digital image processing

1. INTRODUCTION TO
DIGITAL IMAGE
PROCESSING
Bibekanand Jena
Sr. Lecturer
Dept of ETE
PIET, Rourkela

2. •What is Digital Image Processing?
Processing of Images which are digital in nature by a
digital computer is known Digital Image Processing
•Important terms:
1. Image
2. Digital Image
3. Processing

3. Why image?

4. •A Picture is worth a thousand words
•Visual imformation is more powerful than textual information
Vs

6. An image is a 2D light intensity function
f(x,y)= i(x,y) . r(x,y)
Where
0<i(x,y)<∞
and 0< r(x,y)<1
i(x,y): Illumination Component
r(x,y): Reflectance component
Y
X

7. What is a Digital Image?
A digital image is a representation of a two-
dimensional image as a finite set of digital values,
called picture elements or pixels
It is discretized both in spatial co-ordinates and
brightness/intensity.
•It can be considered as a matrix
whose row, column indices
specify a point in the image and
the element value identifies
gray level value at that point
•These elements are referred as
pixels

8. Conventional Coordinate for Image Representation

9. Digital Image Representation
No. of rows: M, No. of Column: N, Size of the image: M × N
No. of gray levels (Quantization level): 2k
No. of bits required to store a digitized image = M×N× k

10. What is a Digital Image? (cont…)
Common image formats include:
– 1 sample per point (B&W or Grayscale)
– 3 samples per point (Red, Green, and Blue)

11. Digital Image Types : Intensity Image
Intensity image or monochrome image
each pixel corresponds to light intensity
normally represented in gray scale (gray
level).
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87
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Digital Image Types : RGB Image
Color image or RGB image:
each pixel contains a vector
representing red, green and
blue components.
RGB components

13. Image Types : Binary Image
Binary image or black and white image
Each pixel contains one bit :
1 represent white
0 represents black
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1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
Binary data

14. Why Processing?
Digital image processing focuses on
three major tasks
– Improvement of pictorial information for
human interpretation
– Efficient storage & Transmission
– Image processing for Autonomous
machine application

15. Image Enhancement

16. Image Deblurring

17. Remote Sensing Weather Forecasting

18. Machine Vision Application:
In this case the interest is the procedure of extraction of
image information suitable for computer processing .
Application:
1. Industrial Machine vision for product assembly and
inspection
2. Automated Target detection and tracking
3. Biometric recognition
4. Many more

19. What is digital image processing?
Low Level Process
Input: Image
Output: Image
Examples: Noise
removal, image
sharpening
Mid Level Process
Input: Image
Output: Attributes
Examples: Object
recognition,
segmentation
High Level Process
Input: Attributes
Output: Understanding
Examples: Scene
understanding,
autonomous navigation

20. Image Formation in the Human Eye
•The distance between the center of the lens and he
retina varies from approximately 17mm to 14mm.
•If ‘h’ is the height of the object in the retinal image ,
then from the geometry of the figure
h/17 = 15/100

21. Fundamental Steps of
Image Processing

22. IMAGE
ENHANCEMENT
IMAGE
RESTORATION
IMAGE
COMPRESSION
MORPHOLOGICAL
ANALYSIS
IMAGE
SEGMENTATION
REPRESENTATION
&
DESCRIPTION
OBJECT
RECOGNITION
COLOR
IMAGE
PROCESSING
WAVELET AND
MULTIRESOLUTION
ANALYSIS
IMAGE
ACQUISITION
Knowledge Base

23. Image Acquisition: An image sensor and the
capability to digitize the signal produced by the
sensor .
Image Enhancement: Enhance the image quality
by highlighting certain features of the image. It is
a subjective area of image processing(Human
subjective preference).
Ex: Contrast / Brightness Enhancement
Image Restoration: Deals with improving the
appearance of an image. It is objective.
Restoration tends to based on mathematical or
probabilistic model of image degradation. Ex:
Noise filtering
Color Image Processing: Deals with fundamental
concept in color model and basic colorimage
processing in digital domain.
Ex: Pseudo-color processing

24. Multi Resolution Analysis: Deals with representing image
in various degrees of resolution using Wavelet
transformation. Ex: Image decomposition
Image Compression: Deals with technique for reducing
the storage required to save and image or the bandwidth
required to transmit it. Ex: Lossy / Lossless compression
Morphological Processing: Deals with tools for extracting
image component that are useful for representation and
description. Ex: Dilation, Erosion etc
Segmentation: Partition an image into constituent parts
or object. Ex: Face detection.
Representation & Description: Deals with representation
of the object in the image in desired form. Ex: Boundary
representation is appropriate when focus is on external
shape. Regional representation for internal properties.
Descriptor also called feature selection, deals with
extracting attributes suitable for further processing.
Recognition: Assigning a label to the object based on the
information provided by the descriptor.

