Image transformations and perspective correction
Images can go through a set of transformations. The simplest ones are listed here.
Translation
Basically, in image coordinates translation, what we do is shift every pixel, p=[x,y], with an amount, t=[
,
]. For example, we can write the translation for pixel p as 
.
Rotation and translation
In this transformation, we apply rotation to every pixel followed by a translation. This transformation is also known as two-dimensional Euclidean transformation as Euclidean distances are preserved.
We can write this transformation as 
, where R is a 2-by-2 matrix, which equals 
and 
is the angle used for rotation.
Scaled rotation
This is also known as similarity transformation, and in this transformation, we add a scaling factor 
so that the transformation can be expressed as 
. This transformation preserves the angles between the lines.
Affine
In the Affine transformation, parallel lines remain parallel and it can be expressed as 
, where 
and A=
.
