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### A4 Problem 2

Verfasst: 13. Jul 2013 21:22
Hi there, I have some questions concerning the fundamental-matrix-task:

1. I tried to build my preliminary F with all right-value columns where the corresponding singular value is really close to 0 (so that matlab actually displays 0). However, the rank of the resulting F-matrix is not always >2. So should I rather than taking the column corresponding to the smallest singular vector choose a column that results in a F-matrix with rank >2, simply to let the enforce-rank function not be totally useless? I am a bit confused here...

2. What are 'small residuals' concerning the epipolar constraints? Depending on which right-value column I choose I get some values between -0.6 and 0.6. Does that fulfill this definition of 'small''?

I would appreciate any clarifications. ### Re: A4 Problem 2

Verfasst: 13. Jul 2013 22:54
ampelmann hat geschrieben:1. I tried to build my preliminary F with all right-value columns where the corresponding singular value is really close to 0 (so that matlab actually displays 0).
What are you trying to say? Building F means doing a SVD on the system matrix A as shown on page 75 of the l10-geometry slides with F being the last column of V (as explained on page 77).

ampelmann hat geschrieben: However, the rank of the resulting F-matrix is not always >2. So should I rather than taking the column corresponding to the smallest singular vector choose a column that results in a F-matrix with rank >2, simply to let the enforce-rank function not be totally useless? I am a bit confused here...
A proper fundamental matrix is of rank 2. For numerical reasons the F you just computed will most likely have a rank of 3.
That is why we should enforce the rank of 2 by the help of the SVD, again.

ampelmann hat geschrieben: So should I rather than taking the column corresponding to the smallest singular vector choose a column that results in a F-matrix with rank >2, simply to let the enforce-rank function not be totally useless?
Just always enforce rank 2. If your matrix is of rank 2, already, your enforce rank function will not change anything.
ampelmann hat geschrieben: 2. What are 'small residuals' concerning the epipolar constraints? Depending on which right-value column I choose I get some values between -0.6 and 0.6. Does that fulfill this definition of 'small''?
Your residuals are definitely too big. You should have a couple of zeros after the dot. Mine are smaller than 1e-3 for each point.