How to determine pose of 3 cameras as two stereo pairs?

I have 3 cameras that I have calibrated as pairs (1-2 & 2-3) with camera 2 in common. I am using the stereo camera calibration script generated from the toolbox.

Does anyone know how I can transform translations and rotations of the 3rd camera so that its pose is in the coordinate system of the 1st camera. The first calibration (1-2) gives me the translation and rotation of camera 2 wrt to camera 1, and the second gives me 3 wrt 2.

This is the way I have been doing it but when I plot the poses it doesn't look right - camera three seems to be in the wrong position.

• For rotations I've simply multiplied the two rotation matrices - C3R
• For translations I've contructed a homogeneous transormation matrix and then extracted the translation elements - C3T

Any know how to solve this one?

%Camera 2 Tranforms
C2T=stereoParams12.TranslationOfCamera2; %translation of 2 wrt 1 
C2R=stereoParams12.RotationOfCamera2; %rotation of 2 wrt 1 
C2=[C2R(1,1) C2R(1,2) C2R(1,3) C2T(1,1);C2R(2,1) C2R(2,2) C2R(2,3) C2T(1,2);C2R(3,1) C2R(3,2) C2R(3,3) C2T(1,3);0 0 0 1];

%Camera 3 Transforms
C3Rot=stereoParams23.RotationOfCamera2; %rotation of 3 wrt 2 
C3Tra=stereoParams23.TranslationOfCamera2; %translation of 3 wrt 2 

C3=[C3Rot(1,1) C3Rot(1,2) C3Rot(1,3) C3Tra(1,1);C3Rot(2,1) C3Rot(2,2) C3Rot(2,3) C3Tra(1,2);C3Rot(3,1) C3Rot(3,2) C3Rot(3,3) C3Tra(1,3);0 0 0 1];
C3Hom=C2*C3; %homogeneous transformation matrix
C3T=[C3Hom(1,4) C3Hom(2,4) C3Hom(3,4)]; %translation of 3 wrt 1 
C3R=C2R*C3Rot; %rotation of 3 wrt 1

% stereoParams12: Calibration of cameras 1&2
% stereoParams23: Calibration of cameras 2&3

Any help would be much appreciated!

Thanks in advance,

Cameron

[John D'Errico]

I lack the appropriate toolbox to know, nor do I have expertise in this particular field. (I'd have made this an answer if I did.)

But it seems to me that you need to be careful with the translation of camera 3. You know the translation of 3 wrt 2, but that translation is described in the coordinate system of camera 2. That leaves you with a disconnect, because you want it all in the camera 1 coordinate system. So you need to back the 2-->3 translation through the camera 2 rotation from 1 to 2.

Logically, it might be better if you did everything with respect to camera 2 anyway, as the camera in common. Then you don't need to back things up to camera 1.

An alternative approach is to pair camera 1 and 2, then camera 1 and 3. That leaves camera 1 as the common camera, so it is much simpler to unravel things.

Just some vague thoughts, that might be helpful.

[Cameron Swanson]

Hi John,

Thanks for your response!

I perhaps should have said in my post that I'd evenetually like to extend this to 3+ cameras, and while the points you make seem like a much more logical approach, I don't know how this would work when scaling up. I think for 3 cameras, as you suggest using camera 2 as the reference makes absolute sense.

The other approach seems like a good option too but my worry again when scaling up would be small FoV overlap. Something else to try out!

Thanks