M1 =3D M2 * M3 only if M1 and M2 are perfectly correct.  There are =20
always errors, unless you have perfect camera calibration and perfect =20=

subpixel corner finding for the four corners of the markers;  neither =20=

of these will be the case with any vision system!   So, small errors =20
in both these will result in small (or even large) errors in the pose =20=

computation of the camera relative to the marker.  Thus, M1 and M2 =20
will have error, and those error will be magnified significantly when =20=

you invert one of the matrices (since a small amount of rotation =20
error on the marker will result in huge translation errors in the =20
inverse).

A better approach would be to figure out the fixed relationship of =20
the 2 cameras on the rig, get the four corners of the markers in the =20
two images, and use a pose computation that takes all 8 corners =20
across both cameras into account!  The stereo info should give you a =20
huge improvement (shouldn't it, folks?).

I thought that people had done this already with the AR Toolkit ...

But, if your goal is to use the ARToolkit to find the relationship =20
between the cameras, it's not accurate enough.  I would suggest =20
looking on the web, there have to be tools for doing this;  I know =20
folks do this sort of thing all the time (multicamera calibration).

On Jul 9, 2005, at 8:52 AM, joele.d@p ........ wrote:

> Hello everybody,
>
> We have 2 camers mounted on a rig. We can get the transformation
> matrix for the first camera and for the second.
>
> Now we are trying to discover a relation between the 2 matrices. Does
> anybody know that relation?
>
> I have been thinking. Basicly you have one image of the marker in the
> first camera,
> and a second image of the (same) marker in the second camera. Could I
> use, in same way, the RelationTest example? I thought I could use the
> relation that the inverse of the first matrix multiplied by the second
> matrix gives the relation between marker2 and marker1,let=B4s say M3.
>
> Would that mean the following: M1 =3D M2*M3?
>
> Then we are going to move the rig, and the marker stays fixed. Then,
> does that relation still hold? I think yes, because with respect to
> each other the cameras do not change.
>
> Any comments are welcome, please.
>

Hello everybody=2C

We have 2 camers mounted on a rig=2E We can get the transformation =

matrix for the first camera and for the second=2E

Now we are trying to discover a relation between the 2 matrices=2E Does =

anybody know that relation=3F

I have been thinking=2E Basicly you have one image of the marker in the =

first camera=2C
and a second image of the (same) marker in the second camera=2E Could I =

use=2C in same way=2C the RelationTest example=3F I thought I could use t=
he =

relation that the inverse of the first matrix multiplied by the second =

matrix gives the relation between marker2 and marker1=2Clet=B4s say M3=2E=


Would that mean the following=3A M1 =3D M2*M3=3F

Then we are going to move the rig=2C and the marker stays fixed=2E Then=2C=
 =

does that relation still hold=3F I think yes=2C because with respect to =

each other the cameras do not change=2E

Any comments are welcome=2C please=2E