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.

Types of operations

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

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

Translate

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’)

Rotation

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

Scale

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)

Sheer