Image Processing Chapter 3

The document discusses image histograms and histogram equalization. It explains that histograms show the distribution of pixel intensities in an image and are useful for tasks like segmentation, enhancement and compression. Histogram equalization spreads out the histogram to increase contrast by making intensity levels more uniform.

Uploaded by

Fatimah Earhart

We take content rights seriously. If you suspect this is your content, claim it here.

Available Formats

Download as PDF, TXT or read online on Scribd

0% found this document useful (0 votes)

52 views30 pages

Image Processing Chapter 3

Uploaded by

Fatimah Earhart

We take content rights seriously. If you suspect this is your content, claim it here.

Available Formats

Download as PDF, TXT or read online on Scribd

You are on page 1/ 30

Image Processing and Pattern

Recognition (IPPR):
(Lecture 3)

Sanjeeb Prasad Panday

sanjeeb77@hotmail.com
2
of
30
Image Histograms
The histogram of an image shows us the
distribution of grey levels in the image
Massively useful in image processing,
especially in segmentation
Frequencies

Grey Levels
3
of
30
Image Histograms
• The histogram of a digital image, f, (with intensities [0,L-1])
is a discrete function
h(rk) = nk
• Where rk is the kth intensity value and nk is the number of
pixels in f with intensity rk
• Normalizing the histogram is common practice – Divide the
components by the total number of pixels in the image –
Assuming an MxN image, this yields
p(rk) = nk/MN for k=0,1,2,....,L-1 – p(rk) is, basically, an estimate
of the probability of occurrence of intensity level rk in an image
Σ p(rk) = 1
4
of
30
Uses for Histogram Processing
• Image enhancements
• Image statistics
• Image compression
• Image segmentation
• Simple to calculate in software
• Economic hardware implementations
– Popular tool in real-time image processing
• A plot of this function for all values of k provides a global
description of the appearance of the image (gives useful information
for contrast enhancement)
• Histograms commonly viewed in plots as
h(rk) = nk versus rk
p(rk) = nk /MN versus rk
Images taken from Gonzalez & Woods, Digital Image Processing (2002)
5
of
30
Histogram Examples
Images taken from Gonzalez & Woods, Digital Image Processing (2002)
6
of
30
Histogram Examples (cont…)
Images taken from Gonzalez & Woods, Digital Image Processing (2002)
7
of
30
Histogram Examples (cont…)
Images taken from Gonzalez & Woods, Digital Image Processing (2002)
8
of
30
Histogram Examples (cont…)
Images taken from Gonzalez & Woods, Digital Image Processing (2002)
9
of
30
Histogram Examples (cont…)
Images taken from Gonzalez & Woods, Digital Image Processing (2002)

of
30
10
Histogram Examples (cont…)
Images taken from Gonzalez & Woods, Digital Image Processing (2002)

of
11

30
Histogram Examples (cont…)
Images taken from Gonzalez & Woods, Digital Image Processing (2002)

of
30
12
Histogram Examples (cont…)
Images taken from Gonzalez & Woods, Digital Image Processing (2002)

of
30
13
Histogram Examples (cont…)
Images taken from Gonzalez & Woods, Digital Image Processing (2002)

of
30
14
Histogram Examples (cont…)
15
of
30
Histogram Examples (cont…)
A selection of images and
Images taken from Gonzalez & Woods, Digital Image Processing (2002)

their histograms
Notice the relationships
between the images and
their histograms
Note that the high contrast
image has the most
evenly spaced histogram
16
of
30
Contrast Stretching
We can fix images that have poor contrast
by applying a pretty simple contrast
specification
The interesting part is how do we decide on
this transformation function?
17
of
30
Histogram Equalisation
• Histogram equalization is a process for increasing the
contrast in an image by spreading the histogram out to be
approximately uniformly distributed
• The gray levels of an image that has been subjected to
histogram equalization are spread out and always reach
white
– The increase of dynamic range produces an increase in
contrast
• For images with low contrast, histogram equalization has
the adverse effect of increasing visual graininess
18
of
30
Histogram Equalisation
• The intensity transformation function we are constructing
is of the form
s=T(r) 0 ≤ r ≤ L−1

• An output intensity level s is produced for every pixel in

the input image having intensity r
• We assume
– T(r) is monotonically increasing in the interval 0≤ r ≤ L-1
– 0 ≤ Τ(r) ≤ L-1 for 0 ≤ r ≤ L-1
• If we define the inverse
r=T^−1(s) 0 ≤ s ≤ L−1
• Then T(r) should be strictly monotonically increasing
19
of
30
Histogram Equalisation
20
of
30
Histogram Equalisation
• Histogram equalization requires construction of a
transformation function sk

• where rk is the kth gray level, nk is the number of pixels

with that gray level, MxN is the number of pixels in the
image, and k=0,1,...,L-1
• This yields an s with as many elements as the original
image’s histogram (normally 256 for our test images)
• The values of s will be in the range [0,1]. For
constructing a new image, s would be scaled to the range
[1,256]
21
of
30
Histogram Equalisation
22
of
30
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 equalisation is given where
– rk: input intensity
– sk: processed intensity
– k: the intensity range
(e.g 0.0 – 1.0)
s  T (r )
k k
– nj: the frequency of intensity j k
– n: the sum of all frequencies   p (r )r j
j 1
The transformation function in the next slide is
k n

Obtained by applying the RHS formula to the j
Original image in the next side.
j 1 n
Images taken from Gonzalez & Woods, Digital Image Processing (2002)

of
30
23
Equalisation Transformation Function
Images taken from Gonzalez & Woods, Digital Image Processing (2002)

of
30
24

1
Equalisation Examples
25
of
30
Equalisation Transformation Functions