Image warping and stiching
Image Warping
Affine transformations
Projective Transformation(homography):
- Homography matrix（单应性矩阵） is up to scale (can be multiplied by a scalar), which means the degree of freedom is 8
- We usually constrain the length of the vector [h00 h01 … h22] to be 1
Image stiching
Solving for homographies
One pair of points provide two functions. We need at least four pairs to decide a homography.
If there are n pair of points:
Defines a least squares problem: minimize \(\|Ah - 0\|^2\)
- Since \(h\) is defined up to scale, solve for unit vector \(\hat{h}\)
- Solution:\(\hat{h}\) = eigenvector of \(A^TA\) with smallest eigenvalue
- Works with 4 or more points
How to find these pairs of points: RANSAC(Random Sampling Consensus)