6
votes
Accepted
Why do we need 4 points for homography but 7/8 points for fundamental matrix calculation?
It is because in the case of fundamental matrix, each correspondence point relates to only one constraint(i.e it maps a point to a line in other image). Hence 8 correspondence points are required.
...
- 241
1
vote
Should we use all $N$ correspondence points to compute Homography or just $4$ points?
It's generally better to use all the points you have, since often, errors are independent per point.
given my correspondence points are good, shouldn't there be an exact
solution
Sure, but in ...
- 111
1
vote
3D world homography matrix calculation
Check out my answer to a somewhat similar problem here. You will need to generalize
$$ x = A_x m^2 + B_x mn + C_x n^2 + D_x m + E_x n + F_x $$
to
$$ x_{new} = A_x x^2 + B_x y^2 + C_x z^2 + D_x x ...
- 7,492
1
vote
Why do we need 4 points for homography but 7/8 points for fundamental matrix calculation?
consider the number of DOFs and number of constraints.
On the one hand, the matrix H contains 9 entries, but is defined only up to scale. Thus, the total number ...
- 133
1
vote
Homography Matrix Correlations
Consider three points $A$ in image 1,$B$ in image 2 and $C$ in image 3.$H1$ is the homography matrix from $A$ to $B$ and $H2$ is the homography matrix from $B$ to $C$.
Then,
$$B = H1A$$
$$C = H2B$$
...
- 700
1
vote
Accepted
How are the scaling parameters included (extracted from) an essential matrix?
The Essential matrix is defined only up to scale, so you cannot extract scale from it. In other words, if you multiply $t$ and all the 3D world points in your scene by a constant factor, the essential ...
- 5,071
1
vote
Obtain motion between image features by means of the homography matrix
First, calibrate your intrinsics: The focal lengths and the principal point. Homography is not really a rigid transformation and rather a mapping of a plane onto another one. What you really need is a ...
- 5,445
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