CEC366 Unit -1 FUNDAMENTALS OF DIGITAL IMAGE PROCESSING

Covers the First Unit of Image Processing in Anna University Syllabus

1. CEC366 IMAGE PROCESSING
A Picture is worth a thousand words
UNIT I DIGITAL IMAGE FUNDAMENTALS
Steps in Digital Image Processing – Components – Elements of Visual Perception –
Image Sensing and Acquisition – Image Sampling and Quantization – Relationships
between pixels - Color image fundamentals - RGB, HSI models, Two-dimensional
mathematical preliminaries, 2D transforms - DFT, DCT

2. IMAGE PROCESSING - OBJECTIVES
Improvement of pictorial information for
human interpretation
Processing of image data for storage,
transmission and representation for
autonomous machine perception

3. IMAGE PROCESSING - IMPORTANCE

4. IMAGE
Image – A two dimensional function
f (x ,y), where x and y are spatial (plane)
coordinates and the amplitude of f at any pair
of coordinates is called intensity or the grey
level of the image at that point
Digital image – When x,y and the amplitude
values of f are all finite and discrete quantities
then the image is called digital image.

5. Digital Image Representation

6. Image represented in the computer.
Image Represented in computer

7. What is digital image Processing?
Processing of digital images by means of a
digital computer is called digital image
processing.
Note : A digital image is composed of finite
number of elements, each of which has a
particular location and value, These elements
are referred to as picture elements,image
elements,pels and pixels.

8. Application of DIP
•Digital photography
•Satellite Imaging- remote sensing
•Human being authentication- Biometrics
•Medical diagnosis
•Autonomous machine perception
•Industrial Inspection
•Law enforcement
•Film industry

9. Application of DIP based on
Illuminating sources
Gamma ray imaging – Nuclear medicine and
astronomical observations.
X-ray imaging – Medical diagnostics (eg: X-
ray films, Angiography), Industrial
inspection.
Imaging in the UV band -Lithography,
Industrial inspection, Biological imaging and
astronomical observation.

10. Areas of application of DIP
Imaging in the visible and infra red bands -
Astronomy, remote sensing, Industry and
law enforcement.
Imaging in the Microwave band – Radar
Imaging in the Radio band – Medicine
(MRI) and astronomy.

11. Examples: Industrial Inspection
• Human operators are
expensive, slow and
unreliable.
• Make machines do the
job instead.

• Industrial vision systems
are used in all kinds of
industries

12. Examples: PCB Inspection
Printed Circuit Board (PCB) inspection
•Machine inspection is used to determine that all
components are present and that all solder joints are
acceptable
•Both conventional imaging and x-ray imaging are used

13. Examples: Law Enforcement
Image processing techniques
are used extensively by law
enforcers
•Number plate recognition for
speed cameras/automated toll
systems
•Fingerprint recognition

14. Fundamental steps in DIP
Colour image
processing
Wavelets and
Multi resolution
processing
Compression Morphological
Processing
Segmentation
Representation
and description
Object
recognition
Image
restoration
Image
enhancement
Image
acquisition
Knowledge base

15. Fundamental Steps in Digital Image Processing:
Image Acquisition
Image
Acquisition
Image
Restoration
Morphological
Processing
Segmentation
Representation
& Description
Image
Enhancement
Object
Recognition
Problem Domain
Colour Image
Processing
Image
Compression

16. Fundamental Steps in Digital Image Processing:
Image Enhancement
Image
Acquisition
Image
Restoration
Morphological
Processing
Segmentation
Representation
& Description
Image
Enhancement
Object
Recognition
Problem Domain
Colour Image
Processing
Image
Compression

17. Fundamental Steps in Digital Image Processing:
Image Restoration
Image
Acquisition
Image
Restoration
Morphological
Processing
Segmentation
Representation
& Description
Image
Enhancement
Object
Recognition
Problem Domain
Colour Image
Processing
Image
Compression

18. Fundamental Steps in Digital Image Processing:
Morphological Processing
Image
Acquisition
Image
Restoration
Morphological
Processing
Segmentation
Representation
& Description
Image
Enhancement
Object
Recognition
Problem Domain
Colour Image
Processing
Image
Compression

