Salman Bin Abdulziz
University
College of Applied Medical
Sciences
Medical Equipment
Technology Department
Computer Image Processing
(BMTS 492)
Dr. Omar Alfarouk
1
Objectives:
Upon completion of this course, students should be able to:
• Understand the basic concepts of digital image processing.
• Perform various image processing techniques such as
image filteration, image segmentation, image enhancement,
and restoration..
• Use MATLAB for image processing.
Course Description. This course deals with digital image
processing on computer includes: statistics on the image, the notion of
pixel, value representation in gray level images, color images, and
operation on pixels for image enhancement. It covers also convolution
application for different type of filters on images for noise reduction,
enhancement using operation on histograms, linear and non linear
filters, image enhancement by histogram equalization, filter based on
Fourier space and image restoration.
2
Topics to be Covered
List of Topics
Introduction to digital image processing, image
representation
Digital Image Fundamentals
Image Transforms
Image Enhancement and Restoration
Image Segmentation
No of Cont
Week actho
s
urs
4
1
2
2
2
2
8
8
8
8
Representation and Description
1
4
Recognition and Interpretation
2
8
Image Compression
2
8
3
1. Required Text(s)
An Introduction to Digital Image Processing with
MATLAB, Alistair Mc.Andrew
ISBN: 0534400116
2. Essential References
1.Digital Image Processing, Gonzalez Rafeal, Prentice
Hall, 2001
2.Digital Image Processing, William Pratt, John Wiley,
1991
3.Digital Image Processing, Kenneth Castleman,
Prentice Hall, 1996
4
• Chapter I: Basics of Image Analysis
– Sampling and Quantization
• To be suitable for computer processing an
image function f(x,y) must be digitized
both spatially and Amplitude.
• Digitization of the spatial coordinates (x,y)
is called image sampling, and amplitude
quantization is called gray-level
quantization.
5
All of the sampling theorem
concepts apply to the
sampling of 2D signals or
images
.
6
In most real-life applications
of imaging and image
processing, it is not possible
to estimate the frequency
content of the images.
7
• Adequate sampling
frequencies need to be
established for each type of
image or application based
upon prior experience and
knowledge.
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(a) 225x250 pixels; (b) 112 x 125 pixels; (c) 56 x
62 pixels; and (d) 28 x 31 pixels. All four images
have 256 gray levels at 8 bits per pixel.
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8-bits (256 grey levels) image
10
1-bit (2-grey levels) image
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• A digitized image function can be
represented by a matrix
F(x,y) ≈
f (0,0)
f (0,1)
f (0, M  1)
f (1,0)
f (1,1)
f (1, M  1)
f ( N  1,0)
f ( N  1, M  1)
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13
•
•
•
•
•
•
•
•
Each element of the matrix represent a picture element or a pixel.
The digitization process requires, as a common practice:
N =
2n , M = 2k
And the gray levels (the pixel amplitude) G = 2m
The total number of bits required to store a digitized image:
B =
NxMxm
If N =M,
B =
mN2
For example a 512x512 image with 256 gray levels requires
2097152 bits or 2Mbytes of space. The resolution of an image
depends very much on the number of pixels and the number of gray
levels.
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1.2 Brightness and Contrast
•
The higher the amplitude or the intensity
I(x,y) of the pixel the brighter the pixel
and hence the image looks brighter if a
large number of pixels have high
intensities, if B=0, identifies an empty
image. The image Brightness is defined
as average pixel value:
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B
M 1 N 1
1
MN
  f ( x, y)
y 0
x 0
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• And image Contrast is defined as the
spread of pixel values about the average,
the lower the spread the lower is the
contrast:
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C
M 1 N 1
1
MN
 [ f ( x, y)  B]
2
Y 0 X 0
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• At the pixel level, the contrast is defined as
the difference between its value I(x,y) and
the average background intensity
normalized by the full intensity range:
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C( x, y) 
I ( x, y ) I
I max 0
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1.3 Arithmetic Operations
• Addition and Subtraction
• The most commonly required arithmetic
operations for combining two separate
images are (pixel-by-pixel) addition and
subtraction:
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• Addition:
I(x,y) = min[I1(x,y) + I2(x,y); Imax],
• Subtraction:
I(x,y) = max[I1(x,y) - I2(x,y); Imin],
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• For an 8-bit gray level image Imin = 0 and
Imax = 255. The most important thing to
be aware is overflow and underflow that
leads to image clipping. In addition if sum
exceeds Imax will be set to Imax. If the
difference falls below 0, it will be set to 0.
