Types of operations

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Types of operations

• The types of operations that can be applied to
  digital images to transform an input image am,n
  into an output image bm,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.

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Types of operations
3
Types of neighborhoods

• Neighborhood operations play a key role in modern
  digital image processing.
• It is therefore important to understand how
  images can be sampled and how that relates to the
  various neighborhoods that can be used to process
  an image.
• Rectangular sampling - In most cases, images are
  sampled by laying a rectangular grid over an
  image as illustrated in Figure 1. This results in
  the type of sampling shown in
• exagonal sampling - An alternative sampling
  scheme is shown in Figure 3c and is termed
  hexagonal sampling.
• Both sampling schemes have been studied
  extensively and both represent a possible
  periodic tiling of the continuous image space. We
  will restrict our attention, however, to only
  rectangular sampling as it remains, due to
  hardware and software considerations, the method
  of choice.

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Types of neighborhoods

• Local operations produce an output pixel value
  bmmo,nno based upon the pixel values in the
  neighborhood of ammo,nno. Some of the most
  common neighborhoods are the 4-connected
  neighborhood and the 8-connected neighborhood in
  the case of rectangular sampling and the
  6-connected neighborhood in the case of hexagonal
  sampling illustrated in Figure 3.

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2D Transformations

• Translate, Scale, Rotate, Sheer, and Homogeneous
  Coordinates

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Translation

• Alter the position of apoint or an object in 2D
  space.

(xdx, ydy)
(x, y)
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Translate
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Rotation

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

(x, y)
(x, y)
a
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Rotation
10
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
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Scale
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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)
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Sheer