Chapter 1 and 2 gonzalez and woods

Chapter-1 and 2
Subject: FIP (181102)
Prof. Asodariya Bhavesh
ECD,SSASIT, Surat

Digital Image Processing, 3rd edition by
Gonzalez and Woods

Optics and Human Vision
The physics of light
http://commons.wikimedia.org/wiki/File:Eye-diagram_bg.svg

Light
 Light
 Particles known as photons
 Act as ‘waves’
 Two fundamental properties
 Amplitude
 Wavelength
 Frequency is the inverse of wavelength
 Relationship between wavelength (lambda) and frequency (f)
fc /
Where c = speed of light = 299,792,458 m / s
4

What is Digital Image Processing?
Digital image processing focuses on two major tasks
 Improvement of pictorial information for human
interpretation
 Processing of image data for storage, transmission and
representation for autonomous machine perception
Some argument about where image processing ends
and fields such as image analysis and computer vision
start

What is DIP? (cont…)
The continuum from image processing to computer
vision can be broken up into low-, mid- and high-level
processes
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
In this course we will
stop here

History of Digital Image Processing
Early 1920s: One of the first applications of digital
imaging was in the news-
paper industry
 The Bartlane cable picture
transmission service
 Images were transferred by submarine cable between
London and New York
 Pictures were coded for cable transfer and reconstructed
at the receiving end on a telegraph printer
Early digital image
ImagestakenfromGonzalez&Woods,DigitalImageProcessing(2002)

History of DIP (cont…)
Mid to late 1920s: Improvements to the Bartlane
system resulted in higher quality images
 New reproduction
processes based
on photographic
techniques
 Increased number
of tones in
reproduced images
Improved
digital image Early 15 tone digital
image

1960s: Improvements in computing technology and
the onset of the space race led to a surge of work in
digital image processing
 1964: Computers used to
improve the quality of
images of the moon taken
by the Ranger 7 probe
 Such techniques were used
in other space missions
including the Apollo landings
A picture of the moon taken
by the Ranger 7 probe
minutes before landing

1970s: Digital image processing begins to be used in
medical applications
 1979: Sir Godfrey N.
Hounsfield & Prof. Allan M.
Cormack share the Nobel
Prize in medicine for the
invention of tomography,
the technology behind
Computerised Axial
Tomography (CAT) scans
Typical head slice CAT
image

Key Stages in Digital Image Processing
Image
Acquisition
Image
Restoration
Morphological
Processing
Segmentation
Representation
& Description
Image
Enhancement
Object
Recognition
Problem Domain
Colour Image
Processing
Image
Compression

Key Stages in Digital Image Processing:
Image Aquisition
Image
Acquisition
Image
Restoration
Morphological
Processing
Segmentation
Representation
& Description
Image
Enhancement
Object
Recognition
Problem Domain
Colour Image
Processing
Image
Compression

Image Enhancement
Image
Acquisition
Image
Restoration
Morphological
Processing
Segmentation
Representation
& Description
Image
Enhancement
Object
Recognition
Problem Domain
Colour Image
Processing
Image
Compression

Image Restoration
Image
Acquisition
Image
Restoration
Morphological
Processing
Segmentation
Representation
& Description
Image
Enhancement
Object
Recognition
Problem Domain
Colour Image
Processing
Image
Compression

Morphological Processing
Image
Acquisition
Image
Restoration
Morphological
Processing
Segmentation
Representation
& Description
Image
Enhancement
Object
Recognition
Problem Domain
Colour Image
Processing
Image
Compression

Segmentation
Image
Acquisition
Image
Restoration
Morphological
Processing
Segmentation
Representation
& Description
Image
Enhancement
Object
Recognition
Problem Domain
Colour Image
Processing
Image
Compression

Object Recognition
Image
Acquisition
Image
Restoration
Morphological
Processing
Segmentation
Representation
& Description
Image
Enhancement
Object
Recognition
Problem Domain
Colour Image
Processing
Image
Compression

