2
of
32
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)
3
of
32
Histogram Examples
Images taken from Gonzalez & Woods, Digital Image Processing (2002)
4
of
32
Histogram Examples (cont…)
Images taken from Gonzalez & Woods, Digital Image Processing (2002)
5
of
32
Histogram Examples (cont…)
Images taken from Gonzalez & Woods, Digital Image Processing (2002)
6
of
32
Histogram Examples (cont…)
Images taken from Gonzalez & Woods, Digital Image Processing (2002)
7
of
32
Histogram Examples (cont…)
Images taken from Gonzalez & Woods, Digital Image Processing (2002)
8
of
32
Histogram Examples (cont…)
Images taken from Gonzalez & Woods, Digital Image Processing (2002)
9
of
32
Histogram Examples (cont…)
Images taken from Gonzalez & Woods, Digital Image Processing (2002)
10
of
32
Histogram Examples (cont…)
Images taken from Gonzalez & Woods, Digital Image Processing (2002)
11
of
32
Histogram Examples (cont…)
Images taken from Gonzalez & Woods, Digital Image Processing (2002)
12
of
32
Histogram Examples (cont…)
Images taken from Gonzalez & Woods, Digital Image Processing (2002)
13
of
32
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
14
of
32
Histogram Equalisation
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
nj: the frequency of intensity j
n: the sum of all frequencies
k
  pr ( r j )
j 1
k
nj
j 1
n

Images taken from Gonzalez & Woods, Digital Image Processing (2002)
15
of
32
Equalisation Transformation Function
Images taken from Gonzalez & Woods, Digital Image Processing (2002)
16
of
32
Equalisation Examples
1
Images taken from Gonzalez & Woods, Digital Image Processing (2002)
17
of
32
Equalisation Transformation Functions
The functions used to equalise the images in
the previous example
Images taken from Gonzalez & Woods, Digital Image Processing (2002)
18
of
32
Equalisation Examples
2
Images taken from Gonzalez & Woods, Digital Image Processing (2002)
19
of
32
Equalisation Transformation Functions
The functions used to equalise the images in
the previous example
Images taken from Gonzalez & Woods, Digital Image Processing (2002)
20
of
32
Equalisation Examples (cont…)
3
4
Images taken from Gonzalez & Woods, Digital Image Processing (2002)
21
of
32
Equalisation Examples (cont…)
3
4
Images taken from Gonzalez & Woods, Digital Image Processing (2002)
22
of
32
Equalisation Transformation Functions
The functions used to equalise the images in
the previous examples
23
of
32
Summary
We have looked at:
– Different kinds of image enhancement
– Histograms
– Histogram equalisation