Image processing 1-lectures

Course No.: CSC 447
Lect.: 3 h
Lab. : 2 h
Marks: 65 final
10 Y. work
25 Lab
Exam hours: 3 h
By Prof. Dr. :
Taymoor Nazmy

Image processing applications,
Picture modeling,
Enhancement in spatial domain,
Enhancement in frequency domain,
Restoration,
Segmentation,
Scene analysis,

1-Applications of image processing
in remote sensing.
2- Image processing using NN.
3- Techniques of images retrieval.
4- Registration of medical images.
5- Image synthesize.
.

6- Image processing using pde.
7- Methods of texture analysis.
8- Reconstruction techniques.
9- Image processing using parallel
algorithm.
10- Multiresolution processing
11- Open.
12- Open

The text book
Digital Image Processing
Using Matlab
Rafael C. Gonzalez
University of Tennessee
Richard E. Woods

Title
LAB. ASS.
No.
Read , view, and display an image file1-
Zooming and Shrinking Images by Pixel Replication.2-
Image Enhancement Using Intensity Transformations.3-
•Histogram equalization & log. transformation.4-
•Arithmetic operations & logic operation5-

Noise Generators & Noise Reduction.6-
Spatial filtering (smoothing & sharpening)7-
Two-Dimensional Fast Fourier Transfor.8-
Lowpass Filtering9-
Convert gray level image to color10-
FFT, and Hough transform11-

Image
Acquisition
Preprocessing Segmentation
Representation &
Description
Recognition &
Interpretation
Problem
Domain
Knowledge
Base
Result

Ultrasound Image Profiles of a
fetus at 4
months, the
face is about
4cm long
Ultra sound
image is
another
imaging
modality
The fetal arm
with the major
arteries
(radial and
ulnar) clearly
delineated.

Section through Visible
Human Male - head,
including cerebellum,
cerebral cortex,
brainstem, nasal passages
(from Head subset)
This is an example of the
“visible human project”
sponsored by NIH

Image processing using Matlab tool box

Example of Matlab functions …
Input / Output
>>imread
>>imwrite
Image Display
>>imshow
Others
>>axis
>>colorbar
>>colormap
>>fft, fft2

Image Storage Formats
 To store an image, the image is represented in a two-
dimensional matrix, in which each value corresponds
to the data associated with one image pixel.
 When storing an image, information about each pixel,
the value of each colour channel in each pixel, has to
be stored.
 Additional information may be associated to the
image as a whole, such as height and width, depth, or
the name of the person who created the image.
 The most popular image storing formats include
PostScript, GIF (Graphics Interchange Format),
JPEG, TIFF (Tagged Image File Format), BMP
(Bitmap), etc.

Image Formation in the Eye
17100
15 x

mmx 55.2
–Calculation of retinal image of an object
•The eye has a sensor plane (100 million pixels)

The eyes have a USB2 data rate!
250,000 neurons in the optic nerve
variable voltage output on EACH nerve
17.5 million neural samples per second
12.8 bits per sample
224 Mbps, per eye (a 1/2 G bps system!).
Compression using lateral inhibition
between the retinal neurons

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

Typical IP System
DIP Corrections
and/or
Enhancements
A/D
Scene Sensor A/D Media
D/A
D/A
Display

An color image
Fundamentals of Digital Images
f(x,y)
x
y
w An image: a multidimensional function of spatial coordinates.
w Spatial coordinate: (x, y) for 2D case such as photograph,
(x, y, z) for 3D case such as CT scan images
(x, y, t) for movies.
w The function f may represent intensity (for monochrome images)
or color (for color images).
Origin

Representing digital image
















)1,1(...)1,1()0,1(
............
)1,1(......)0,1(
)1,0(...)1,0()0,0(
),(
MNfNfNf
Mff
Mfff
yxf
Digital Image Picture Elements
(Pixels)
The value of f at (x,y)  the intensity (brightness) of
the image at that point.

