Can't figure out symbology of Matrix formula

[Leelio]

Hi guys - I need to implement a formula on a computer but cannot get a valid result - because I am not sure what the formula is asking me to do

I have all the matrices (Even F found using another method - so I can check results)

I assumed P^+ is pseudo-Inverse of P

P'C and P'P^+ are just Matrix multiplication?

If a kind soul can explain the sequence that would be fantastic!


Some more data from my notes:

 

[tkhunny]

Some notes:
1) "pad out"? No. Something else must be wrong.
2) Is your pseudo-inverse from the Moore-Penrose world or Drazin? Does it matter?
3) You WILL have to clarify the little "x". No guessing.

 

[Leelio]

Some notes:
1) "pad out"? No. Something else must be wrong.
2) Is your pseudo-inverse from the Moore-Penrose world or Drazin? Does it matter?
3) You WILL have to clarify the little "x". No guessing.

thank you for responding


1) its an XYZ vector - I read that you pad out with a 0 for a direction and a 1 for a translation - otherwise I cant do the multiplication
2)the pseudo-inverse is Moore-Penrose - I am not sure if it matters. I will try the alternative
3) I have no idea what the little "x" is - I am not familiar with maths. I assumed it was cross-product? I could not find an answer and hoped it was standard symbology

 

[tkhunny]

1) its an XYZ vector - I read that you pad out with a 0 for a direction and a 1 for a translation - otherwise I cant do the multiplication

Well, that's a challenge. Not understanding what one is doing is a difficult place to be. What field of study, research, or analysis are we in? Is there a research paper on the matter? What, really are you doing, here. Website from which you are obtaining this formula?

2) the pseudo-inverse is Moore-Penrose - I am not sure if it matters. I will try the alternative.

How are you implementing this? Did you write your own algorithm? What software is aiding you on this pathway?

3) I have no idea what the little "x" is - I am not familiar with maths. I assumed it was cross-product? I could not find an answer and hoped it was standard symbology

It may be standard, but printed poorly. It is the author's fault for failing to be clear. On the other hand, "I am not familiar with maths." is less than encouraging. Keep trying.

 

[Leelio]

thank you for your time

1) its an XYZ vector - I read that you pad out with a 0 for a direction and a 1 for a translation - otherwise I cant do the multiplication

Well, that's a challenge. Not understanding what one is doing is a difficult place to be. What field of study, research, or analysis are we in? Is there a research paper on the matter? What, really are you doing, here. Website from which you are obtaining this formula?

Its epipolar geometry - and in particular 3D reconstruction from stereo images. So in this case for each pixel in one image, I find the epipolar line in the other - and use that to constrain the next stage. My problem is I want to use stereo pairs that haven't been specifically calibrated together (Fundamental matrix and Projection matrices are known) - but have a common partner that has - so I can extract the projection matrices and recalculate F



2) the pseudo-inverse is Moore-Penrose - I am not sure if it matters. I will try the alternative.

How are you implementing this? Did you write your own algorithm? What software is aiding you on this pathway?

A maths library called "numpy" provides a function to calculate this

3) I have no idea what the little "x" is - I am not familiar with maths. I assumed it was cross-product? I could not find an answer and hoped it was standard symbology

It may be standard, but printed poorly. It is the author's fault for failing to be clear. On the other hand, "I am not familiar with maths." is less than encouraging. Keep trying.

OK so its not clear what that means.. I will try and contact the author if I can find his details

 

[tkhunny]

Just thinking about the premise, here - recovering 3D from two stereoscopic images.

Points come in three varieties:
1) Neither camera sees it. Can't expect to recover that.
2) One camera sees it. Only one projection works and that fails to pinpoint a unique position..
3) Both cameras see it. I'm not real clear on the effect on hidden lines.

In other words, we can't expect a particularly good reproduction. You might think that human brains do this all day long. Not so. The human brain fills in gaps that it actually can't see. An equation won't do that. Sometimes, the brain's extrapolation is wrong.

Just documenting thoughts until you come back.

 

[Leelio]

Just thinking about the premise, here - recovering 3D from two stereoscopic images.

Points come in three varieties:
1) Neither camera sees it. Can't expect to recover that.
2) One camera sees it. Only one projection works.
3) Both cameras see it. I'm not real clear on the effect on hidden lines.

In other words, we can't expect a particularly good reproduction. You might think that human brains do this all day long. Not so. The human brain fills in gaps that it actually can't see. An equation won't do that. Sometimes, the brain's extrapolation is wrong.

Just documenting thoughts until you come back.

Ah that reminds me - in case anyone in the future encounters this symbology


is a skew-symmetric matrix

So to implement this :