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
5
votes
Apply Low Pass (Smoothing) Filter on a Set of Matrices and Reject Outliers
I would build a tensor of those matrices and use low rank or some thresholding methods on it.
You may have a look for Tensor SVD.
- 511
5
votes
Accepted
Apply Low Pass (Smoothing) Filter on a Set of Matrices and Reject Outliers
The method used was a parametric representation of the matrix $ H $.
For intuition, think of rotation matrix in $ \mathbb{R}^{2} $, namely $ H \in \mathbb{R}^{2 \times 2} $.
Since we have series of ...
- 50.5k
4
votes
Step by Step Camera Pose Estimation for Visual Tracking and Planar Markers
While explaining the two-dimensional case very well, the answer proposed by Jav_Rock does not provide a valid solution for camera poses in three-dimensional space. Note that for this problem multiple ...
- 226
4
votes
Finding Homography Matrix Using Lines
I am not aware of any library which works directly on lines.
A by pass would be, that given 2 line, you'd use a finites sample of point on the lines to calculate the Homography.
To derive the ...
- 50.5k
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
$$ x_{new} = A_x x^2 + B_x y^2 + C_x z^2 + D_x x ...
- 7,022
1
vote
Why do we need 4 points for homography but 7/8 points for fundamental matrix calculation?
consider the number of DOFs and number of constraints.
On the one hand, the matrix H contains 9 entries, but is defined only up to scale. Thus, the total number ...
- 133
1
vote
Homography Matrix Correlations
Consider three points $A$ in image 1,$B$ in image 2 and $C$ in image 3.$H1$ is the homography matrix from $A$ to $B$ and $H2$ is the homography matrix from $B$ to $C$.
Then,
$$B = H1A$$
$$C = H2B$$
...
- 680
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 ...
- 5,041
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 ...
- 5,325
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