Image Types
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
Image Types
Color image or RGB image:
each pixel contains a vector
representing red, green and
blue components.
RGB components

Color image:
For example, 24-bit image or 24 bits per
pixel. There are 16,777,216 (224) possible
colors.
In other words, 8 bits for R(Red), 8 bits
for G(Green), 8 bits for B(Blue).
Since each value is in the range 0-255,
this format supports 256 x 256 x 256.

Image Types
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
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

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

Sampling & Quantization
• The spatial and amplitude digitization of f(x,y) is
called:
• - image sampling when it refers to spatial coordinates
(x,y) and
• - gray-level quantization when it refers to the amplitude.
The digitization process requires decisions about: values
for N,M (where N x M: the image array) and
the number of discrete gray levels allowed for each
pixel.

Effect of Quantization Levels
16 levels 8 levels
2 levels4 levels

• Different versions (images) of the same
object can be generated through:
– Varying N, M numbers
– Varying k (number of bits)
– Varying both

Isopreference curves (in the NK plane)
• Isopreference curves (in the NK plane)
– Each point: image having values of N and k
equal to the coordinates of this point
– Points lying on an isopreference curve
correspond to images of equal subjective
quality.

Examples for images with different details

• Conclusions:
– Quality of images increases as N & k increase
– Sometimes, for fixed N, the quality improved
by decreasing k (increased contrast)
– For images with large amounts of detail, few
gray levels are needed

Some Basic Relationship Between Pixels
(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)
y
x
(0,0)
Definition: f(x,y): digital image, Pixels: q, p
S: Subset of pixels of f(x,y).

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
• Two pixels are connected if:
– They are neighbors (i.e. adjacent in some sense
e.g. N4(p), N8(p), …)
– Their gray levels satisfy a specified criterion of
similarity (e.g. equality, …)
• V is the set of gray-level values used to
define adjacency (e.g. V = {1} for
adjacency of pixels of value 1)

Adjacency
• We consider three types of adjacency:
– 4-adjacency: two pixels p and q with values
from V are 4-adjacent if q is in the set N4(p)
– 8-adjacency : p & q are 8- adjacent if q is in the
set N8(p)

Adjacency
• The third type of adjacency:
• -m-adjacency: p & q with values from V are m-
adjacent if:
- q is in N4(p) or
- q is in ND(p) and the set N4(p)N4(q) has
no pixels with values from V
Two image subsets S1 and S2 are adjacent if some pixel in
S1 is adjacent to some pixel in S2
S1
S2

Adjacency
• Mixed adjacency is a modification of 8-
adjacency and is used to eliminate the
multiple path connections that often arise
when 8-adjacency is used.
100
010
110
100
010
110
100
010
110

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.

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)
D (p, q) = D (q, p)
D (p, z) D (p, q) + D (q, z)
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.
Pixels with D4 (p) = 2 is not 4-diagonl 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

Our objectives of studying this topic:
1- To know how to read the transformations
charts & histograms,
2- To evaluate the image quality,
3- To understand the principals of IP techniques.
4- To be able to develop IP algorithms,
Most IP techniques depend on the concepts used in this
chapter.

Spatial Domain Methods
Procedures that operate directly on the
aggregate of pixels composing an
image

A neighborhood about (x,y) is defined
by using a square (or rectangular)
subimage area centered at (x,y).
)],([),( yxfTyxg 

Spatial Domain Methods
When the neighborhood is 1 x 1 then g
depends only on the value of f at (x,y) and T
becomes a gray-level transformation (or
mapping) function:
s=T(r)
Where: r denotes the pixel intensity before
processing.
s denotes the pixel intensity after
processing.

Image Enhancement in the Spatial Domain
Contrast Stretching: the values
for r below m are expanded
into wide range of s.
Thresholding: produce binary
image from gray level one.

