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View Full Version : Re: Your "Black Holes"



jwalton86
10-11-1996, 06:59 AM
On Thu, 10 Oct 1996, judith d redling biom fac/staff
wrote:
>Greetings fellow researchers:
>
>We our utilizing the Vicon 370 3D motion analysis system to acquire kinematic
>data and have recently encountered a problem known as a "black hole".
>While each camera (our system has six) can see a given marker, this marker is
>"lost" in the reconstruction process. I don't know the details,
>but apparently it has to do with the cancellation of intersecting rays in the
>reconstruction algorithm. I was wondering if anyone had encountered a similar
>problem and perhaps could offer some insight.
>
>Thank you,

Judy:

I'm not sure that I fully understand the conditions under which
your problem is occuring, but at the very least it is wrong to
describe what you are seeing as a "cancellation of intersecting
rays". What you MAY be experiencing is a special (geometric)
condition which produces an infinite number of "solutions" for
the intersection of two (or more rays). It is very unlikely
that this will occur when three or more cameras can see the
target (this would require the front nodes of all three
cameras to lie on a single straight line.) However, a problem
can arise when a target lies on the line joining the front
nodes of two cameras and no other camera can provide
information. Under these conditions there are insufficient
constraints to define a single "point of intersection"--in
mathematical terms the equations become "underdetermined".
>From a geometric standpoint [it's a lot easier to
understand this ;-) ] the two rays which project out from
the two available views become collinear--so the target can
occupy any position along the line joining the two lenses.
>From a practical standpoint, you can "see" when this is
likely to occur when a target occupies a position in the
image which is similar to that of the lens of the "other"
camera. When a third (fourth, etc.) camera can see the
target the problem "goes away"--because the rays from
these cameras do intersect the "coincident" rays from
the first two cameras at a finite point.

Apart from the problem I have described, and camera
geometries which produce very similar conditons (i.e.,
very slowly converging rays), I know of no reason why
any reconstruction algorithm would fail. The problem
may be in the software--or the algorithm used to solve
the system of equations.

Hope all this helps.

By the way, just a reminder for friends and colleagues
working in biomechanics, the 22nd International
Congress on High-Speed Photography and Photonics
will be taking place later this month ...

October 27 to November 1, in Santa Fe, New Mexico

If anyone would like additional information, please
drop me a note.

Jim Walton
Chairman, SPIE Working Group on High-Speed Photography,
Videography and Photonics
Exhibit & Commercial Chair, 22nd International Congress
on High-Speed Photography and Photonics.

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