19. Fundamental Steps in Digital Image Processing:
Segmentation
Image
Acquisition
Image
Restoration
Morphological
Processing
Segmentation
Representation
& Description
Image
Enhancement
Object
Recognition
Problem Domain
Colour Image
Processing
Image
Compression

20. Fundamental Steps in Digital Image Processing:
Representation & Description
Image
Acquisition
Image
Restoration
Morphological
Processing
Segmentation
Representation
& Description
Image
Enhancement
Object
Recognition
Problem Domain
Colour Image
Processing
Image
Compression

21. Fundamental Steps in Digital Image Processing:
Object Recognition
Image
Acquisition
Image
Restoration
Morphological
Processing
Segmentation
Representation
& Description
Image
Enhancement
Object
Recognition
Problem Domain
Colour Image
Processing
Image
Compression

22. Fundamental Steps in Digital Image Processing:
Image Compression
Image
Acquisition
Image
Restoration
Morphological
Processing
Segmentation
Representation
& Description
Image
Enhancement
Object
Recognition
Problem Domain
Colour Image
Processing
Image
Compression

23. Fundamental Steps in Digital Image Processing:
Colour Image Processing
Image
Acquisition
Image
Restoration
Morphological
Processing
Segmentation
Representation
& Description
Image
Enhancement
Object
Recognition
Problem Domain
Colour Image
Processing
Image
Compression

24. Elements of digital image
processing systems

25. Computer
NETWORK
Image Display Mass Storage
Hard Copy Image processing
Hardware
Image Processing
Software
Image Sensor
Problem Domain

26. Cont.,
• Image acquisition
• Storage
• Processing
• Communication
• Display
• Image acquisition: Two elements are required
1) Physical device - x- ray imaging systems
(Electrical o/p proportional to light intensity)
2) Digitizer

27. Cont.,
• Storage: 8 bit image of size 1024 X 1024 pixels
require one million bytes of storage.
• Digital storage for image processing 3 types
1) Short term storage- use during processing
(eg. Computer memory)
2) On-line storage – Fast recall.
(eg. Magnetic disks, Magneto optical)
3) Archival storage – Infrequent access.
(eg. Magnetic tapes, Optical disks)

28. CONT.,
• Processing and Networking: processing digital
images- algorithm or software.
• Some of the applications – need specialized
image processing hardware (require fast
throughputs).
• Recently- use computer for image processing and
ALU is used in averaging images (noise
reduction).
• Large scale IP –small computer with image
processing hardware.
• Software: specialized modules that performs
specific tasks.

29. Cont.,
• Communication:
1) local communication between IP systems.
2) Remote communication
• Display :
•Monochrome and color TV monitors.
•Random access CRT.
•Printing devices.

30. ELEMENTS OF VISUAL
PERCEPTION

31. Introduction
•In many image processing applications, the
objective is to help a human observer perceive the
visual information in an image. Therefore, it is
important to understand the human visual
system.
•The human visual system consists mainly of the
eye (image sensor or camera), optic nerve
(transmission path), and brain (image information
processing unit or computer).
•It is one of the most sophisticated image
processing and analysis systems.

32. Outline
•Structure of the human eye
•Image formation in the human eye
•Brightness adaptation and discrimination

33. Structure of Human Eye

34. •Three Membranes enclose the eye:
1. The cornea and sclera - outer cover
2. The choroid
3. The Retina
CORNEA and SCLERA
• Cornea -Tough, Transparent tissue that covers
the anterior surface of the eye
• Sclera - Continuous with cornea, Opaque
membrane, covers remaining part

35. CHOROID
• Below the sclera
• Networks of blood vessels-major source of nutrition
• Ciliary body and Iris diaphragm
LENS
•Concentric layers of fibrous cells
•60%-70% water, 6% fat and more protein
•The lens and the ciliary muscle focus the reflected
lights from objects into the retina to form an image
of the objects.