Some Simple Intensity Transformations
Linear:
Negative,
Identity
Logarithmic:
Log, Inverse
Log
Power-Law: nth
power, nth root

1-Image Negatives
Are obtained by using the
transformation function s=T(r).
[0,L-1] the range of gray levels
S= L-1-r

Image Enhancement in the
Spatial Domain

=c=1: identity

Piecewise-Linear Transformation Functions
- 1-Contrast Stretching transformation:
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.
Generally, r1≤r2 and s1≤s2 is assumed.

2- Gray-Level Slicing Transformation
To highlight a specific range of gray
levels in an image (e.g. to enhance
certain features).
One way is 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).

Gray-Level Slicing
The second approach is to brighten the
desired range of gray levels but preserve the
background and gray-level tonalities in the
image:

Histogram Processing
•The histogram of a digital image with gray levels
from 0 to L-1 is a discrete function where:
»rk is the kth gray level
–nk is the # pixels in the image with that gray
level
–n is the total number of pixels in the image
k = 0, 1, 2, …, L-1
•Normalized histogram: p(rk) = nk / n
•sum of all components = 1

Histogram Is Invariant Under Certain
Image Operations
Rotation, scaling, flip
Rotate Clockwise
Scale
Flip

Histogram for an image with total n pixels

Histogram stretching:
For an image f(x,y) with gray level r at x,y this value can be transformed
to another gray level value s in the new image g(x,y), using the following
equ.:
g(x,y) = [(r- rmin) / ( rmax- rmin)] * [Max-Min] +Min
Where: rmax is the largest gray level in the image f(x,y).
rmin is the smallest gray level in the image f(x,y).
Max, Min correspond to the maximum and minimum
gray level values possible for the image g(x,y), (0-255).
Histogram shrinking :
g(x,y) = [( Max - Min ) / (rmax-rmin)] * [r – rmin] + Min
Where: Max, Min correspond to the maximum and minimum
desired gray level in the compressed (shrink) histogram.

Histogram Processing
•Histograms are the basis for numerous
spatial domain processing techniques, in
addition it is providing useful image
statistics.
•Types of processing:
Histogram equalization
Histogram matching (specification)
Local enhancement

To get a histogram equalization:
-Ex: if the gray levels for an image is given by k = 0, 1, 2, 3 and
number of pixels corresponding to these gray levels are 10,7,8,2
(histogram values), and the maximum k can be 7 (3bits/pixel).
-1- The sum of these values are 10, 17 , 25, 27.
-2- Normalize these values by dividing by the total number of
pixels, 27, we get 10/27, 17/27, 25/27, 27/27.
-3- Multiply these values by the maximum gray level value
available , 7, and then round the result to the closest integer. So, we
get the equalized values to be, 3,4, 6, 7 .
-4- The final step is done by putting all pixels in the original
image with k = 0, 1, 2, 3 to be with the new gray level distribution, 3,
4, 6 ,7.

.The global mean and variance are measured over an entire
image and are useful for overall intensity ad contrast
adjustments.The more powerful use of these parameters is in
local enhancement.
Let (x,y) be the coordinates of a pixel in an image, and let
Sx,y
denote a neighborhood (subimage) of specified size, centered
at (x,y). The mean value of mSx,y of the pixels Sx,y can be
computed using the equ.;
Use of histogram statistics for image enhancement

Where rs,t is the gray level at coordinates (s,t) in
the neighborhood, and p(rs,t) is the neighborhood
normalized histogram component corresponding to
that value of gray level.
The local mean is a measure of average gray level
in neighborhood Sx,y , and the variance is a
measure of contrast in that neighborhood.

- =
(absolute difference)
Image subtraction

Image Averaging
A noisy image:
),(),(),( yxnyxfyxg +
Averaging M different noisy images:


M
i
i yxg
M
yxg
1
),(
1
),(

Image Averaging
As M increases, the variability of the pixel
values at each location decreases.
This means that g(x,y) approaches f(x,y) as the
number of noisy images used in the averaging
process increases.
Registering of the images is necessary to
avoid blurring in the output image.