25. IMAGE DISPLAY
HARD COPY
IMAGE
SENSOR
COMPUTER
SPECIALIZED
IMAGE PROCESSING
HARDWARE
MASS
STORAGE
IMAGE
PROCESSING
SOFTWARE
COMPONENTS OF AN IMAGE PROCESSING SYSTEM
NETWORK

26. SENSOR. Two elements are required to acquire digital images. The
first is a physical device that is sensitive to the energy radiated by
the object we wish to image. The second, called a digitizer, for
converting the output of the physical sensing device into digital
form.
SPECIALIZED IMAGE PROCESSING HARDWARE usually consists of
the digitizer just mentioned, plus hardware that performs other
primitive operations, such as an arithmetic logic unit (ALU), which
performs arithmetic and logical operations in parallel on entire
images. Example: averaging images as quickly as they are
digitized, for the purpose of noise reduction.
THE COMPUTER It is a general-purpose computer and can range
from a PC to a supercomputer. In dedicated applications, some-
sometimes specially designed computers are used to achieve a
required level of performance.
SOFTWARE It consists of specialized modules that perform specific
tasks. A well-designed package also includes the capability for the
user to write code that, as a minimum, utilizes the specialized
modules.
MASS STORAGE Digital storage for image processing applications
falls into three principal categories: A) short-term storage for use
during processing, B) on-line storage for relatively fast recall, and
C) archival storage, characterized by infrequent access.

27. The lens focuses light from
objects onto the retina
• The retina is covered with
light receptors called cones
(6-7 million) and rods (75-
150 million)
• Cones are concentrated
around the fovea and are
very sensitive to
colour(Photopic)
• Rods are more spread out
and are sensitive to low
levels of illumination
(Scotopic)
Brightness Adaptation of Human Eye : Mach Band Effect

28. • Experimental evidence indicates
that subjective brightness is a
logarithmic function of the light
intensity incident on the eye.
•The total range of distinct intensity
levels the eye can discriminate
simultaneously is rather small when
compared with the total adaptation
range.
•For any given set of conditions, the
current sensitivity level of the visual
system is called the brightness
adaptation level.
•Since digital images are displayed as a discrete set of intensities,
the eye’s ability to discriminate between different intensity levels is
an important issue.
•The range of light intensity levels adapted by human visual system
is enormous, on the order of 1010, from the scotopic threshold to the
glare limit.

29. •An increment of illumination,ΔI , is added to the
field in the form of a short-duration flash.
•If ΔI is not bright enough, the subject says “no”.
•As ΔI gets stronger, the subject may give a
positive response of “yes”
•Finally, when ΔI becomes strong enough, the
subject will give a positive response of “yes” all
the time.
•The quantity ΔI /I, where ΔI denote the increment
of illumination discriminable 50% of the time with
background illumination I is called the Weber
ratio.
•A small value of ΔI /I means that a small change
in intensity is discriminable. It represents “good”
brightness discrimination.
BRIGHTNESS DISCRIMINATION
•Another important issue is the ability of the eye to discriminate
between changes in light intensity at any specific adaptation level.
•Figure shows the idea of a basic experiment to determine the
human visual system for brightness discrimination

30. Figure shows that brightness discrimination improves
significantly as background illumination increases.

31. Position
Intensity
Brightness Adaptation of Human Eye : Mach Band Effect

32. Mach Band Effect
Intensities of surrounding points
effect perceived brightness at each
point.
In this image, edges between bars
appear brighter on the right side
and darker on the left side.

33. In area A, brightness perceived is darker while in area B is
brighter. This phenomenon is called Mach Band Effect.
Position
Intensity
A
B
Mach Band Effect (Cont)

34. Simultaneous contrast. All small squares have exactly the same intensity
but they appear progressively darker as background becomes lighter.
Brightness Adaptation of Human Eye : Simultaneous Contrast

35. Visible Spectrum

36. Digital Image Acquisition Process

37. Generating a Digital Image

38. Image Sampling and Quantization
Image sampling: discretize an image in the spatial domain
Spatial resolution / image resolution: pixel size or number of pixels

39. How to choose the spatial resolution
= Sampling locations
Original
image
Sampled
image
Under sampling, we lost some image details!
Spatial resolution

40. How to choose the spatial resolution : Nyquist Rate
Original
image
= Sampling locations
Minimum
Period
Spatial resolution
(sampling rate)
Sampled image
No detail is lost!
Nyquist Rate:
Spatial resolution must be less or equal
half of the minimum period of the image
or sampling frequency must be greater or
Equal twice of the maximum frequency.
2mm
1mm