Representation & Description
Image
Acquisition
Image
Restoration
Morphological
Processing
Segmentation
Representation
& Description
Image
Enhancement
Object
Recognition
Problem Domain
Colour Image
Processing
Image
Compression

Image Compression
Image
Acquisition
Image
Restoration
Morphological
Processing
Segmentation
Representation
& Description
Image
Enhancement
Object
Recognition
Problem Domain
Colour Image
Processing
Image
Compression

Colour Image Processing
Image
Acquisition
Image
Restoration
Morphological
Processing
Segmentation
Representation
& Description
Image
Enhancement
Object
Recognition
Problem Domain
Colour Image
Processing
Image
Compression

Visible Spectrum
(Images from Rafael C. Gonzalez and Richard E
Wood, Digital Image Processing, 2nd Edition.

Light
Diagram of a light wave.
22

Conventional Coordinate for Image Representation

Digital Image Types : Intensity Image
Intensity image or monochrome image
each pixel corresponds to light intensity
normally represented in gray scale (gray
level).












39871532
22132515
372669
28161010
Gray scale values













39871532
22132515
372669
28161010












39656554
42475421
67965432
43567065












99876532
92438585
67969060
78567099
Digital Image Types : RGB Image
Color image or RGB image:
each pixel contains a vector
representing red, green and
blue components.
RGB components

Image Types : Binary Image
Binary image or black and white image
Each pixel contains one bit :
1 represent white
0 represents black












1111
1111
0000
0000
Binary data

Image Types : Index Image
Index image
Each pixel contains index number
pointing to a color in a color table










256
746
941
Index value
Index
No.
Red
component
Green
component
Blue
component
1 0.1 0.5 0.3
2 1.0 0.0 0.0
3 0.0 1.0 0.0
4 0.5 0.5 0.5
5 0.2 0.8 0.9
… … … …
Color Table

Cross Section of the Human Eye

Anatomy of the Human Eye
30 Source:
http://webvision.med.utah.edu/

Human Visual System
 Human vision
 Cornea acts as a protective lens that roughly focuses
incoming light
 Iris controls the amount of light that enters the eye
 The lens sharply focuses incoming light onto the retina
 Absorbs both infra-red and ultra-violet light which can damage
the lens
 The retina is covered by photoreceptors (light
sensors) which measure light
31

Photoreceptors
 Rods
 Approximately 100-150 million rods
 Non-uniform distribution across the retina
 Sensitive to low-light levels (scotopic vision)
 Lower resolution
 Cones
 Approximately 6-7 million cones
 Sensitive to higher-light levels (photopic vision)
 High resolution
 Detect color by the use of 3 different kinds of cones each of
which is sensitive to red, green, or blue frequencies
 Red (L cone) : 564-580 nm wavelengths (65% of all cones)
 Green (M cone) : 534-545 nm wavelengths (30% of all cones)
 Blue (S cone) : 420-440 nm wavelengths (5% of all cones)
33

Cone (LMS) and Rod (R) responses
http://en.wikipedia.org/wiki/File:Cone-response.svg34

Photoreceptor density across retina
35

Comparison between rods and cones
36
Rods Cones
Used for night vision Used for day vision
Loss causes night blindness Loss causes legal blindness
Low spatial resolution with higher
noise
High spatial resolution with lower
noise
Not present in fovea Concentrated in fovea
Slower time response to light Quicker time response to light
One type of photosensitive pigment Three types of photosensitive
pigment
Emphasis on motion detection Emphasis on detecting fine detail

Color and Human Perception
 Chromatic light
 has a color component
 Achromatic light
 has no color component
 has only one property – intensity
37

Image Formation in the Human Eye
(Picture from Microsoft Encarta 2000)

Brightness Adaptation
Actual light intensity is (basically)
log-compressed for perception.
Human vision can see light
between the glare limit and
scotopic threshold but not all
levels at the same time.
The eye adjusts to an average
value (the red dot) and can
simultaneously see all light in a
smaller range surrounding the
adaptation level.
Light appears black at the bottom
of the instantaneous range and
white at the top of that range.
39

