On Fuzzy image processing
By
A. Lecture KARRAR DH. MOHAMMED
History
In the 1970s, digital image processing proliferated,
when
cheaper computers and dedicated hardware became
available.
Images could then be processed in real time, for
some dedicated problems such as television standards
conversion. As general-purpose computers became
faster,
they started to take over the role of dedicated hardware
for all but the most specialized and compute-intensive
operations.
History
With the fast computers and signal
processors available
in the 2000s, digital image processing has
become the
most common form of image processing, and
is generally
used because it is not only the most versatile
method,
but also the cheapest.
What is an Image
1. An image f (x, y) is 2-dimensional light intensity
function ,where f measures brightness at
position (x, y).
2. A digital image is a representation of an image
by a 2-D array of discrete samples.
3. The amplitude of each sample is represented by
a finite number of bits.
4. Each element of the array is called a pixel.
Terminology
Images: An image is a two-dimensional
signal whose intensity
at any point is a function of two spatial
variables.
Examples are photographs, still video
images, radar and
sonar signals, chest and dental X-rays.
An image sequence such as that seen in a
television is a three dimensional signal for
which the image intensity at any point is
a function of three variables: two spatial
variables and time.
1. Digital image processing is a term used to describe
the manipulation of image data by a computer.
2. The process of transforming an image to a set of
numbers, which a computer can utilized, is called
digitization.
3. Digitization is to divide an image up into several
picture elements called pixels. A pixel is the smallest
resolvable unit of an image which the computer
handles.
4. The value of a pixel is referred to as its gray level and can
be thought of as the intensity or brightness (or darkness)
of the pixel.
5. The number of different gray-levels a pixel can have
varies from system to system, and is determined by the
hardware that produces or displays the image.
Why do we process images
Images (and videos) are every where .This
includes different imaging modalities such as
visual, X-ray, ultrasound, ] etc. Multimedia
information will be the wave of the future.
Diverse applications in astronomy, biology,
geology, geography, medicine, law enforcement,
defense,
Industrial inspection, require processing of
images.
Grayscale and Color Images
1. For grayscale image, 256 levels or 8 bits/pixel is
sufficient for most applications
2. For color image, each component (R, G, B)
needs 256 levels or 8 bits/pixel
3. Storage for typical images
(a) 512 × 512, 8 bits grayscale image: 262,144B
(b) 1024×768,
2,359,296B
24
bits
true
color
image:
Grayscale Image
Color Images
X R (n,m), X G (n,m), X B (n,m)
F(x, y)
F(m, n), 0 ≤ m ≤ M − 1,0 ≤ n ≤ N − 1
A digital image can be written as a matrix
x(0,1) ..... x(0,N - 1)
 x(0,0)

 x(1,0)

x
(1,
1)
.....
x(1,
N
1)


....

....
....


F  ....
....
....

....

....
....


....
....
....

 x(M - 1, 0) x(M- 1,1) ... x(M - 1, N - 1)


