Digital Image Processing
Lecture 04
Image Enhancement-II
(Histogram Processing)
Naveed Ejaz
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A Note About Grey Levels
So far when we have spoken about image
grey level values we have said they are in
the range [0, 255]
– Where 0 is black and 255 is white
There is no reason why we have to use this
range
– The range [0,255] stems from display
For many of the image processing
operations in this lecture grey levels are
assumed to be given in the range [0.0, 1.0]
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Image Histograms
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Image Histograms
Frequencies
The histogram of an image shows us the
distribution of grey levels in the image
Massively useful in image processing,
especially in segmentation
Grey Levels
Images taken from Gonzalez & Woods, Digital Image Processing (2002)
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Histogram Examples (cont…)
Images taken from Gonzalez & Woods, Digital Image Processing (2002)
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Histogram Examples (cont…)
Images taken from Gonzalez & Woods, Digital Image Processing (2002)
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Histogram Examples (cont…)
Images taken from Gonzalez & Woods, Digital Image Processing (2002)
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Histogram Examples (cont…)
Images taken from Gonzalez & Woods, Digital Image Processing (2002)
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Histogram Examples (cont…)
Images taken from Gonzalez & Woods, Digital Image Processing (2002)
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Histogram Examples (cont…)
A selection of images and
their histograms
Notice the relationships
between the images and
their histograms
Note that the high contrast
image has the most
evenly spaced histogram
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Contrast Stretching through Histogram
C
If rmax and rmin are the maximum and minimum gray
level of the input image and L is the total gray levels of
output image The transformation function for contrast
stretching will be
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Histogram Equalization
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Histogram Equalization
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Background (Probability Distribution)
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Histogram Equalization
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Histogram Equalization
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Histogram Equalization
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Histogram Equalization
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Histogram Equalisation(Summary)
Spreading out the frequencies in an image
(or equalising the image) is a simple way to
improve dark or washed out images
The formula for histogram
sk  T (rk )
equalisation is given where
– rk: input intensity
– sk: processed intensity
– k: the intensity range
(e.g 0.0 – 1.0)
– nj: the frequency of intensity j
– n: the sum of all frequencies
k
  pr ( r j )
j 1
k
nj
j 1
n

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Example
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Example: cdf
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Example
Initial Image
Image After Equalization
Notice that the minimum value (52) is now 0 and the maximum value (154) is now 255.
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Example
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Histogram Equalization-Examples
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Histogram Equalization-Examples
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Histogram Equalization-Examples
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Histogram Equalization-Examples
Images taken from Gonzalez & Woods, Digital Image Processing (2002)
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Equalisation Transformation Function
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Histogram Equalization-Examples
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Histogram Equalization-Examples
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Histogram Equalization-Examples
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Histogram Equalization-Examples
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Histogram Specification/Matching
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Histogram Specification/Matching
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Histogram Specification/Matching
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Histogram Specification/Matching
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Histogram Specification/Matching
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Histogram Matching Example
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Histogram Matching Example(continued)
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Histogram Matching Example
(continued)