Human Visual Perception
 Light intensity:
 The lowest (darkest) perceptible intensity is the scotopic
threshold
 The highest (brightest) perceptible intensity is the glare limit
 The difference between these two levels is on the order of 1010
 We can’t discriminate all these intensities at the same time! We
adjust to an average value of light intensities and then discriminate
around the average.
 Log compression.
 Experimental results show that the relationship between the
perceived amount of light and the actual amount of light in a
scene are generally related logarithmically.
 The human visual system perceives brightness as the logarithm of the
actual light intensity and interprets the image accordingly.
 Consider, for example, a bright light source that is approximately
6times brighter than another. The eye will perceive the brighter light as
approximately twice the brightness of the darker.
42

Brightness Adaptation and Mach Banding
43
 When viewing any scene:
 The eye rapidly scans across the ﬁeld of view while
coming to momentary rest at each point of particular
interest.
 At each of these points the eye adapts to the average
brightness of the local region surrounding the point of
interest.
 This phenomena is known as local brightness
adaptation.
 Mach banding is a visual effect that results, in part, from local
brightness adaptation.
 The eye over-shoots/under-shoots at edges where the
brightness changes rapidly. This causes ‘false perception’ of
the intensities

Brightness Adaptation and Mach Banding
44

Brightness Adaptation(Hermann Grid)
45

Optical illusion

Simultaneous Contrast
 Simultaneous contrast refers to the way in which two
adjacent intensities (or colors) affect each other.
 Example: Note that a blank sheet of paper may appear
white when placed on a desktop but may appear black
when used to shield the eyes against the sun.
 Figure 2.9 is a common way of illustrating that the
perceived intensity of a region is dependent upon the
contrast of the region with its local background.
 The four inner squares are of identical intensity but are
contextualized by the four surrounding squares
 The perceived intensity of the inner squares varies from bright
on the left to dark on the right.
48

Image Sensing and acquisition
Single sensor
Line sensor
Array sensor

Image Sensors : Single Sensor

Image Sensors : Line Sensor
Fingerprint sweep sensor
Computerized Axial Tomography

CCD KAF-3200E from Kodak.
(2184 x 1472 pixels,
Pixel size 6.8 microns2)
Charge-Coupled Device (CCD)
w Used for convert a continuous
image into a digital image
w Contains an array of light sensors
w Converts photon into electric charges
accumulated in each sensor unit
Image Sensors : Array Sensor

Horizontal Transportation Register
OutputGateAmplifier
VerticalTransportRegister
Gate
Gate
Gate
Photosites Output
Image Sensor: Inside Charge-Coupled Device

Image Sensor: How CCD works
abc
ghi
def
abc
ghi
def
abc
ghi
def
Vertical shift
Horizontal shift
Image pixel
Horizontal transport
register
Output

Digital Image Acquisition Process

Generating a Digital Image

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

How to choose the spatial resolution
= Sampling locations
Originalimage
Sampledimage
Under sampling, we lost some image details!
Spatial resolution

How to choose the spatial resolution : Nyquist Rate
Originalimage
= 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

0 0.5 1 1.5 2
-1
-0.5
0
0.5
1
0 0.5 1 1.5 2
-1
-0.5
0
0.5
1
1),2sin()(1  fttx 
6),12sin()(2  fttx 
Sampling rate:
5 samples/sec
Aliased Frequency
Two different frequencies but the same results !

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

Spatial Resolution
 It is a measure of the smallest discernible detail in an
image
 Can be stated in line pairs per unit distance, and
dots(pixels) per unit distance
 Dots per unit distance commonly used in printing
and publishing industry (dots per inch)
 Newspaper are printed with a resolution of 75 dpi,
magazines at 133 dpi, and glossy brochures at175
dpi
 examples

Effect of Spatial Resolution

Can we increase spatial resolution by interpolation ?
Down sampling is an irreversible process.

