, depending on which camera combinations cause
the jump, and what frequency content you signal has.
What kind of an advise is the best in figuring out how many cameras you
need? Well it's easy. Use as many cameras as you can afford, and if it
happens to be 3 or 2, perform some measurements where you momentarily
block the view of one of the 3 cameras. The above mentioned jump is then
visible right away.

Henk C. Schamhardt


-How are things in Ottawa. Interesting problem of cameras for tracking
3D motion. Most articles focus on the number of calibration points and
the error as you expand past the calibration area. As you may remember,
Doris Miller and I conducted a 3D study of axel jumps in figure
skating. We used 4 cameras in our work due to the spinning nature of
the skill. However, if my memory serves me correctly we did not see a
large increase in accuracy with increased camera views when the choice
was available. Our program was written to use alll 4 cameras if the
landmark was visible else select the next best configuration of camera
views. I remember looking at the errors using various combinations,
while they were affected, I do not think it is a large concern if you
can clearly see the markers in ever case. A study similar to ours by
King et al., used only 3 cameras to record the motion. A third camer
would eliminate any problems or potential concerns of missing markers.
If you only have two and you miss a marker in a camera view your left
interpolating points.

Wayne Albert


-Great question. Unfortunately, I do not have any definitive answer for
you from my own experience, but it would seem to make sense that if you
had redundant data, then you could somehow use this to improve the
accuracy of your calculations. FYI, a similar question exists with
whether or not you should use more than three markers per segement to
reconstruct the approximate rigid body motion. Only three markers are
needed in theory, but skin and soft tissue motion add noise to the data.

I think someone has done some work on this to show when adding more
markers per segment might be beneficial. You may want to try to track
down this work, since similar reasoning may apply to the issue of using
more than two cameras.

B.J. Fregly


-Theoretically, 2 cameras are enough, but one always riscs getting
ghostmarkers when tracking the data, since there are situations when
there are 2 possibilities for the positions of the markers to be
calculated from the marker images:

^ ^ - A 3rd camera
solves this ambiguity. My works in the lab led to the
H H -experience that
it is always better to have as many cameras as possible,
/_\ /_\ -but the costs
are the limiting factor. The more marker images from
.. .. -different
perspectives there are, the better is the approximation of the
. . -real
markerposition in space.
. . -
. . . . -
.*. -
. . . . -
O O -
- Arnim
Henze
. .

. .

*


This question was intensively answered by Woltring , Spoor and Veldpaus
in different issues of the J. Biomech. I wonder why this very important
articles are not known in the canadian literature

H Bär


Once again thanks, to all who took the time to respond. I will be
communicating with individuals.

--
*+*+*+*+*+*+*+*+*+*+*+*+*+*+*+*+*+*+*+*+*+*+*+*+*+ *+*+*+*+

J.Peter Stothart
School of Human Kinetics
University of Ottawa
Ottawa, On K1N 6N5
(613) 562-5800 ext4264
(613) 562-5149 fax
(819) 827-4794 (home)

"In skating on thin ice, our safety is in our speed"
Ralph WaldoEmerson




Hello Biomch-L Readers,
The following is a summary of responses to a question
posted to the list last week. Thank you to all who responded.
The original posting was:
 I am requesting your help on an issue of accuracy
in 3D kinematic data analysis. We are conducting a project using 60 and
200 hz video cameras to capture images of an activity in a field width
of 1.5 - 3 metres.
We have determined that we can see our joint/segment
markers sufficientlywell with the 2 cameras but we are trying to decide
whether we need more than two cameras to achieve maximum accuracy. The
research literature
does not appear to clearly indicate whether greater
accuracy can be achieved with 3 or 4 cameras as opposed to 2 cameras. Is
anyone out there aware of studies that can help us with this question?
Does anyone have first hand experience with the issue? Thanks for any assistance
you can give us.
 
-Can't help you there, but I am curious if you have ever
used a magnetic tracking system. This would be a non-issue
since each sensor (or "marker") records all 6 degrees
of freedom, xyz, roll, pitch, yaw, automatically.
Let me know if you are interested in our biomechanic
motion capture systems.
Gregory S. Erdmann
-This is off the top of my head, so I can't document it,
but when I did some research with 4 cameras, I checked to see if accuracy
improved.  I think 3 was better than 2, but 4 didn't add any accuracy. 
I think if you have a good calibration and can see markers well from both
cameras, 2 will be just as accurate as 4.  I think the biggest key
to accuracy is to make sure the move is within/close to your control volume.
Martha Nichols-Ketchum
 
