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.

************************************************** ****

************************************************** ****

* * *

* JAMES S. WALTON, Ph.D. * *

* President * INTERNET: Jim@4DVideo.com *

* 4D VIDEO * *

* 3136 Pauline Drive, * PHONE: 707/829-8883 *

* SEBASTOPOL, CA 95472 * FAX: 707/829-3527 *

* * *

************************************************** ****

************************************************** ****

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.

************************************************** ****

************************************************** ****

* * *

* JAMES S. WALTON, Ph.D. * *

* President * INTERNET: Jim@4DVideo.com *

* 4D VIDEO * *

* 3136 Pauline Drive, * PHONE: 707/829-8883 *

* SEBASTOPOL, CA 95472 * FAX: 707/829-3527 *

* * *

************************************************** ****

************************************************** ****