View Full Version : Responses of finding the centre of an object

05-23-2005, 02:33 PM
Hi all,

I sincerely would like to thank everyone who provided
their response in regarding to my question and it
certainly helped very much. I do thank very much for
your valuable time. Greatly appreciated!

If you are interested in the responses, please read
the followings:

1)The issue regarding to APAS's cursor's box

In APAS there is an auto-digitizing function. I
assumed you have a white ball in front of a dark
background. In this function you can track the
bright marker automatically. You can change the
threshold in this function for APAS to determine how
big the marker is. Try different value from
0-255 to make it looks good to fit your ball size.
Then the digitized marker should be at the middle of
the big white marker (the ball).

Daniel T.P. FONG,
Department of Orthopaedics and Traumatology,
Prince of Wales Hospital, The Chinese University of
Hong Kong,
Shatin, Hong Kong, China.
Phone: (852) 26096079 / 96020151
Fax: (852) 26035781
Email: dfong@ort.cuhk.edu.hk
Department URL: http://www.ort.cuhk.edu.hk
Laboratory URL: http://www.cuhk.edu.hk/spe/hmlab
Personal URL: http://cuhklsc.no-ip.com/daniel

>Dr. Fong,

Yes this would certiainly work if we put markers on
the ball. However, we try not to put markers on the
ball in our experiment. The reason is because we'll
have pitchers throwing the ball and we don't want the
pitchers to feel awkward in their grip from the
markers when they are holding the ball. Otherwise,
this would be a good solution. Thanks a lot!

Best regards,


__________________________________________________ ____
If the ball is white or black then you can digitize
within APAS manually with a high degree of accuracy.
If you desire to automatically digitize within APAS
your accuracy may decrease.

I hope this helps. There are options even on Version 1
of APAS that allow you to change the cursor size of
the digitizer.

Toran Furch

>Dr. Furch,
Unfortunatley the cursor size is unchangable. You may
find the response from Ariel in the followings. We
don't have version 1 of APAS in our lab so perhaps it

Best regards,



I am located at Indiana State University and I have 12
APAS systems and I use the APAS to track balls or
devices all the time. To accomplish what you indicated
that couldn't been done on the Ariel
system, you need to go to the Digi 4 module. Open your
project, your trial view, your avi video file. Now
you should be ready to digitize the data points that
you determined in your project model but prior to
digitizing anything you need to select the Options
tab, then the MISC options, then highlight the cursor
shape to box, I set my width/height to about 40 pixels
and it makes a nice box that encloses a 3/4 inch
marker from a 30 ft filming distance. You'll have to
play with this setting in order to size it to your
golf ball. Then begin digitizing your movement and
the cursor box will fit the ball. The shape of the
ball will change from a tall rectangle to a wide
rectangle because of the alternating rasters in the
interlacing of the monitor.

I just replicated your project on my office APAS
computer with a dropped golf ball and these steps
worked perfectly. There are a lot of other neat
features located in the tab functions of the APAS, but
you'll either need read the manual or just explore
with each function one by one.

Al Finch
Biomechanics Lab
Indiana State University
off tel:812-237-3927
lab tel:812-237-4174
__________________________________________________ ____

The resizing of the digitizing box appears only to
affect the fixed box. In my example my marker size on
the video is within 1 row of rasters of the cursor box
which makes it easy to digitize. You can
also use the view, zoom option to increase the image
size such that the marker pretty much matches the
cursor box. Also, if you want to very accurately find
the center of the marker, I'll enlarge the image such
that it represents 8/6 pixels and by counting the
pixels you can find the center of the ball at the sub
pixel level of the monitor resolution. The autodigitze
mode for that one point (ball) will find the center of
the centroid area. The marker shape will change
between the odd and even fields. Again your subject
to camera distance can be altered to
control your marker size on the original video image.
Good Luck.
Al Finch
__________________________________________________ ____

I am writing a follow-up message to my previous
message concerning changing the cursor to a box....
and being able to change the size of the box
for digitizing. After re-reading your request, it
seems I might have mis-understood your question. My
original message is correct..... you can
change the cursor from a cross to a box but the size
of this box is not currently adjustable.

If you are using the ball as a marker and
automatically digitizing the ball,then you do have the
option to adjust the size of the "search window"
that looks for each marker. This can be done by
adjusting the height and width of the box. Access to
this option by selecting AUTOMATIC, and then GLOBAL
OPTIONS. You will see these options under the Search
Values section.

John Probe
Ariel Dynamics, Inc.
Email: ARIEL1@ix.netcom.com

>Dr. Finch from Indiana State University and Mr. Probe
from Ariel has certainly clarified this issue for me
and provided great feedback. Thank you so much.

Best regards,

__________________________________________________ ____
2)The followings are regarding to finding the centre
of an object in general.

Have you considered tracking four small markers on the
ball, then calculating the center of the ball as the
center of the sphere containing those markers?

