Howtosignalprocessing
- How do you find the affine transformation matrix?
- How many points are needed for affine transformation?
- Why is a translation matrix 4x4?
- How many corresponding point pairs do we need from the images to recover the affine transformation matrix?
How do you find the affine transformation matrix?
The affine transforms scale, rotate and shear are actually linear transforms and can be represented by a matrix multiplication of a point represented as a vector, [x y ] = [ax + by dx + ey ] = [a b d e ][x y ] , or x = Mx, where M is the matrix.
How many points are needed for affine transformation?
To define a unique affine 2D transformation, we need 3 points in the original position, and 3 points in the corresponding new position, . The elements of matrix M, for are what we need to determine.
Why is a translation matrix 4x4?
the reason to use a 4x4 matrix is so that the operation is a linear transformation. this is an example of homogeneous coordinates. The same thing is done in the 2d case (using a 3x3 matrix).
How many corresponding point pairs do we need from the images to recover the affine transformation matrix?
In other words you need (at least) 6 points (= 3 pairs) to compute your transformation. Note: you need at least 6 points in the sense that if you get more than that, then your system is overdetermined which means you can find an approximate solution e.g with least squares, which is the point of your article.
