Chapter 3 - Image Enhancement in the Spatial Domain

1. Digital Image Processing
(2nd Edition)
Rafael C. Gonzalez
Richard E.Woods
Dr Moe Moe Myint
Technological University (Kyaukse)
www.slideshare.net/MoeMoeMyint
moemoemyint@moemyanmar.ml
drmoemoemyint.blogspot.com

2. Miscellanea
 Lectures: Class A
 Monday 5-6
 Tuesday 6-7
 Lectures: Class B
 Monday 1-2
 Wednesday 5-6
 Labs:
 Tuesday for Class A and Wednesday for Class B
 Web Site:
 www.slideshare.net/MoeMoeMyint
 drmoemoemyint.blogspot.com
 E-mail: moemoemyint@moemyanmar.ml
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3. Contents for Chapter 3
 This lecture will cover:
 Background
 Some Basic Gray Level Transformations
 Histogram Processing
 Enhancement Using Arithmetic/Logic Operations
 Basics of Spatial Filtering
 Smoothing Spatial Filters
 Sharpening Spatial Filters
 Combining Spatial Enhancement Methods
 Summary
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4. Introduction
“It makes all the difference whether one sees darkness through
the light or brightness through the shadows”
David Lindsay
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5. Preview
 The principal objective
to process an image so that the result is more suitable than the
original image for a specific application
The word specific is important because algorithms development for
enhancing X-ray images may not necessarily be the best approach
for enhancing pictures of Mars transmitted by a space probe.
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6. Image enhancement example6

7. Two categories
 There is no general theory of image enhancement
 Spatial domain
image plane itself (the ‘natural’ image) and based on
direct manipulation of pixels in an image
 Frequency domain
based on modifying the Fourier transform of an image
(modify the image frequency components)
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8.  No general theory
Image Enhancement
Enhancement
technique
Input image “Better”
image
Specific Application
Spatial Domain
Manipulate pixel intensity
directly
Frequency Domain
Modify the Fourier transform
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9. x
y
Origin(0,0)
*(x,y)
x
y
Origin(0,0)
*(x,y)
Spatial coordinate system Cartesian coordinate system
g (x, y)=T [ f (x, y)]
Image Enhancement in Special Domain
The processed image Operator on f input image
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10. Background
 Spatial domain processing
the aggregate of pixel composing an image procedures that
operate directly on these pixels
By expression: g(x, y)=T[ f(x, y) ]
Where f(x, y): input image
g(x, y): output (processed) image
T: operator on f
(Defined over some neighborhood of (x, y))
T
f(x,y) g(x,y)
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11. The operator T can be defined over
a) The set of pixels (x, y) of the image
b) The set of ‘neighborhoods’ N(x, y) of each pixel
c) A set of images f1,f2,f3,…
a)
6 8 2 0
12 200 20 10
3 4 1 0
6 100 10 5
(Operator: Div. by 2)
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12. b)
c)
6 8 2 0
12 200 20 10
226
6 8
12 200
(Operator: sum)
6 8 2 0
12 200 20 10
5 5 1 0
2 20 3 4
11 13 3 0
14 220 23 14
(Operator: sum)
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13. Cont’d13
Defining the neighborhood
around (x, y)
Use a square/rectangle
subimage area that is
centered at (x, y)
Operation
Move the center of
the subimage from pixel
to pixel and apply
the operation T at
each location (x, y)
to compute the output
g(x, y)

