Sections 3.1-3.3

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Intensity Transformations

• Sections 3.1-3.3
• Digital Image Processing
• Gonzales and Woods
• Irina Rabaev

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Representing digital image
value f(x,y) at each x, y is called intensity
level or gray level
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Intensity Transformations and Filters
g(x,y)Tf(x,y) f(x,y) input image, g(x,y)
output image T is an operator on f defined over a
neighborhood of point (x,y)
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Intensity Transformation

• 1 x 1 is the smallest possible neighborhood.
• In this case g depends only on value of f at a
  single point (x,y) and we call T an intensity
  (gray-level mapping) transformation and write
• s T(r)
• where r and s denotes respectively the
  intensity of g and f at any point (x, y).

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Some Intensity Transformation Functions
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Image Negatives
Denote 0, L-1 intensity levels of the
image. Image negative is obtained by s L-1-r
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Log Transformations

• s clog(1r), c const, r 0
• Maps a narrow range of low intensity values in
  the input into a wider range of
• output levels. The opposite is true for higher
  values of input levels.

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PowerLaw (Gamma) transformation

• s cr?, c,? positive constants
• curve the grayscale components either to brighten
  the intensity (when ? lt 1)
• or darken the intensity (when ? gt 1).

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Power Law (Gamma) transformation
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Power Law (Gamma) transformation
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Contrast stretching

• Contrast stretching is a process that expands the
  range of intensity levels in a image
• so that it spans the full intensity range of the
  recording medium or display device.
• Contrast-stretching transformations increase the
  contrast between the darks and the lights

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Thresholding function
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Intensity-level slicing

• Highlighting a specific range of gray levels in
  an image

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Histogram processing

• The histogram of a digital image with
• gray levels in the range 0, L-1 is a discrete
• function h(rk)nk , where rk is the kth gray
• level and nk is the number of pixels in the
• image having gray level rk.
• It is common practice to normalize a
• histogram by dividing each of its values by
• the total number of pixels in the image,
• denoted by the product MN.
• Thus, a normalized histogram is given by
  h(rk)nk/MN
• The sum of all components of a
• normalized histogram is equal to 1.

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Histogram Equalization

• Histogram equalization can be used to improve the
  visual appearance of an image.
• Histogram equalization automatically determines a
  transformation function that produce and output
  image that has a near uniform histogram

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Histogram Equalization

• Let rk, k?0..L-1 be intensity levels and let
  p(rk) be its normalized histogram function.
• The intensity transformation function for
  histogram equalization is

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Histogram Equalization - Example

• Let f be an image with size 64x64 pixels and L8
  and let f has the intensity distribution as shown
  in the table

round the values to the nearest integer
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Local histogram Processing
Define a neighborhood and move its center from
pixel to pixel. At each location, the histogram
of the points in the neighborhood is computed and
histogram equalization transformation is obtained.
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Using Histogram Statistics for Image Enhancement
Denote ri intencity value in the range 0,
L-1, p(i) - histogram component corresponding to
value ri .
The intensity variance
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Using Histogram Statistics for Image Enhancement

• Let (x, y) be the coordinates of a pixel in an
  image, and let Sxy denote a
• neighborhood (subimage) of specified size,
  centered at (x, y).
• The mean value of the pixels in this
  neighborhood is given by
• where is the histogram of the pixels in
  region Sxy.
• The variance of the pixels in the neighborhood is
  given by

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Using Histogram Statistics for Image Enhancement
Tungsten filament
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Using Histogram Statistics for Image Enhancement
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Using Histogram Statistics for Image Enhancement