Basic of spatial filtering
Template, Window, and Mask Operation
Question: How to compute the 3x3 average values at every pixels?
4
4
67
6
1
9
2
2
2
7
5
2
26
4
4
5
212
1
3
3
4
2
9
5
7
7
Solution: Imagine that we have
a 3x3 window that can be placed
everywhere on the image
Masking Window

4.3
Template, Window, and Mask Operation (cont.)
Step 1: Move the window to the first location where we want to
compute the average value and then select only pixels
inside the window.
4
4
67
6
1
9
2
2
2
7
5
2
26
4
4
5
212
1
3
3
4
2
9
5
7
7
Step 2: Compute
the average value
Sub image p
Original image
4 1
9
2
2
3
2
9
7
Output image
Step 3: Place the
result at the pixel
in the output image
Step 4: Move the
window to the next
location and go to Step 2

The 3x3 averaging method is one example of the mask
operation or one of the Spatial filters .
w The mask operation has the corresponding mask (sometimes
called window or template).
wThe mask of size m x n contains coefficients to be multiplied
w with pixel values.
w(-1,1) w(-1,1)
w(1,1)
w(0,0)
w(1,0)
w(0,1)
w(-1,-1)
w(0,-1)
w(1,-1)
Mask coefficients
1 1
1
1
1
1
1
1
1
9
1
Example : moving averaging
The mask of the 3x3 moving average
filter has all coefficients = 1/9

The mask operation at each point is performed by:
1. Move the reference point (center) of mask to the
location to be computed
2. Compute sum of products between mask coefficients
and pixels in subimage under the mask.
Ex: For a 3*3 mask the response R of the linear filter at a
point (x,y) in the image is:
R = w(-1,-1) f( x-1,y-1)+ w(-1,0) f(x-1,y) +
w(-1,1) f(x-1,y+1) +
w(0,-1) f(x,y-1) + w(0,0) f(x,y) + w(0,1) f(x,y+1)
+ w(1,-1) f(x+1,y-1)+ w(1,0) f(x+1,y) +
w(1,1)f(x+1,y+1)

Examples of the masks
Sobel operators
0 1
1
0
0
1
-1
-2
-1
-2 -1
1
0
2
0
-1
0
1
1 1
1
1
1
1
1
1
1
9
1
3x3 moving average filter
3x3 sharpening filter
-1 -1
-1
8
-1
-1
-1
-1
-1

a)Original
image,
b,c,d,e, f
,smoothed
images
with
square
averaging
filter
Masks of
size
N=3,5,9,15
c d
e f
a b

A low pass filter (kernal) would
blur the original
•All positive values in a filter indicate a blurring operation
•The larger the kernal, the higher the blur
•The flatter the kernal, the higher the blur
1 1 1
1 1 1
1 1 1
1 1 1
1 2 1
1 1 1
1 1 1
1 4 1
1 1 1
Less blur
1/9 1/121/10

Nonlinear smoothing filters
(Order-Statistics filters)
They are nonlinear spatial filters whose
response is based on ordering the pixels
contained in the image area encompassed by the
filter, and then replacing the value of the center
pixel with the value determine by the ranking
(ordering) result.
Median , max, and min filters are examples of
order filters.However, median filter is the most
useful order-statistics filter.

Sharpening Filters
To highlight fine detail or to enhance
blurred detail.
smoothing ~ integration => summation
sharpening ~ differentiation => differences
Categories of sharpening filters:
Derivative operators
- High-boost filtering

Derivatives
• First derivative
• for one dimensional digital function is defined in term of
differences such as:
• Second derivative

f
x
 f (x +1)  f (x)
2
f
x2
 f (x +1) + f (x 1) 2 f (x)

Digital Function Derivatives
First derivative:
0 in constant gray segments
Non-zero at the onset of steps or ramps
Non-zero along ramps
Second derivative:
0 in constant gray segments
Non-zero at the onset and end of steps or ramps
0 along ramps of constant slope.