36. RETINA
•Pattern vision is afforded by the distribution of
discrete light receptors over the surface of the retina.
•Two types of photoreceptors: rods and cones (light
sensors)
 Cones
•There are 6 to 7 million cones in each eye.
•Concentrated in the central portion of the retina
called the fovea.
•Highly sensitive to color.
•Each cone is connected to its own nerve end, so
human can resolve fine details.
• Cone vision is called photopic or BRIGHT-LIGHT
VISION

37.  Rods
•There are 75 to 150 million rods in each eye.
•Distributed over the retina surface.
•Several rods are connected to a single nerve end.
•Rods don’t discern fine details.
•Rods give a general picture of the field of view.
•Not involve in color vision and sensitive to low
levels of illumination.
• Rod vision is called scotopic or DIM-LIGHT
VISION.

38.  Fovea
•Circular indentation in center of retina, about
1.5mm diameter, dense with cones.
•Photoreceptors around fovea responsible for spatial
vision (still images).
•Photoreceptors around the periphery responsible for
detecting motion.
 Blind spot
• Point on retina where optic nerve emerges, devoid
of photoreceptors.

39. •Fovea size is 1.5 mm in diameter
•1.5 mm  1.5 mm square contain 337000 cones
•5mm  5mm CCD imaging chip

40. Image formation of the eye
•Flexible lens : the principal difference from an
ordinary optical lens.
•Controlled by the tension in the fibers of the ciliary
body
•To focus on distant objects – flattened
•To focus on objects near eye – thicker
•Near-sighted and far-sighted

41. y
x h
Focal length = f = 14 to 17 mm
x
y
=
f
h
f
h = 2.55 mm
FDP ON DIP - DEPT. OF ECE, SAEC

42. •Focal length of the eye : 14 to 17 mm
•Let h be the height in mm of that object in the retinal
image, then
15/100 = h / 17 , h = 2.55mm
•The retinal image is reflected primarily in the area of
the fovea.
FDP ON DIP - DEPT. OF ECE, SAEC

43. Brightness Adaptation
•The range of light intensity human can adapt to is
in the range of 10
10
•Subjective brightness is a logarithmic function of
the light intensity incident on the eye.
•The visual system does not operate simultaneously
over the 10
10
range. It accomplishes this large
variation by changes in its overall sensitivity, a
phenomenon known as brightness adaptation
•The current sensitivity level of the visual system is
called brightness adaptation level
FDP ON DIP - DEPT. OF ECE, SAEC

44. FDP ON DIP - DEPT. OF ECE, SAEC

45. Brightness Discrimination
•Brightness discrimination is the ability of the eye
to discriminate between changes in light intensity
at any specific adaptation level.
•The quantity I
c
/I, where I
c is the increment of
illumination discriminable 50% of the time with
background illumination I, is called the Weber
ratio.
FDP ON DIP - DEPT. OF ECE, SAEC

46. •Weber ratio (the experiment) :
•I: the background illumination
• : the increment of illumination
•Small Weber ratio indicates good discrimination
•Larger Weber ratio indicates poor discrimination
FDP ON DIP - DEPT. OF ECE, SAEC
CI
II
C/

47. •Brightness discrimination is poor at low levels of
illumination.
•The two branches in the curve indicate that at
low levels of illumination vision is carried out by
the rods, whereas at high level by the cones.
FDP ON DIP - DEPT. OF ECE, SAEC

48. Perceived Brightness
•Two phenomena clearly demonstrate that perceived
brightness is not a simple function of intensity.
๏ Mach band pattern
๏ Simultaneous contrast
๏ Optical illusion
FDP ON DIP - DEPT. OF ECE, SAEC

49. •First Phenomena –
Mach Band
•Visual system tends
to undershoot or
overshoot around
boundary of regions
of different
intensities.
FDP ON DIP - DEPT. OF ECE, SAEC

50. •The second phenomena, called simultaneous
contrast, a spot may appears to the eye to become
darker as the background gets lighter.
FDP ON DIP - DEPT. OF ECE, SAEC

51. •Optical illusions occurs when the eye fills in non-
existing information or wrongly perceives
geometrical properties of objects.
FDP ON DIP - DEPT. OF ECE, SAEC

52. FDP ON DIP - DEPT. OF ECE, SAEC

53. FDP ON DIP - DEPT. OF ECE, SAEC

54. Content
•2D Transforms
1.DFT
2.DCT
3.KLT
4.SVD

55. Why Do Transforms?
•Fast computation
•Conceptual insights for various image processing
•Obtain transformed data as measurement
•For efficient storage and transmission

56. Image Transforms
•Many times, image processing tasks are best
performed in a domain other than the spatial domain.
•Key steps:
(1) Transform the image
(2) Carry the task(s) in the transformed domain.
(3) Apply inverse transform to return to the spatial
domain.

