### Eight-point problem (Fundamentalmatrix)

Verfasst:

**14. Jul 2012 16:10**With the Eight-point algorithm, I can build the homogeneous linear equation system to estimate the fundamental matrix.

For building up the equation system I need least 8 correspondences (so 8 interest points in each Image or perspective).

The equation system

After solving the equation system using SVD with:

I obtain F_tilde by the matrix V' which is to reshape to a Matrix (3x3), so has rank of 3.

Until now, there is no understanding problem (I suppose).

But now for solving this problem, F_tilde should be of rank(F_tilde) = 2. (Slides 74-79)

For building up the equation system I need least 8 correspondences (so 8 interest points in each Image or perspective).

The equation system

**A**is solved with the SVD, but before I need to scale and shift all interest points to [-1 .. 1] by applying the transformation matrix.After solving the equation system using SVD with:

Code: Alles auswählen

`[U, D, V'] = SVD(A,0);`

Until now, there is no understanding problem (I suppose).

But now for solving this problem, F_tilde should be of rank(F_tilde) = 2. (Slides 74-79)

*Why we need rank of 2 ?*

I do not understand this step.I do not understand this step.