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• Image clipping can be avoided if the range
of intensity values is rescaled before the
images are combined. You need to identify
maximal and minimal output intensities (I1
+ I2)max and (I1 - I2)min respectively.
These values are used as scale factors.
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• Modified Addition
I(x,y) = [I1(x,y) + I2(x,y)]x255
(I1 + I2)max
• Modified Subtraction
I(x,y) = [I1(x,y) - I2(x,y) + |(I1-I2)min|]x255
[255 + |(I1 - I2)min|]
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• Example 1.0
• Add the following 4-pixel images:
• Image (1) 90 200 Image (2) 70
•
70
0
10
100
50
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• Solution: By scanning the two images,
• (I1 + I2)max = 200+100=300
• Image (1) + Image (2) =
(90+70)x255/300 (200+100)x255/300
(70+10)x255/300 ( 0 + 50)x255/300
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• = 139
68
255
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• Example 1.1
• Image (1) 90 200 Image (2) 70
•
70
0
10
Subtract Image (2) from Image (1)
______________________________
• Solution
•
(I1 - I2)min = - 50
• Image (1) - Image (2) =
100
50
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(90-70+50)x255/(255+50)
(200 -100+50)x255/(255+50)
(70-10+50)x255/(255+50)
(0 - 50 +50)x255/(255+50)
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=
59
92
125
0
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• Addition has application in noise averaging
and subtraction is used in digital
angiography.
• Division
I(x,y) =
• [I1(x,y)/((I2(x,y) + 1))]x255
((I1/(I2+1))max
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• Addition has application in noise averaging
and subtraction is used in digital
angiography.
• Division
I(x,y) =
• [I1(x,y)/(I2(x,y) + 1)]x255/((I1/(I2+1))max
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• Division is used in flat fielding as in video
microscopy when images are recorded
with cameras that exhibit nonlinear output
characteristics. Boolean combination of
images also possible.
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Addition noise reduction
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Spinal column subtraction
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Types of Digital images
• Four Basic types of images
• Binary. Each pixel is just black or white (see Fig
1.2b), 1-bit per pixel. Such images are very
efficient in terms of storage. Text, fingerprints,
or architectural plans are examples of binary
images. The matrix of binary images contain one
and zeros.
• Grayscale. Each pixel is a shade of gray from 0
(black) to 255 (white), needs 8-bits
representation, see Fig 1.2a. Find application in
medicine (x-rays).
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RGB
•
True color or red-green-blue RGB.
Each pixel is a mixture of three amount
of RGB colors. If each component has a
range of 0-255, this gives a total of 2563
= 16777216 different possible colours.
The total number of bits for each pixel is
24. RGB image consists of a stack of
three matrices.
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39
RGB Color Model
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A NERVE CELL
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Indexed Images
• Index color images uses a colormap. The
colormap sets colors to the matrix. A
colormap is an m-by-3 matrix of real
numbers between 0.0 and 1.0. Each row is
an RGB vector that defines one color. The
kth row of the colormap defines the k-th
color.
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An Indexed Image
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Image Format
• Tagged image file format (TIFF), is
particularly general format, because it
allows binary, grayscale, RGB, and
indexed color images, as well as different
amounts of compression. TIFF is thus a
good format for transmitting images
between different operating systems and
environments. TIFF also allows more than
one image per file.
44
1.4 Intensity Histogram
• A histogram is a plot
showing the number of
image pixels that display
each of the possible
discrete intensity values.
45
• The
number
of
pixels
is
represented by a histogram pin
height. If only one bin is occupied
then the corresponding image is
completely featureless (uniformly
white, black, or gray).
46
• If all the bins are occupied
then the image brightness is
well spread or the contrast is
high. For examples (see
Fig1.0 and Fig1.1)
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Fig 1.0 (a) An image of a liver tissue biopsy (b) The histogram
computed from the image in (a). Note that the larger peak represent
the gray background and the smaller (plateau like) represents the
small black regions foreground
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Fig1.1 (a) Gaafer : Three distinct
regions, gives three Histogram
peaks (b) Gaafer Histogram.