Observations
1st order derivatives produce thicker edges in an
image,
2nd order derivatives have stronger response to fine
detail,
1st order derivatives have stronger response to a
gray level step,
2nd order derivatives produce a double response at
step changes in gray level,
2nd order derivatives have stronger response to a line
than to a step and to a point than to a line.

Perwitt First derivative
Filter mask of size 3*3
in x and y directions

Sobel first derivative
Filter mask of size 3*3
in x and y directions

Roberts
operators
Sobel
operators

Combining
Spatial
Enhancement
Methods

2-D, 2nd Order Derivatives
for Image Enhancement
Laplacian (linear operator):
Discrete version:

2
f 
2
f
x2
+
2
f
y2
2
f
2
x2
 f (x + 1, y) + f (x 1, y)  2 f (x, y)
2
f
2
y2
 f (x, y + 1) + f (x, y 1)  2 f (x, y)

Laplacian Spatial Filtering
• The sum of the coefficients is 0, indicating
that when the filter is passing over regions
of almost stable gray levels, the output of
the mask is 0 or very small.
• Some scaling and/or clipping is involved (to
compensate for possible negative gray levels
after filtering).

Laplacian
Digital implementation:
Two definitions of Laplacian: one is the negative of the other
Accordingly, to recover background features:
: if the center coefficient of the Laplacian mask is negative
II: if the center coefficient of the Laplacian mask is positive.
2
f [f (x +1,y)+ f (x1,y)+ f (x,y +1)+ f (x,y1)]4 f (x,y)
g(x,y) { f ( x,y)+2 f ( x,y)( II )
f ( x,y)2 f ( x,y)( I )

Simplification
Filter and recover original part in one step:
g(x,y) f(x,y)[f(x+1,y)+ f(x1,y)+ f(x,y+1)+ f(x,y1)]+4f(x,y)
g(x,y) 5f (x,y)[ f (x +1,y)+ f (x 1,y)+ f (x,y +1)+ f (x,y 1)]

A high pass filter (kernal) would
sharpen the original
• Negative values in a filter surrounding a center positive value
indicate a sharpening operation
• The larger the negative values, the higher the sharpening
• “Noise” is also sharpened when sharpening an image
More sharpening
0 -1 0
-1 5 -1
0 -1 0
1 -2 1
-2 5 -2
1 -2 1

Highpass filtered image = Original – lowpass filtered image.
where fs(x,y) denotes the sharpened image obtained by
unsharp mask process.
High-boost filter is generalization of unsharp masking, If A is an
multiplication factor, then high-boost filter is given by:
fhb(x,y) = (A-1) f(x,y)+ fs(x,y)
= (A-1) · original + original – lowpass
= (A-1) · original + highpass

fs(x,y)  f (x,y)  f (x,y)

))(,(2),(
))(,(2),(
{
IyxfyxAf
IIyxfyxAfhbf

+

I: if the center coefficient of the Laplacian mask is negative
II: if the center coefficient of the Laplacian mask is positive.
fhb(x,y) = (A-1) f(x,y)+ fs(x,y)
If we use Laplacian as an image sharper, then one
Can replace fs(x,y) by g(x,y)(for Laplacian)

High-boost Filtering
A=1 : standard highpass result
A>1 : the high-boost image looks more like
the original with a degree of edge
enhancement, depending on the value of
A.
-1 -1
-1
A+8
-1
-1
-1
-1
-1
-1 0
0
A+4
-1
-1
0
-1
0

Steps in processing an image
“noise cleanup”
ex. median filtering
Determining content of image
(ex. histograms)
Image Sharpening and Blurrring
(ex. Convolution, Unsharp Masking, etc)
Adjust
Brightness/Contrast/Tonal
Range
(ex. histogram manipulations)
Capture
(digitize)
image
Output
(print/displa
y)
image

Image processing 1-lectures

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