41. Effect of Spatial Resolution
256x256 pixels
64x64 pixels
128x128 pixels
32x32 pixels

42. Effect of Spatial Resolution

43. Image Quantization
Image quantization:
discretize continuous pixel values into discrete numbers
Color resolution/ color depth/ levels:
- No. of colors or gray levels or
- No. of bits representing each pixel value
- No. of colors or gray levels Nc is given by
b
c
N 2

where b = no. of bits

44. Quantization function
Light intensity
Quantization
level
0
1
2
Nc-1
Nc-2
Darkest Brightest

45. Effect of Quantization Levels
16 levels 8 levels
2 levels
4 levels
In this image,
it is easy to see
false contour.

46. Basic Relationship of Pixels
x
y
(0,0)
Conventional indexing method
(x,y) (x+1,y)
(x-1,y)
(x,y-1)
(x,y+1)
(x+1,y-1)
(x-1,y-1)
(x-1,y+1) (x+1,y+1)

47. Neighbors of a Pixel
p (x+1,y)
(x-1,y)
(x,y-1)
(x,y+1)
4-neighbors of p:
N4(p) =
(x-1,y)
(x+1,y)
(x,y-1)
(x,y+1)
Neighborhood relation is used to tell adjacent pixels. It is
useful for analyzing regions.
Note: q N4(p) implies p N4(q)
4-neighborhood relation considers only vertical and
horizontal neighbors.

48. p (x+1,y)
(x-1,y)
(x,y-1)
(x,y+1)
(x+1,y-1)
(x-1,y-1)
(x-1,y+1) (x+1,y+1)
Neighbors of a Pixel (cont.)
8-neighbors of p:
(x-1,y-1)
(x,y-1)
(x+1,y-1)
(x-1,y)
(x+1,y)
(x-1,y+1)
(x,y+1)
(x+1,y+1)
N8(p) =
8-neighborhood relation considers all neighbor pixels.

49. p
(x+1,y-1)
(x-1,y-1)
(x-1,y+1) (x+1,y+1)
Diagonal neighbors of p:
ND(p)=
(x-1,y-1)
(x+1,y-1)
(x-1,y+1)
(x+1,y+1)
Neighbors of a Pixel (cont.)
Diagonal -neighborhood relation considers only diagonal
neighbor pixels.

50. .
For p and q from the same class
4-Adjacency: Two pixels p and q with values from V (a set of
gray level) are 4-adjacent if q N4(p)
 8-Adjacency: Two pixels p and q with values from V (a set of
gray level) are 8-adjacent if q N8(p)
 mixed-Adjacency (m-Adjacency): Two pixels p and q with values
 from V (a set of gray level) are m-adjacent
• if q N4(p) or
• q ND(p) and N4(p) N4(q) = 
Adjacency

51. Path
A path from pixel p at (x,y) to pixel q at (s,t) is a sequence
of distinct pixels:
(x0,y0), (x1,y1), (x2,y2),…, (xn,yn)
such that
(x0,y0) = (x,y) and (xn,yn) = (s,t)
and
(xi,yi) is adjacent to (xi-1,yi-1), i = 1,…,n
p
q
We can define type of path: 4-path, 8-path or m-path
depending on type of adjacency.

52. Adjacency
A pixel p is connected to pixel q is they are adjacent.
Two image subsets S1 and S2 are connected if some pixel
in S1 is adjacent to some pixel in S2
S1
S2
We can define type of adjacency: 4-adjacency, 8-adjacency
or m-adjacency depending on type of connectivity.

53. Path (cont.)
p
q
p
q
p
q
8-path from p to q
results in some ambiguity
m-path from p to q
solves this ambiguity
8-path m-path

54. Distance
For pixel p, q, and z with coordinates (x,y), (s,t) and (u,v),
D is a distance function or metric if
 D(p,q) 0 (D(p,q) = 0 if and only if p = q)
 D(p,q) = D(q,p)
 D(p,z) D(p,q) + D(q,z)
Example: Euclidean distance
2
2
)
(
)
(
)
,
( t
y
s
x
q
p
De -
+
-


55. Distance (cont.)
D4-distance (city-block distance) is defined as
t
y
s
x
q
p
D -
+
-

)
,
(
4
1 2
1
0
1 2
1
2
2
2
2
2
2
Pixels with D4(p) = 1 is 4-neighbors of p.

