Zoom in (interpolation) and zoom out.
Suppose we want to shift our image in $(t_x, t_y)$ direction. We need to define a matrix $M$ as:
Then we can simply use this equation to get the new position of a certain point $(x,y)$.
Rotation of an image for an angle $\theta$ is achieved by the transformation matrix of the form
In affine transformation, all parallel lines in the original image will still be parallel in the output image. To find the transformation matrix, we need 3 points from input image and their corresponding locations in output image.
- Pespective Transformation
For perspective transformation, you need a $3\times 3$ transformation matrix. Straight lines will remain straight even after the transformation. To find this transformation matrix, you need 4 points on the input image and corresponding points on the output image. Among these 4 points, 3 of them should not be collinear.
NOTE: It does not preserve parallelism, length, and angle. But it still preserves collinearity and incidence.