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• 2.0 Image Enhancements in the
Spatial Domain
• 2.1 Histogram Expansion:
Low contrast images (characterized
by a histogram with a narrow peak)
can result from limited dynamic range
in the imaging system. The idea
behind histogram expansion is to
increase the dynamic range of the
gray level. It is a straightforward and
conservative linear transformation.
50
• First, the histogram of
the original image is
examined to determine
the value limits (lower =
a, upper = b) in the
unmodified picture.
51
• Next step is to determine the limits
over which image intensity values
will be extended. These lower and
upper limits will be called c and d,
respectively (for standard 8-bit
grayscale pictures, these limits are
usually 0 and 255).
52
• Then for each pixel, the
original value r is
mapped to output value s
using the function:
53
• (linear mapping, an equation of a straight
line)
54
• Example 2.1
• The image in Fig 2.1a is enhanced by
histogram expansion. Where c= 0, d =256,
a =7 and b = 120. a and b are found from
the histogram shown in Fig 2.1b. Fig 2.1c
is the resultant enhanced image and Fig
2.1d is its histogram. Note that the
histogram expansion did not change the
shape of the histogram.
55
56
• Example 2.2
• The image in Fig 2.2a, a MRI of brain is
enhanced by histogram expansion. Where
c = 0, d =255, a =60 and b = 188. a and b
are found from the histogram shown in Fig
2.2b. Fig 2.2c is the resultant enhanced
image and Fig 2.2d is its histogram. Note
that the histogram expansion did not
change the shape of the histogram.
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58
• Example :
• Suppose we have a 4-bit image with the
histogram shown in Figure 2.3, which is
associated with a table of the numbers r of
gray values,
• (with the total number of pixels = 330). We
can stretch out the gray levels in the
center of the range by applying the linear
function shown earlier. This function has
the effect of stretching the gray levels 5—9
to gray levels 2—14.
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60
a = 5, b = 9, c = 2, d = 14.
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• Yields:
•
rk 5
•
Sk 2
6
5
7
8
8
11
9
14
62
63
B
C
M 1 N 1
1
MN
  f ( x, y)
y 0
x 0
M 1 N 1
1
MN
 [ f ( x, y)  B]
2
Y 0 X 0
64
The brightness B = 6.67 and Contrast C = 1.31
Orignal Gray levels
No. of Pixels
∑∑f(x,y)
[f(x,y)-B]^2
5
70
350
202.3
6
110
660
53.9
7
45
315
4.05
8
70
560
118.3
9
35
315
185.15
2200
563.7
Sum =
B=2200/330
6.7
C= 1.31
65
New Gray levels
No. of Pixels
∑∑f(x,y)
[f(x,y)-B]^2
2
70
140
1750
5
110
550
440
8
45
360
45
11
70
770
1120
14
35
490
1715
2310
5070
Sum=
B=2310/330
7
C=3.92
66
• Histogram piecewise linear stretching
could be effected by a transformation
shown in Fig2.5 (implemented by histpwl
Matlab function). The location of the points
(r1,S1) and (r2,S2) control the shape of the
transformation function. If r1 = S1 and r2 =
s2, the transformation is a linear function
that produces no change in gray levels. If
r1 = r2 and S1 = 0 and S2 = L-1, the
transformation becomes a thresholding
function that creates a binary image.
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A piecewise linear stretching
68
Histogram Equalization
• Histogram stretching is that they require
user inputs.
• A better approach is provided by
histogram equalization, which is an
entirely automatic procedure.
• The idea is to change the histogram to one
that is uniform;
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• Suppose our image has L different gray levels, 0,
1, 2, . , L-1, and gray level i occurs n, times in
the image. Suppose also that the total number
70
EXAMPLE: Suppose a 4-bit
grayscale image has the histogram
shown in Figure 3.1, associated
with a table of the numbers n of
gray values
(with n = 360).
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To equalize this histogram, we form running totals
of the ni and multiply each by 15/360 = 1/24.
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73
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75
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Intensity Transformations
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A non-linear stretching can be achieved by
using power of gamma
79
Intensity Transformations
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Intensity Transformations
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Thresholding
• A gray image is turned into binary image
(1 & 0, white or black) by choosing a gray
level T and then turning every pixel into 1
or 0 according to
82
Thresholding Bacteria
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