Image Operations can be classified as Linear and
non-linear Operations:
H is a linear operator if if satisfies the
superposition
principle:
H(af +bg) = aH(f)+bH(g)
for all images f and g and all constants a
and b.
1. Mean filtering: Linear
2. Median filtering: Non-linear
Simple Operations On Images
Digital Negative: Given an image F, the Digital
Negative of F is defined as
F Negative (m, n) = 255 − F(m, n)
Feature Enhancement by
Subtraction
A Brief History of Lena (Lenna)
Anyone familiar with digital image processing will surely
recognize the image of Lena. While going through some
old usenet discussions, I got to know that Lena has a
history worth all the attention that has been paid to her
over the years by countless image processing researchers.
Lena Sjblom, (also spelled Lenna by many publications)
was the Playboy playmate in November 1972 and rose
to fame in the computer world when researchers at the
University of Southern California scanned and digitized
her image in June 1973. (Lena herself never know of her
fame until she was interviewed by a computer magazine
in Sweden where she lives with her husband and children).
A Brief History of Lena (Lenna)
According to the IEEE PCS Newsletter of May/June
2001, they were hurriedly searching for a glossy image
which they could scan and use for a conference paper
when someone walked in with a copy of Playboy. The
engineers tore off the top third of the centerfold and
scanned it with a Muirhead wire photo scanner (a distant
cry from the flatbed scanners of today) by wrapping it
around the drum of the scanner. (Now you know why
the image shows only a small part of the entire picture..
discounting of course, the fact that the complete picture
would raise quite a few eyebrows.
Linear Stretching
1. Enhance the dynamic range by stretching
the original gray levels to the range of 0 to
2. Example
(a) The original gray levels are [100, 150].
(b) The target gray levels are [0, 255].
(c) The transformation function
g(f) = ((f − 100)/50) ∗ 255 for100 ≤ f ≤ 150
Illustration of Linear Stretching
Image/video Processing Methods
1. Image Enhancement
2. Image Restoration
3. Compression
4. Image reconstruction
5. Morphological image processing
6. Feature extraction and recognition,
computer vision
Other Image Operations
Image algebra includes mathematical
comparisons, altering values of pixels,
thresholding, edge detection and noise
reduction.
1. Neighborhood averaging is to avoid extreme
fluctuations in gray level from pixel to pixel. It is
also very effective tool for noise reduction.
2. Image Scaling is a means of reducing or
expanding the size of an image using existing
image data.
3. Histogram Equalization is an adjustment of gray
scale based on gray-level histogram. This is effective
in enhancing the contrast of an image.
4. Edge Detection is an operation of measuring and
analyzing the features in an image by detecting and
enhancing the edges of the features. The most common
edge detection method is gradient detection.
5. Image Restoration: Given a noisy image y(m, n)
y(m, n) = x(m, n)+v(m, n)
where x(m, n) is the original image and v(m, n) is
noise. The objective is to recover x(m, n) from y(m, n).
Color Restoration
Photo Restoration
6. Contrast Enhancement: how to enhance the
contrast of an image?
1. Low contrast image values concentrated near
narrow range (mostly dark, or mostly bright, or
mostly medium values)
2. Contrast enhancement change the image value
distribution to cover a wide range
3. Contrast of an image can be revealed by its
histogram
Histogram The histogram of an image with L
possible
gray levels, f = 0, 1, · · · , L − 1 is defined as:
nl
p(l ) 
n
where
– nl is the number of pixels with gray level l.
– n is the total number of pixels in the image.
Examples of Histograms
Applications
Astronomy: Hubble Space Telescope : This
telescope has limitation in resolution due to
atmospheric turbulence.
Optical problem in a telescope results in blurred, out
of focus image. Digital image processing is normally
used to recover the desired information from these
images.
Applications
Medical Imaging: Most of advanced
medical imaging tools are based on DSP
tools. X-Ray computerized Tomography
(X-ray CT) is capable of generating a
cross-sectional display of the body. This
involves X-ray generation, detection,
digitization, processing and computer
image reconstruction. Similarly, NMRCT
(nuclear magnetic resonance).
MRI
Ultrasound
Fingerprint
In 1684, an English plant morphologist
published the first scientific paper reporting
his systematic study on the ridge and pore structure
in fingerprints.
A fingerprint image may be
classified as:
(a) Offline: Inked impression of the fingertip on a
paper is scanned
(b) Live-scan: Optical sensor, capacitive sensors,
ultrasound sensors, ...
At the local level, there are different local ridge
characteristics. The two most prominent ridge
characteristics, called minutiae, are:
(a) Ridge termination
(b) Ridge bifurcation
At the very-fine level, intra-ridge details (sweat pores) can
be detected. They are very distinctive; however, very
high-resolution images are required.
Face Recognition
Face Recognition Methods
(a) Template matching using minimum-distance
classifiers metrics
(b) Linear discriminants
(c) Bayesian approach
Watermarking
The World Wide Web and the
progress in multimedia storage and transmission
technology expanded the possibility of illegal copying
and reproducing of digital data. Digital watermarking
represents a valid solution to the above
problem, since it makes possible to identify the
source, author, creator, owner, distributor or authorized
consumer of digitized images, video recordings
or audio recordings. A digital watermark
is an identification code, permanently embedded
into digital data, carrying information pertaining
to copyright protection and data authentication.
(a) Copyright protection and authentication
Image Compression Techniques
1. JPEG 2000 standard is based on wavelets
2. JPEG (original) is based on the Discrete Cosine
An Example of Image Compression
What does Fuzzy Image
?Processing mean
Fuzzy image processing is not a unique theory. It is a
collection of different fuzzy approaches to image
processing. Nevertheless, the following definition can be
regraded as an attempt to determine the boundaries:
Fuzzy image processing is the collection of all
approaches that understand, represent and process the
images, their segments and features as fuzzy sets. The
representation and processing depend on the selected
fuzzy technique and on the problem to be solved( From :
Tizhoosh, Fuzzy Image Processing ,Springer )1997 (
Fuzzy image processing has three main stages: image
fuzzification, modification of membership values, and, if
necessary, image defuzzification see figure below
.The general structure of fuzzy image processing