1. Types of operations
The types of operations that can be applied to digital images to transform an input image a[m,n] into an output image b[m,n] (or another representation) can be classified into the following three categories
Point : the output value at a specific coordinate is dependent only on the input value at that same coordinate.
Local : the output value at a specific coordinate is dependent on the input values in the neighborhood of that same coordinate.
Global : the output value at a specific coordinate is dependent on all the values in the input image.

2. Types of operations

3. Translate, Scale, Rotate, Sheer, and Homogeneous Coordinates
2D Transformations
Translate, Scale, Rotate, Sheer, and Homogeneous Coordinates

4. Translation Alter the position of a point or an object in 2D space.
(x+dx, y+dy)
(x, y)

5. Translate

6. Rotation Rotate a pixel P(x, y) around the origin by an angle α.
The results pixel position is P’(x’,y’)
(x, y) α
(x’, y’)

7. Rotation

8. Scale Scale a region of pixels by a factor (Sx,Sy).
Each pixel in this region P(x, y) is “scaled” to a new position is P’(x’,y’)
(x’, y’)
(x, y)
The scale of include additional translation when no point of the scaled region is in the origin

9. Scale

10. Sheer Scale a region of pixels by a factor (SHx,SHy).
Each pixel in this region P(x, y) is “Sheered” to a new position is P’(x’,y’)
(x’, y’)
(x, y)

11. Sheer