-I can say to you two things :
    1/  the errors due to DLT can
be really reduced with the use of 3 cameras (or more). Only 2 cameras are
needed in order to determine 1 point in space. but with more cameras (better
4 +), the errors are reduced by the leastsquare method. So the more you
have cameras the better are the results. But by experience the best number
of cameras depend on the field. Consequently what are your limit level
of error ?
    2/  2 cameras cannot see every
point because of complex movements. So a greater number of cameras than
2 has to be used if you want to cover correctly your field.I think that
4 cameras will be better in anycase. I can't give you a lot of information
today because of not enough time. But remail me after 11/11/1998 for references.
Nicolas BELLUYE
 
- Of course it depends on what you are going to measure.
If it is a movement primarily in the x,y coordinate, 2 cameras are enough.
If it is a rotational movement and you need all the x,y,z coordinates,
then 3 or 5 cameras will give you higher accuracy. From my experience,
additional 3rd camera can increase the accuracy by as much as 5 percent.
4 Cameras
do not add much more. Check at: http://www.arielweb.com/Topics/comparison/default.htm
 Gideon Ariel
 
-I have not seen any specific study nor standard calculation
of accuracy. Especially with 2,3,or 4 cameras. At Motion Analysis we used
the following in investigations many years ago to determine 3D accuracy
and precision.
In determining accuracy, you are actually measuring the
"Error"  in the system. Accuracy also starts with the camera / lens
distortion mapping and calibrations as well as your volume calibrations.
In theory you can calculate the average accuracy  of 3D Measurements
using the following:
             
Error = Measured Length -Known Length                            
Accuracy = Error / Field of View
For example:  if you are using a rigid triangle for
a dynamic test and the distance between the lengths are as follows:
Sides                   
Measured        Known       
Error            
Average Error   = .467       
Field of view  = 3000 mm
Distance  1- 2       
86.672           
86.327        .345 mm
Distance  2-3        
86.908           
86.031        .949 mm       
Ave Accuracy = .467 mm (Error) / 3000 mm (FOV)or
Distance 2-3         
86.586           
86.475        .111 mm                                
000155666  or 1:6424 parts
Therefore Accuracy is defined as the difference between
the average system measurement and the known measurement within your field
of view.
Secondly, go one step further into precision defined
as the standard deviation of the length of measurement, usually expressed
in relation to the entire field of view.
For example
Sides                   
Measured        Stnd Dev               
Average  = 1.02 mm
Distance  1- 2       
86.672               
93 mm
Distance  2-3        
86.908             
1.01 mm            
Average Precision = 1.02 mm (Ave S.D) / 3000 mm (F.O.V)
Distance 2-3         
86.586             
1.12 mm                                           
or 1:2941
Finally, you can do the same calculation to determine
Angular error which is derived from the above precision and accuracy measures.
The Dynamic Triangle measures the following:
Error                                      
Mean           
SD          Known      
Angular error = .247 degrees
Angle 1,2,3 (.233 degrees)       
59.945        .87           
59.712
Angle 1,3,2 (.371 degrees)       
59,843        .85           
60.214      Average Angular Error =  .247
degrees / 3000 mm
Angle 2,1,3 (.138 degrees)       
60.212        .80           
60.074
Daniel India
 
-I am assuming that you are using the DLT procedure to
get the 3-D coordinates. The basic requirement of the DLT procedure regarding
the number of cameras is that each marker has to be captured by at least
two cameras at any
moment during the movement.  There is no evidence
that increasing number of cameras will improve the accuracy.  As far
as I understand, the main purpose of using more than two cameras is to
make sure that the basic requirement of the
DLT procedure is satatisfied for every marker, not to
improve the accuracy of the estimated 3-D coordinates.  When using
more than two cameras and a marker was captured by all cameras, it is not
necessary to use the digitized data from
all cameras to estimate the 3-D coordinates.  Idealy,
only the data from the two cameras with the optimum optical axis angle
(about 90 degrees) should be used. That may give you the best accuracy. 
Adding a camera with a poor optical axis angle (less than 45 degrees) with
other cameras may actually cause extra error in the estimated 3-D coordinates. 
In adding an extra camera will increase your digitizing time.  With
all these considerations, I suggest you use only two cameras as long as
the basic requirement of the DLT procedure is satistied for every marker. 
Good luck.
Bing Yu
 
-The following journal article may be of benefit: Ehara
Y et al. 1995 Technical note: comparison of the performance of 3D
camera systems. Gait and Posture, Vol. 3, 166-169. This
article compares the accuracy of eight motion analysis systems.
Could you send me a summary of your replies? I am presently
completing a doctorate that requires subjects to be filmed as they approach
(10 m approach) a raised surface. I am trying to determine how many cameras
I need to film the approach. At present, it appears that I may only be
able to use a camera field of approx. 2.5 m width and 2 m high. Therefore
4 cameras may be required. Have you considered panning? The new Motus Peak
system can accomodate
panned film, but I have no idea of the accuracy.
Noel Lythgo
 