57. Image Transforms (cont’d)
•Forward Transformation
•Inverse Transformation






1
0
1
0
1,...,1,0,1,...,1,0),,,(),(),(
M
x
N
y
NvMuvuyxryxfvuT






1
0
1
0
1,...,1,0,1,...,1,0),,,(),(),(
M
u
N
v
NyMxvuyxsvuTyxf
inverse transformation kernel
forward transformation kernel

58. Image Transforms (cont’d)
•A kernel is said to be separable if:
•A kernel is said to be symmetric if:
),(),(),,,(
21
vyruxrvuyxr 
),(),(),,,(
11
vyruxrvuyxr 
(i.e., r
1
and r
2
are functionally equal)

59. Cont.,
•Continuous Fourier Transform (FT)
–1D
–2D
•Discrete Fourier Transform (DFT)
–1D
–2D
•Fast Fourier Transform (FFT)

60. Continuous Fourier Transform (FT)
•Transforms a signal (i.e., function) from the spatial
domain to the frequency domain.
where

61. How do frequencies show up in an image?
•High frequencies correspond to quickly varying
information (e.g., edges)
•Low frequencies correspond to slowly varying
information (e.g., continuous surface)
Original Image High-passed Low passed

62. Discrete Fourier Transform (DFT)
(cont’d)
•Forward DFT
•Inverse DFT

63. Extending DFT to 2D
•Assume that f(x,y) is M x N image.
•Forward DFT
•Inverse DFT:

64. Extending DFT to 2D (cont’d)
•Special case: f(x,y) is N x N image.
•Forward DFT
•Inverse DFT

65. DFT Properties: (1) Separability
•The 2D DFT can be computed using 1D transforms
only:
Forward DFT:
Inverse DFT:
2 ( ) 2 ( ) 2 ( )
ux vy ux vy
j j j
N N N
e e e
  

  

kernel is
separable:

66. DFT Properties: (1) Separability
(cont’d)
•Rewrite F(u,v) as follows:
•Let’s set:
•Then:

67. DFT Properties: (1) Separability (cont’d)

68. DFT Properties: (2) Periodicity
•The DFT and its inverse are periodic with period N

69. DFT Properties: (3) Symmetry
• If f(x,y) is real, then

70. DFT Properties: (4) Translation
N
f(x,y) f (u,v)
• Translation is spatial domain:
• Translation is frequency domain:

71. DFT Properties: (4) Translation
(cont’d)
•To move F(u,v) at (N/2, N/2), take
no translation after translation

72. DFT Properties: (5) Rotation
•Rotating f(x,y) by θ rotates F(u,v) by θ

73. DFT Properties: (6) Distributive
but …

74. DFT Properties: (7) Scale

75. DFT Properties: (8) Average value
So:
Average:
F(u,v) at u=0, v=0:

76. Magnitude and Phase of DFT
•What is more important?
•Hint: use inverse DFT to reconstruct the image using
magnitude or phase only information
magnitude phase

77. Magnitude and Phase of DFT (cont’d)
Reconstructed image using
magnitude only
(i.e., magnitude determines the
contribution of each component!)
Reconstructed image using
phase only
(i.e., phase determines
which components are present!)

78. Energy Compaction !
Most unitary transforms pack a large fraction of the
energy of the image into relatively few of the transform
coefficients. This means that relatively few of the
transform coefficients have significant values. This
property is very useful for compression purposes

79. Energy Preservation

1-D

2-D 









1
0
1
0
2
1
0
1
0
2
),(),(
N
u
N
v
N
x
N
y
vugyxf
22
fg
a unitary transformation preserves the signal energy. This property is called energy preservation property.