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
cN 2
where b = no. of bits

Quantization function
Light intensity
Quantizationlevel
0
1
2
Nc-1
Nc-2
Darkest Brightest

Intensity Resolution
 It refers to the smallest discernible change in
intensity level
 Number of intensity levels usually is an integer
power of two
 Also refers to Number of bits used to quantize
intensity as the intensity resolution
 Which intensity resolution is good for human
perception 8 bit, 16 bit, or 32 bit

Effect of Quantization Levels or Intensity resolution
256 levels 128 levels
32 levels64 levels

Effect of Quantization Levels (cont.)
16 levels 8 levels
2 levels4 levels
In this image,
it is easy to see
false contour.
Effect of Quantization Levels or Intensity resolution

How to select the suitable size and pixel depth of images
Low detail image Medium detail image High detail image
Lena image Cameraman image
To satisfy human mind
1. For images of the same size, the low detail image may need more pixel dep
2. As an image size increase, fewer gray levels may be needed.
The word “suitable” is subjective: depending on “subject”.

Isopreference Curve
 Curves tend to become more vertical as the detail in
the image increases
 Image with a large amount of detail only a few
intensity levels may be needed

Image Interpolation
 Used in image resizing (zooming and shrinking),
rotating, and geometric corrections
 Interpolation is the process of using known data to
estimate values at unknown locations
 Nearest Neighbor interpolation
 It assigns to each new location the intensity of its nearest
neighbor in the original image
 Produce undesirable artifacts, such as severe distortion of
straight edges
 Bilinear Interpolation
 We use the four nearest neighbors to estimate the
intensity
 V(x, y) = ax + by + cxy + d

Image Interpolation
 Need to solve four equations
 Better results than nearest neighbor interpolation, with a
modest increase in computational burden
 Bicubic Interpolation
 Involves sixteen neighbors to estimate intensity
 V(x, y) = ∑∑aij xi yj ( i, j = 0 to 3)
 Need to solve sixteen equations
 Gives better results than other methods
 More complex
 Used in Adobe Photoshop, and Corel Photopaint

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)

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.

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.

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.

Connectivity
Connectivity is adapted from neighborhood relation. Two pixels are connected
if they are in the same class (i.e. the same color or the same range of intensity)
and they are neighbors of one another.
For p and q from the same class
w 4-connectivity: p and q are 4-connected if q N4(p)
w 8-connectivity: p and q are 8-connected if q N8(p)
w mixed-connectivity (m-connectivity):
p and q are m-connected if q N4(p) or
q ND(p) and N4(p) N4(q) = 

Adjacency
A pixel p is adjacent to pixel q is they are connected.
Two image subsets S1 and S2 are adjacent 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.

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.

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

Distance
For pixel p, q, and z with coordinates (x,y), (s,t) and (u,v),
D is a distance function or metric if
w D(p,q) 0 (D(p,q) = 0 if and only if p = q)
w D(p,q) = D(q,p)
w D(p,z) D(p,q) + D(q,z)
Example: Euclidean distance
22
)()(),( tysxqpDe -+-

Distance (cont.)
D4-distance (city-block distance) is defined as
tysxqpD -+-),(4
1 2
10
1 2
1
2
2
2
2
2
2
Pixels with D4(p) = 1 is 4-neighbors of p.

Distance (cont.)
D8-distance (chessboard distance) is defined as
),max(),(8 tysxqpD --
1
2
10
1
2
1
2
2
2
2
2
2
Pixels with D8(p) = 1 is 8-neighbors of p.
22
2
2
2
222
1
1
1
1

111
 Boundary (Border or Contour)
of a region R is the set of points that are adjacent to
points in the complement of R.
of a region is the set of pixels in the region that have
at least one background neighbor.
Inner Border
Outer Border

Moire Pattern Effect : Special Case of Sampling
Moire patterns occur when frequencies of two superimposed
periodic patterns are close to each other.

Human vision: Spatial Frequency vs Contrast

Human vision: Distinguish ability for Difference in brightness
Regions with 5% brightness difference

Chapter 1 and 2 gonzalez and woods

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Chapter 1 and 2 gonzalez and woods