Types of operations

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

4. Translation • Alter the position of apoint 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