Jason Long
MCW Department of Orthopaedic Surgery
(414) 805-7456

>Dr. Long,

Actually we were trying to use APAS software and
hoping to find the centre of object right away while
we were doing the digitzing. Yes, if that doesn't
work out, we may have to use your advice. Thank you
very much.

Best regards,


__________________________________________________ ____
I have attached a document describing how we determine
the center of a soccer ball. In APAS, I believe that
you can put some reflective tape
on the ball (since this will not affect the flight of
the ball significantly). The attached document will
probably be an appendix to our next publication on
soccer kicking.

Yours sincerely,

Thomas Bull Andersen

Thomas Bull Andersen
Associate Professor, M.Sc., Ph.D.
Department of Sport Science
University of Aarhus
Katrinebjergvej 89 C
8200 Aarhus N
Tel. +45 89 42 44 48

>> Dr. Andersen,

Thank you very much for your article and it is a great
article. If anyone is interested in this particulary
article, feel free to let me know and I'll email it to

Best Regards,

__________________________________________________ ____
I didnt' use APAS but : You can possibly recognize
simply the contour of the ball. Once recognized, it's
easy to calculate the center.
==> With 3 points, you definite two arcs of circle.
With these 2 arcs, you definite the center.

Good luck,

Dr Nicolas BELLUYE PhD
R&D Project Manager
Centre de Recherche Decathlon Création
Tél. : +33 (0)3 20 19 70 41
Email : nicolas.belluye@decathlon.com

>>>Dr. Belluye,

Thank you very much for the response. Yes, that'd
probably be the easiest way to do it if I can
determine the coordinates of those three points, which
shouldn't be too hard.

Best regards,

__________________________________________________ ____
I have no experience with the APAS software that you
mentioned in your message, howver Bodybuilder for
Biomechanics (from Oxford Metrics) is a modelling
software package that I use in human gait studies.

If you have the capacity for 3D motion capture, using
something like VICON, you could simply put a marker
anywhere on the balls surface. Then what you would
need to do is, in Bodybuilder set up a local axis
system with it's origin at the ball marker. Next you
can very simply create a virtual point anywhere along
this axis system. This should enable you to create a
virtual point at the shpere's exact centre, the core
if you like, providing you know the dimensions of the

This is a technique that I have used to create virtual
points at internal joint centres in the human body. I
am sure that this technique could be applied to your


Andrew Murphy
8 Thornlea Drive
G46 6DB
United Kingdom
0141 637 9435

>Dr. Murphy,

We do not have VICON in our lab but we do have
Qualysis. However with Qualysis system, we wouldn't
be able to have the actual film image. Therefore this
wouldn't work us right now but I'll certainly keep
that in mind. Thank you very much.

Best regards,

__________________________________________________ ____
1. I am not sure of the cursor box issue - which could
be the
solution I'm talking about...

Decades ago (when video analysis was used and we had
to do lots of manual identification) we had to define
the size of the marker within a minimum and maximum
number of pixels. When a marker was recognised
within this range the Centroid of the pixel set was
used as the co-ordinate of the marker...

So my guess is (if you can change the magnitude of the
pixel set), if you treat the ball as a marker then the
centroid of the set of pixels will be pretty close to
the centre of the ball.

The error of this will be associated with the shadows
and reflective characteristics (thresholds) of the
ball surface.

2. Maybe a method by lighting from an obtuse angle so
the reflection of the ball is only from the trailing/
leading edge (crescent shaped marker). (This may fit
into the size limits). From this edge trajectory, the
centre trajectory can be estimated.

Good luck.

Garry T Allison PT, PhD, Associate Professor of
The Centre for Musculoskeletal Studies
School of Surgery and Pathology, The University of
Western Australia.
Level 2 Medical Research Foundation Building
Rear 50 Murray Street
Perth Western Australia 6000.
ph: (618) 9224 0219
Fax (618) 9224 0204

>Dr. Allison,

Thank you very much for your response. This does
sound like a good idea. My only concern is the
accuracy so I'll have to look into it and play around
with the computer and software to see how this can
work the best.

Best regards,


__________________________________________________ ____
You might try digitizing X # of points around the
circumference of the ball in each image. As the
radius of the ball is known, you could then perform a
least squares fit of the known circumference of the
ball to your digitized landmarks. Once you have
performed the fit, computation of the center
of the ball is trivial. A bit of pilot testing should
allow you to determinethe minimum # of digitized
points necessary to get a good fit of the

Hope this helps


Michael E. Feltner, Ph.D, FACSM
Dept. of Sports Medicine
Pepperdine University
Malibu, CA 90263 USA
EMAIL: michael.feltner@pepperdine.edu
WEB: http://faculty.pepperdine.edu/mfeltner/
VOICE: (310) 506-4312
FAX: (310) 506-4785

>Dr. Feltner,

Thank you very much for your response. I've read your
PhD dissertation of three-dimensional segment
interactions of the throwing arm during overarm
fastball pitchign in baseball. I wonder if you had a
chance to track the centre of the ball and if you did,
did you use the same method as you pointed out.