56. Distance (cont.)
D8-distance (chessboard distance) is defined as
)
,
max(
)
,
(
8 t
y
s
x
q
p
D -
-

1
2
1
0
1
2
1
2
2
2
2
2
2
Pixels with D8(p) = 1 is 8-neighbors of p.
2
2
2
2
2
2
2
2
1
1
1
1

57. What Is Image Enhancement?
Image enhancement is the process of
making images more useful
The reasons for doing this include:
– Highlighting interesting detail in images
– Removing noise from images
– Making images more visually appealing

58. Image Enhancement Examples (cont…)

59. Image Enhancement Examples (cont…)

60. Spatial & Frequency Domains
There are two broad categories of
image enhancement techniques
– Spatial domain techniques
Direct manipulation of image pixels
– Frequency domain techniques
Manipulation of Fourier transform or
wavelet transform of an image
For the moment we will concentrate on
techniques that operate in the spatial
domain

61. 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
Grey Levels
Frequencies

62. 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

63. Basic Spatial Domain Image Enhancement
Origin x
y Image f (x, y)
(x, y)
Most spatial domain enhancement
operations can be reduced to the form
g (x, y) = T[ f (x, y)]
where f (x, y) is the
input image, g (x, y) is
the processed image
and T is some
operator defined over
some neighbourhood
of (x, y)

64. Point Processing
The simplest spatial domain operations
occur when the neighbourhood is simply
the pixel itself
In this case T is referred to as a grey level
transformation function or a point
processing operation
Point processing operations take the form
s = T ( r )
where s refers to the processed image
pixel value and r refers to the original
image pixel value

65. Point Processing Example: Negative Images
Negative images are useful for enhancing white
or grey detail embedded in dark regions of an
image
– Note how much clearer the tissue is in the
negative image of the mammogram below
s = 1.0 - r
Original
Image
Negative
Image

66. Point Processing Example:
Negative Images (cont…)
Original Image x
y Image f (x, y)
Enhanced Image x
y Image f (x, y)
s = intensitymax - r

67. Point Processing Example: Thresholding
Thresholding transformations are
particularly useful for segmentation in
which we want to isolate an object of
interest from a background
s =
1.0
0.0 r <= threshold
r > threshold

68. Basic Grey Level Transformations
There are many different kinds of grey
level transformations
Three of the most
common are shown
here
– Linear
Negative/Identity
– Logarithmic
Log/Inverse log
– Power law
nth power/nth root

69. Logarithmic Transformations
The general form of the log
transformation is
s = c * log(1 + r)
The log transformation maps a
narrow range of low input grey level
values into a wider range of output
values
The inverse log transformation
performs the opposite transformation

70. Logarithmic Transformations (cont…)
Log functions are particularly useful when
the input grey level values may have an
extremely large range of values
In the following example the Fourier
transform of an image is put through a log
transform to reveal more detail
s = log(1 + r)

71. Logarithmic Transformations (cont…)
Original Image x
y Image f (x, y)
Enhanced Image x
y Image f (x, y)
s = log(1 + r)
We usually set c to 1
Grey levels must be in the range
[0.0, 1.0]

72. Power Law Transformations
Power law
transformations have
the following form
s = c * r γ
Map a narrow range
of dark input values
into a wider range of
output values or vice
versa
Varying γ gives a whole
family of curves

73. Power Law Transformations (cont…)
We usually set c to 1
Grey levels must be in the range
[0.0, 1.0]
Original Image x
y Image f (x, y)
Enhanced Image x
y Image f (x, y)
s = r γ

74. Power Law Example

75. Power Law Example (cont…)
γ = 0.6
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.2 0.4 0.6 0.8 1
Old Intensities
Transformed
Intensities

76. Power Law Example (cont…)
The images to the
right show a
magnetic resonance
(MR) image of a
fractured human
spine
Different curves
highlight different
detail
s = r 0.6
s
=
r
0.4

77. Power Law Example

78. Power Law Example (cont…)
γ = 5.0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.2 0.4 0.6 0.8 1
Original Intensities
Transformed
Intensities

79. Power Law Transformations (cont…)
An aerial photo
of a runway is
shown
This time
power law
transforms are
used to darken
the image
Different
curves
highlight
different detail
s = r 3.0
s
=
r
4.0

80. Gamma Correction
Many of you might be familiar with
gamma correction of computer monitors
Problem is that
display devices do
not respond linearly
to different
intensities
Can be corrected
using a log
transform

81. Piecewise Linear Transformation Functions
Rather than using a well defined mathematical
function we can use arbitrary
user-defined transforms
The images below show a
contrast stretching linear
transform to add contrast
to a poor quality image

82. Gray Level Slicing
Highlights a specific range of grey levels
– Similar to thresholding
– Other levels can be
suppressed or maintained
– Useful for highlighting
Features in an image

83. Bit Plane Slicing
Often by isolating particular bits of the
pixel values in an image we can highlight
interesting aspects of that image
– Higher-order bits usually contain most
of the significant visual information
– Lower-order bits contain
subtle details

84. Bit Plane Slicing (cont…)
[01000000]
[10000000]
[00001000]
[00000001]
[00100000]
[00000100]

85. 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?

86. 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)
– nj:the frequency of intensity j
– n: the sum of all frequencies
)
( k
k r
T
s 



k
j
j
r r
p
1
)
(



k
j
j
n
n
1

87. Equalisation Transformation Function

88. Equalisation Examples

89. Equalisation Examples (cont…)