80. DCT
One dimensional signals
The DCT is defined below
Cu=au∑
x=0
N−1
fxcos[
2x1uπ
2N ]

u=0,1,,N−1
au={
1/N u=0
2/N u=1,,N−1}
The inverse DCT (IDCT) is defined below
fx=∑
u=0
N−1
auCucos[
2x1uπ
2N ]

81. DCT CONT.,
Two dimensional signals
For 2-D signals it is defined as
Cu,v=auav∑
x=0
N−1
∑
y=0
N−1
fx,ycos[
2x1uπ
2N ]
cos[
2y1vπ
2N ]
fx,y=∑
u=0
N−1
∑
v=0
N−1
auavCu,vcos[
2x1uπ
2N ]
cos[
2y1vπ
2N ]
au u,v=0,1,,N−1 is defined as above and

82. 1-D Basis Functions N=8
1.0
0.5
0
-0.5
-1.0
u=0
1.0
0.5
0
-0.5
-1.0
u=1
1.0
0.5
0
-0.5
-1.0
u=2
1.0
0.5
0
-0.5
-1.0
u=3
1.0
0.5
0
-0.5
-1.0
u=4
1.0
0.5
0
-0.5
-1.0
u=5
1.0
0.5
0
-0.5
-1.0
u=6
1.0
0.5
0
-0.5
-1.0
u=7

83. Properties of the DCT transform
•The DCT is a real and orthogonal transform. This
property makes it attractive in comparison to the
Fourier transform.
•The DCT has excellent energy compaction
properties. For that reason it is widely used in
image compression standards (as for example
JPEG standards).
•The NxN cosine transform is very close to KL
transform.
•There are fast algorithms to compute the DCT, similar to
the FFT for computing the DFT.

84. 2-D Basis Functions N=4
0
1
2
3
0 1 2 3
u
v

85. 2-D Basis Functions N=8

87. Cont.,

94. DRAWBACKS

95. Original Images

96. Karhunen-Loeve Images

97. Properties of KLT
•KL transform co-efficients are uncorrelated and have 0
mean and data dependent.
•Error can be minimized and optimality.
•It has good energy compaction.
•Fast transform.
•It also minimized the expected number of transforms co-
efficients requiered.
•Minimum value of distortion.
Applications 1. (non-universal) compression
2. Pattern recognition: e.g., eigen faces
3. Analyze the principal (“dominating”) components

98. Applications of KLT
Applications
1. (non-universal) compression
2. Pattern recognition: e.g., eigen faces
3. Analyze the principal (“dominating”) components

99. SVD Transform
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102. Color Image Processing
Session III

103. Contents
•Color fundamentals.
•Types of Color Models.
•RGB Models.
•HIS Models.
•Conversion of Color Models.

104. Cont.,
•Color is a powerful descriptor that often
simplifies object identification and extraction
from a scene.
•Humans can differentiate thousands of color
shades and intensities of gray scale.

105. Color Fundamentals

106. Color Fundamentals
•Primary colors:
•Red ®, Green (G)
and Blue(B).
•Secondary colors:
magenta (red +
blue), cyan (green
+ blue), and yellow
(red + green)

107. Color Fundamentals
The characteristics generally used to distinguish
one color from another are Brightness, Hue, and
Saturation.
Hue: Represents dominant color as perceive by
an observer.
Saturation: Relative purity or the amount of white
light mixed with a hue

108. Cont.,
•Hue and saturation taken together are
called Chromaticity, and therefore, a color
may be characterized by its Brightness and
Chromaticity.

109. Color Models
The purpose of a color model (also called color space or
color system) is to facilitate the specification of colors
in some standard, generally accept way.
RGB (red, green, blue) : monitor, video camera.
CMY(cyan, magenta, yellow),CMYK (CMY, black)
model for color printing.
HSI model, which corresponds closely with the way
humans describe and interpret color.