-As you mentioned correctly, 2 cameras are sufficient
to collect 3D data.Basically, the correct statement should read: you need
at least 2 cameras that can "see" you markers all the time. Depending on
the movement you
are considering, this might ask for at least 2, but may
be 3, 4 or even 6 cameras. There is one big however, though, and that is
normally never mentioned by the analysis equipment manufacturers. Any camera
has its own accuracy and off set. During calibration, these camera parameters
are determined. When calculating 3D data the camera parameters of the camera
combination that "see" the marker are used. In case of 2 cameras, there
is no problem, because the DLT is unique. When 3 or more cameras "see"
the marker, usually a certain averaging is applied so that the data of
all cameras are effectively used in determining the 3D data. This is claimed
to improve the accuracy of the 3D data. Basically a
statement that is true. Now the "however". Suppose you
have a situation where 3 cameras see the marker, and 1 camera loses the
view. From that moment onwards only 2 cameras must be used to calculated
the data from. Inevitably, there will be a (small) jump in calculated 3D
data because the camera parameters of all 3 cameras are not identical.
Basically, a (minimal) jump in 3D data will occur any time there is a change
in number of cameras that see a marker. Is this jump a problem? Usually
not in determining normal 3D position data. However, when you want to calculate
position derivatives, such as velocity, or even worse, acceleration, these
jumps might seriously interfere with accurate and reliable data (understatement!).
Keep in mind, that data smoothing might be effective in getting rid of
these jumps, but not
necessarily in all cases, depending on which camera combinations
cause the jump, and what frequency content you signal has.
What kind of an advise is the best in figuring out how
many cameras you need? Well it's easy. Use as many cameras as you can afford,
and if it happens to be 3 or 2, perform some measurements where you momentarily
block the view of one of the 3 cameras. The above mentioned jump is then
visible right away.
Henk C. Schamhardt
 
-How are things in Ottawa.  Interesting problem of
cameras for tracking 3D motion.  Most articles focus on the number
of calibration points and the error as you expand past the calibration
area.  As you may remember, Doris Miller and I conducted a 3D study
of axel jumps in figure skating.  We used 4 cameras in our work due
to the spinning nature of
the skill.  However, if my memory serves me correctly
we did not see a large increase in accuracy with increased camera views
when the choice was available.  Our program was written to use alll
4 cameras if the landmark was visible else select the next best configuration
of camera views.  I remember looking at the errors using various combinations,
while they were affected, I do not think it is a large
concern if you can clearly see the markers in ever case.  A study
similar to ours by King et al., used only 3 cameras to record the motion. 
A third camer would eliminate any problems or potential concerns of missing
markers. If you only have two and you miss a marker in a camera view your
left
interpolating points.
Wayne Albert
 
-Great question. Unfortunately, I do not have any definitive
answer for you from my own experience, but it would seem to make sense
that if you had redundant data, then you could somehow use this to improve
the accuracy of your calculations. FYI, a similar question exists with 
whether or not you should use more than three markers per segement to reconstruct
the approximate rigid body motion. Only three markers are needed in theory,
but skin and soft tissue motion add noise to the data.
I think someone has done some work on this to show when
adding more markers per segment might be beneficial. You may want to try
to track down this work, since similar reasoning may apply to the issue
of using more than two cameras.
B.J. Fregly
 
-Theoretically, 2 cameras are enough, but one always riscs
getting ghostmarkers when tracking the data, since there are situations
when there are 2 possibilities for the positions of the markers to be calculated
from the marker images:
              
^              
^                       
- A 3rd camera solves this ambiguity. My works in the lab led to the
              
H              
H                     
-experience that it is always better to have as many cameras as possible,
             
/_\            
/_\                     
-but the costs are the limiting factor. The more marker images from
              
.            
.                        
-different perspectives there are, the better is the approximation of the
                 
         .                           
-real markerposition in space.
                   
     .                             
-
                
    . .    .                          
-
                     
*.                               
-
                 
.     . .                           
-
                  
O       O                         
-
                                                         
-    Arnim Henze
                   
     .
                    
   .
                      
*
 
This question was intensively answered by Woltring , Spoor
and Veldpaus in different issues of the J. Biomech. I wonder why this very
important articles are not known in the canadian literature
H Bär
 
Once again thanks, to all who took the time to respond.
I will be communicating with individuals.
--
*+*+*+*+*+*+*+*+*+*+*+*+*+*+*+*+*+*+*+*+*+*+*+*+*+ *+*+*+*+
J.Peter Stothart
School of Human Kinetics
University of Ottawa
Ottawa, On  K1N 6N5
(613) 562-5800 ext4264
(613) 562-5149 fax
(819) 827-4794 (home)
"In skating on thin ice, our safety is in our speed"
     Ralph WaldoEmerson