Howtosignalprocessing
- How do you apply a homography matrix to a point?
- How many points are needed for homography?
- Why does homography have 8 degrees of freedom?
- Is homography an affine transformation?
How do you apply a homography matrix to a point?
This spatial relationship is represented by a transformation known as a homography, H, where H is a 3 x 3 matrix. To apply homography H to a point p, simply compute p' = Hp, where p and p' are (3-dimensional) homogeneous coordinates. p' is then the transformed point.
How many points are needed for homography?
We have seen that a homography can be used to map one image to the other in the case of pure camera rotation or a planar scene. If such a homography exists between the images, four points are sufficient to specify it precisely.
Why does homography have 8 degrees of freedom?
Also, homography is defined upto a scale (c in above equation) i.e. it can be changed by a non zero constant without any affect on projective transformation. Thus, homography has 8 degree of freedom even though it contains 9 elements (3x3 matrix) i.e. the number of unknowns that need to be solved for is 8.
Is homography an affine transformation?
Homographies are transformations of a Euclidean space that preserve the alignment of points. Specific cases of homographies correspond to the conservation of more properties, such as parallelism (affine transformation), shape (similar transformation) or distances (Euclidean transformation).