110. Cont.,
• Most color models in use today are oriented either
towards hardware or towards applications (such as
creation of color graphics for animation).
•In digital image processing , the hardware oriented
models used in practice is the RGB model.(color
monitor and color videos cameras).

111. Color Models -- RGB Model
•In RGB model each color appears in its primary
spectral components of red, green and blue.
• This model is based on a Cartesian co-ordinate
system.

112. Color Models -- RGB Model

113. •R, G, B at 3 axis ranging in [0 1] each
Gray scale along the diagonal.
•If each component is quantized into 256 levels
[0:255], the total number of different colors that
can be produced is (2
8
)
3
= 2
24
= 16,777,216
colors.
• RGB safe color:
Quantize each components into 6 levels from 0 to
255.
Cont.,

114. Cont.,
•Image represented in the RGB color model consists
of three component images, one for each primary
color.
•When fed into an RGB monitor, these three images
combine on the phosphor screen to produce a
composite color image.
•The number of bits used to represent each pixel in
RGB space is called the pixel depth.

115. Cont.,
•RGB image in which each of the red, green and
blue images is an 8bit image.
•RGB model having depth of 24 bits.
•The term full color image is used often to denote a
24 bit RGB Color image.
•The 24 bit RGB color cube corresponding to the
diagram is shown below.

116. 24 bit RGB color cube

117. Color Models -- RGB Model

118. Color Models -- RGB Model
•For most
graphics
images used
for Internet
applications, a
set of 216
colors has
been selected
to represent
“safe colors”
which should
be reliably
displayed on
computer
monitors.

119. Color Models -- RGB Model

120. Cont.,
• RGB and CMY are ideally suited for hardware
implementation.
•These models are not suited for human
interpretation.
•When human view color object, it can be described
by its Hue, Saturation and Brightness.

121. The HSI Color Model
•Human describes color in terms of hue, saturation
and brightness.
–Hue: describe the pure color, pure yellow,
orange, green or red.
–Saturation measures the degree to which a pure
color is diluted by white light.
– Brightness is a subjective descriptor difficult
to be measured.
•Comparison:
–The RGB model is ideal for image color
generation.
–The HSI model is an ideal tool for developing
image processing algorithms based on color
descriptions.

122. Cont.,
•Color images are not based on the three primary
colors.
•The intensity ( is a most useful color descriptor
of monochromatic images.
• This quantity definitely is measurable and easily
interpretable.

123. Conceptual Relationship RGB - HSI
•All pointes contained in the plane segment are
defined by the intensity and boundary of the cube
have the same hue.

124. Hue Measurement

125. The HSI Color Model

126. Conversions
•From RGB to HSI
•S=1-[3/(R+G+B)][min(R, G, B)]
•I=(R+G+B)/3






GBif
GBif
H


360










2/12
1
)])((()[(
)]()[(2/1
cos
BGBRGR
BRGR


127. Conversions (Cont.)
•RG sector (0<H<120)
B = I(1-S)

G = 3I-(R+B)








)60cos(
cos
1
H
HS
IR
o

128. Conversions (Cont.)
•GB sector (120≤H<240)
–First, let H = H -120
R=I(1-S)

B=3I-(R+G)








)60cos(
cos
1
H
HS
IG
o

129. Conversions (Cont.)
•BR sector (240 ≤ H ≤ 360)
–First, let H = H -240
G = I(1-S)

R = 3I-(G+B)








)60cos(
cos
1
H
HS
IB
o

130. The HSI Color Model

131. Color Models -- HSI Model

132. Color Models -- HSI Model

133. Full Color Image Processing
•Two processing methods:
–(1) process each channel (or color
component) separately, as if the color image
were three gray scale images;
–(2) process all channels with each pixel
represented as a vector.

134. Color Transformations
RGB<->HSI<->CMYK

135. Color Transformations
Example

136. Color Complement Transformations
Example

137. Tone and Color Corrections
Tone Corrections

138. Smoothing and Sharpening
Color Image Smoothing

139. Smoothing and Sharpening
Color Image Smoothing

140. Color Edge Detection

141. Color Edge Detection

142. Noise in Color Images

143. Noise in Color Images
Fig. 6.48(d)