Accept solutions that do not exactly solve the system in case of noise

[EnricoBarbieri1997]

I've built a two view system for camera resectioning.
The equations are all like that:
equation = line' * intrinsic * R * point_at_infinity = 0
Where:

• variables:
• intrinsic: shared, they are the same for each view
• R: each view has it's R matrix with it's own variables
• parameters:
• point_at_infinity: real 3d point in Homogeneous coordinates that is the same between them
• line: different for each view because it's the projection of a real contour but seen from two different views

Solving works perfectly in absence of noise and I get the right perfect solution. The moment I introduce noise (on the projection) I get zero solutions.
I believe it is because intrinsic, R, and point_at_infinity are still treated equally but as the line from view 1 and line from view 2 are deformed in different ways there is no more a set of variables that exactly solves the system. There is no real pair of projection that achieves those two views.
Which trackers or endgame options do I need to set to accept solutions that do not equal zero but are within certain boundaries?

I tried differentiating the above system and solving a minimization problem like in some of the guides but the solving times changes from 10 minutes to months even.

I can provide code or systems dumps if needed but I'm not using macro to generate variables and instead using Variable function directly as I have a dynamic number of parameters depending on the exact configuration so it's not straightforward.

Thanks

[PBrdng]

Which trackers or endgame options do I need to set to accept solutions that do not equal zero but are within certain boundaries?

There are no such trackers. The software solves "equal to zero". In the presence of noise one can solve the ED minimization problem (as you describe), but of course the system becomes more complex then. I think your problem is a question on theory rather then about the implementation. Can you describe the problem that you want to solve in another way?

[PBrdng]

Can I close this issue?

[saschatimme]

Move the issue to a discussion.
I think the "solution" here is to understand that under noise there are no more real solution but instead complex. So your real solutions without noise are drifting into the complex plane under noise. So you probably want to look for solutions that are "close" in some useful metric to real solution