14.  The easiest case of operators
When the neighborhood is 1 x 1(i.e, a single pixel) then g
depends only on the value of f at (x,y)
T becomes a gray-level transformation ( an intensity or
mapping) function:
s = T(r)
where;
r = gray-level at (x,y) in original image f(x,y)
s = gray-level at (x,y) in original image g(x,y)
This kind of processing is referred as point processing
 Point processing techniques (e.g., contrast stretching ,
thresholding)
Cont’d
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15. Point processing
a) T(r) performs contrast stretching by producing an image of
higher contrast than the original by darkening the levels below
m and brightening the levels above m in the original image.
b) T(r ) produces a two-level (binary) image. (thresholding
function)
Contraststretching
thresholding
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16. Contrast Stretching
Original Enhanced
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17.  Thresholding transformations are particularly useful for
segmentation in which we want to isolate an object of interest
from a background.
Thresholding
Original Enhanced
s = 1.0 r > threshold
s = 0.0 r<= threshold
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18.  If neighborhood is greater than 1 x 1,
 General approach: to use a function of the values of f in a
predefined neighborhood of (x, y) to determine the value of g
at (x, y).
The use of masks (or filters, kernels, template, or windows)
 a mask is a small (e.g., 3x3 ) 2-D array
 The values of mask coefficients
determine the nature of the process
(image sharpening)
Enhancement technique :
mask processing or filtering
Neighborhood Processing
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19. Some Basic Gray Level Transformations
Gray–level transformation functions are among the simplest
of all image enhancement techniques
The values of pixels, before and after processing are related
by an expression s = T (r)
For an 8-bit environment, a lookup table will have 256
entries
Some basic gray level transformations functions:
Image Negatives
Log Transformations
Power-Law Transformations
Piecewise Transformation
oContrast Stretching
oGray-level Slicing
oBit-plane Slicing
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20. Image Negatives
 The negative of an image with gray levels in the range [0, L-1]
is obtained by using the negative transformation which is
given by the expression
s = L – 1 – r
where; r is value of input pixel
s is value of processed pixel
input gray level ranges from 0 to L-1 ( [0, L-1] )
 Reversing the intensity level of image
 Suited for enhancing white or gray detail embedded in dark
regions of an image, especially when the black areas are
dominant in size
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21. Image negatives
 Original Image : Digital Mammogram showing a small
lesion
 Much easier : to analyze the breast tissue in the negative
image
Original mammogram Negative image
Small
lesion
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22. Some basic gray-level transformation functions used for
image enhancement
Linear:
Negative, Identity
Logarithmic:
Log, Inverse Log
Power-Law:
nth power, nth root
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23. Log Transformation
 General form:
s = c log (1 + r )
where; c is a constant and r>=0
 Maps a narrow range of low gray-level values in the input
image into a wider range of output levels
 Use to expand the values of dark pixels in an image while
compressing the higher-level values
 The opposite is true of the inverse log transformation
 Compress the dynamic range of images with large variations in
pixel values
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24. (a)Fourier spectrum with vales in the range 0 to 1.5x106
(b) Result of applying the log transformation with c = 1
If c = 1, values of result become 0 to 6.2
Log Transformation Example
s = log (1+r)
(a) (b)
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25.  Basic form: s = c r γ
where; c and γ are positive constants
 To account for an offset (a measurable output when the input is
zero) :
s = c (r + ε )γ
 Power law is similar to
log when γ < 1 and similar
to inverse log when γ > 1
 Varying  obtains
family of possible
transformation curves
Power-Law Transformation
Figure: Plots of the equation s = c r γ for various
values of γ (c=1); γ = c = 1, identity
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26. Power-Law Transformation Examples
 A variety of device used for image capture, printing and
display respond
 The power law equation is referred to as gamma
 The process used to correct power-law response is called
gamma correction
 Example:
Cathode ray tubes have
an intensity-to-voltage
response that is a power
function with exponent
varies from 1.8 to 2.5.
=2.5
=1/2.5
=2.5
(a) (b)
(c) (d)
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27. Cont’d
 Also useful for general-
purpose contrast
manipulation
 Different curves highlight
different detail
  < 1
Expand dark gray levels
 = 0.6
 = 0.4  = 0.3
Figure : Magnetic
resonance (MR) image
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28. Cont’d
>1
Expand light gray levels
 = 3
 = 5 = 4
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29. Why power laws are popular?
 A cathode ray tube (CRT), for example, converts a video
signal to light in a nonlinear way. The light intensity I is
proportional to a power (γ) of the source voltage VS
 For a computer CRT, γ is about 2.2
 Viewing images properly on monitors requires γ-correction
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30.  Advantage: the form of piecewise functions can be
arbitrarily complex
a practical implementation of some implementation of
some important transformations can be formulated only
as piece wise functions
 Disadvantage: specification requires considerably more
user input
 Contrast Stretching
 Gray-level slicing
 Bit-plane slicing
Piecewise-Linear Transformation Functions
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31.  One of the simplest piecewise linear functions
 To increase the dynamic range of the gray levels in the image
being processed
 The locations of (r1,s1) and (r2,s2) control the shape of the
transformation function
 If r1= s1 and r2= s2 the transformation is a linear function
and produces no changes
 If r1=r2, s1=0 and s2=L-1, the transformation becomes a
thresholding function that creates a binary image
 Intermediate values of (r1,s1) and (r2,s2) produce various
degrees of spread in the gray levels of the output image,
thus affecting its contrast
Contrast Stretching
31

32.  Generally, r1≤r2 and s1≤s2
is assumed
to preserve the order of
gray levels
prevent the creation of
intensity artifacts in the
processed image
Cont’d
control point
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33. Example of contrast stretching
Contrast stretching
8-bit image with
low contrast
Thresholding
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34.  Highlight a specific range of gray levels in an image (e.g. to
enhance certain features)
 Tow basic approaches:
To display a high value for all
gray levels in the range of interest
and a low value for all other
gray levels (binary image)
Brightens the desired range of
gray levels but preserves
the background and gray-level
tonalities in the image
Gray-level slicing
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35. Cont’d Highlight the major blood
vessels and study the shape of
the flow of the contrast
medium (to detect blockages,
etc.)
Measuring the actual flow of the
contrast medium as a function of
time in a series of images
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36. Gray-level slicing
 Highlighting a specific range of gray levels
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37. Bit-plane slicing
 Highlight the contribution made to total image appearance by specific bits
 Example: - each pixel is represented by 8 bits
- the image is composed of eight 1-bit planes
- plane 0 contains the least significant bit and
plane 7 contains the most significant bit.
 Plane 0 contains all the lowest order bits and plane 7 contains all the high-order bits
 Only the higher-order bits (especially the top four) contain the majority of the
visually significant data. The other bit planes contribute the more subtle details
 Is useful for analyzing the relative importance played by each bit of the image
 Determine the adequacy of the number of bits used to quantize each pixel
 Plane 7 corresponds exactly with an image thresholded at gray level 128
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38. Bit-plane slicing
* Highlight specific bits
bit-planes of an image
(gray level 0~255)
Ex. 15010
1
0
0
1
0
1
0
0
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39. 10110011
1
1
0
0
1
1
0
1
Bit-plane 0
(least significant)
Bit-plane 7
(most significant)
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40. 7 6
5 4 3
2 1 0
For image
compression
An 8-bit fractal image
MSB
LSB
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41. References
 “Digital Image Processing”, 2/ E, Rafael C. Gonzalez & Richard
E. Woods, www.prenhall.com/gonzalezwoods.
 Only Original Owner has full rights reserved for copied images.
 This PPT is only for fair academic use.
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42. Chapter 3 – Next Section
(Coming Soon)
Questions?