Yes, this is certainly a good method and I'll try it

Best regards,

__________________________________________________ ___
If the ball shape is still spherical, why can't you
just put the marker at the center of the ball. We do
an experiment like this in our physics lab
and we have not had any significant problems marking
the position of the ball. I would guess that the ball
will be pretty small in the field of
view of the camera and your eye is quite good at
estimating the center of the ball. Consequently you
should be able to digitize the position of
the center quite well.

Ivan E. Rouse,
Professor of Physics

>Dr. Rouse,

The reason we are not trying to put markers on the
ball is because we are hoping not to make our pitchers
to feel uncomfortable with their grip of the ball.
However, you are very right. The ball will be pretty
small so perhaps we can just simply digitize the
centre of the ball. Thank you for your advice.

Best regards,

__________________________________________________ ____
What camera system will you be using? How big is the
ball; how fast is it moving?

If it is a system with infra red strobes around the
camera lens(es) capable of tracking passive
retro-reflective markers (like Peak or VICON or Motion

Analysis for example) you could simply cover the
entire ball with 3M scotchlite retro-reflective tape.
You will get a cluster of targets
identified by the system, which will look like a
blotch. After collection, you could calculate the
centroid of the ball's image frame by frame, camera by

It is the basic idea of these passive marker systems
anyways... just with a
larger than usual target sphere.

Stephen W. Hill, Ph.D.
Post-Doctoral Fellow, Mobility Team
Research, University Centre
Toronto Rehabilitation Institute
550 University Avenue, Room 1207
Toronto, Ontario, Canada
M5G 2A2

>Dr. Hill,

As I pointed out earlier, we try not to put markers on
the ball. That's why we were seeking for alternative
solutions. Thank your for your response.

Best regards,

__________________________________________________ ____
How about assigning four markers (upper-, bottom-,
left- and right-most)around the ball? By calculation
from the coordinates of these four markers
you should be able to locate the ball center. It
should work in 2D case.

Daniel T.P. FONG,
Department of Orthopaedics and Traumatology,
Prince of Wales Hospital, The Chinese University of
Hong Kong,
Shatin, Hong Kong, China.
Phone: (852) 26096079 / 96020151
Fax: (852) 26035781
Email: dfong@ort.cuhk.edu.hk
Department URL: http://www.ort.cuhk.edu.hk
Laboratory URL: http://www.cuhk.edu.hk/spe/hmlab
Personal URL: http://cuhklsc.no-ip.com/daniel

>Dr. Fong,

Yes, this would certianly work and I am currently
invistigating this. Thanks very much!

Best regards,

__________________________________________________ ___
Would it be possible to put 2 markers on points
exactly opposite each other? Then if you track both
points the center of the ball is always the midpoint
between the markers, even when the ball is spinning.
My apologies if you've already considered this but
it's not a practical option.

Good luck.


David J. Gutekunst, M.S.
Research Physiologist
Military Performance Division
U.S. Army Research Institute of Environmental Medicine
Natick, MA 01760-5007
Phone: 508.233.5892
Fax: 508.233.4195
Email: david.gutekunst@na.amedd.army.mil

>Mr. Gutekunst,

In order to do this method, we'll need to put more
than 2 markers because our pitchers will be putting
the spin on the ball so sometimes the markers will be
out of view. However, if we put too many markers
which is something that we are trying avoid to do, we
feel it may make our pitchers uncomfortable in their
grip. Thank you so much for your response.

Best regards,

__________________________________________________ ____
Can you track two markers on the surface of the ball?
If so, you can place the two markers such that they
describe a line which also includes the
ball's geometric center. Then it is just math to
determine the location of the center relative to the
two markers. I am not familiar with APAS
but many software packages will allow you to create
"virtual markers" based on the location of real
markers. Even if your software does not support
this,it should be a trivial calculation in Matlab or
your favorite programming
language. I hope you find this helpful.

Laura C. Marin
Military Performance Laboratory
Brooke Army Medical Center
Fort Sam Houston, Texas

>Dr. Marin,

Thank you for your reply. As you may have already
noticed, we are trying not to put markers on the ball
in our experiment; therefore, this method will not
work very well for us.

Best regards,

__________________________________________________ ____
Dr. Jackie Hudson published a paper on using three
points on the edge of a sphere for triangulation of
the center of a ball in the 1990 ISBS proceedings
(Prague) pp. 351-355.


>Dr. Knudson,

Thank you very much for pointing this article out and
I'm currently looking into it. Greatly appreciated!

Best regards,

__________________________________________________ ___
I's simply cover it in retro-reflective tape and then
it will become a single (big) marker.


>Dr. Kirtley,

Yes if we could do that, it would certainly work;
however, we try not to put markers on the ball because
our experiment involves in pitchers griping the ball.
Thank you for your response.

Best regards,

__________________________________________________ ____

__________________________________________________ ____________________
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