Noise recognition in digital image

Gurunanak Institute of Technology (GNIT)
M.Tech (CSE)
Presentation on
Submitted by:
MD: Reyad Hossain
Submitted to:
Mr: Moloy Dhar
19/16/2015MD:Reyad Hossain (GNIT)

9/16/2015 2MD:Reyad Hossain (GNIT)
1.What is an Image page- (3-4)
2.What is Digital Image page-(5)
3.What is Digital Image Processing page-(6-7)
4.Types of Images page-(8-10)
5.Formats of Images page-(11)
6.Image Noise page-(12-13)
7.Types of Noises in Image page-(14-30)
8.Filtering page-(31-35)
9.Conclussion page-(36)
10.Referencess page-(37)

An image (from Latin: imago) is an artefact that depicts or records visual
perception, for example a two-dimensional picture, that has a similar appearance
to some subject—usually a physical object or a person, thus providing
a depiction of it.
Images may be two-dimensional, such as a photograph, screen display, and as well
as a three-dimensional, such as a statue or hologram. They may
be captured by optical devices – such
as cameras, mirrors, lenses, telescopes, microscopes, etc. and natural objects and
phenomena, such as the human eye or water.
The word image is also used in the broader sense of any two-dimensional figure
such as a map, a graph, a pie chart, or a painting. In this wider sense, images can
also be rendered manually, such as by drawing, the art of painting, carving,
rendered automatically by printing or computer graphics technology,
or developed by a combination of methods, especially in a pseudo-photograph.

The word ‘Spatial Domain’ means that we have to work in the given space, in this
case, the image. In other words, the term spatial domain implies working with the
pixel values or working directly with the available raw data.
(0,0)
g( x , y )
(255,255)x
y
Let g(x , y) be the original image where g is the gray level value and (x , y) are the
image coordinates. For a 8-bit image, g can take values from 0-255 where 0
represents black, 255 represents white and all the intermediate values represent
shades of gray. In an image of size 256*256, x and y can take values from (0 , 0) to
(255 , 255) as shown in the figure.

DIGITAL IMAGES are electronic snapshots taken of a scene or scanned from
documents, such as photographs, manuscripts, printed texts, and artwork. The
digital image is sampled and mapped as a grid of dots or picture elements (pixels).
Each pixel is assigned a total value (black, white, shades of gray or colour), which is
represented in binary code (zeros and ones). The binary digits ("bits") for each pixel
are stored in a sequence by a computer and often reduced to a mathematical
representation (compressed). The bits are then interpreted and read by the
computer to produce an analogy version for display or printing
Pixel Values: As shown in this bifocal image, each pixel is assigned a tonal value,
in this example 0 for black and 1 for white.

The Digital Image Processing (DIP) refers to processing digital images by means
of a digital computer. The digital image processing encompasses a wide and
various field of applications. We can also say that this field of digital image
processing encompasses whose input and outputs are images and in addition
encompasses processes that extract attributes from images including the
recognition of the individual objects.
Digital image processing is the use of computer algorithms to perform image
processing on digital images. As a subcategory or field of digital signal
processing, digital image processing has many advantages over analogy image
processing. It allows a much wider range of algorithms to be applied to the input
data and can avoid problems such as the build-up of noise and signal distortion
during processing. Since images are defined over two dimensions (perhaps more)
digital image processing may be modelled in the form of multidimensional
systems

Many of the techniques of digital image processing, or digital picture
processing as it often was called, were developed in the 1960s at the Jet
Propulsion Laboratory, Massachusetts Institute of Technology, Bell
Laboratories, University of Maryland, and a few other research facilities, with
application to satellite imagery, wire-photo standards conversion, medical
imaging, videophone, character recognition, and photograph enhancement.
The cost of processing was fairly high, however, with the computing equipment
of that era. That changed in the 1970s, when digital image processing
proliferated as cheaper computers and dedicated hardware became available.
Images then could 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 computer-intensive operations.

It was stated earlier that images are 2-dimensional functions. Images are
classified as follows.
1.Monochrome Images: Monochrome images or Binary images. In this, each
pixel is stored as a single bit (0 or 1). Here, 0 represents black while 1 represents
white. It is a black and white image in the strictest sense. These images are also
called bit mapped images. In such images, we have only black and white pixels
and no other shades of gray.
2.Gray scale Image: Here, each pixel is usually stored as a byte (8-bits). Due to
this, each pixel can have values ranging from 0 (black) to 255 (white). Gray scale
images, as the name suggests have black, white and various shades of gray
presents in the image.

3.Colour Image (24-bit): Colour images are based on the fact that a variety of
colours can be generated by mixing the three primary colours viz. Red, Green, and
Blue in proper proportions. In colour images, each pixel is composed of RGB values
and each of these colours require 8-bits (one byte) for its representation. Hence,
each pixel is represented by 24-bits [R (8-bits), G (8-bits), B (8-bits)].
A 24-bit colour image supports 16,777,216 different combination of colours.
Colour images can be easily converted to gray scale images using the equation.
X=0.30 R + 0.59 G + 0.11 B
An easier formula that could achieve similar results is.
X=
R + G + B
3

4. Half Toning: We have all read newspapers at some point of time (hopefully).
The images do look like gray level images. But if you look closely, all the images
generated are basically using black colour.
Even the images that you see in most of the books (including this one) are
generated using black colour on a white background. In spite of this we do get an
Illusion of seeing gray levels. The technique to achieve an illusion of gray levels from
only black and white levels is called half-toning.

Image file formats are standardized means of organizing and storing digital
images. Image files are composed of digital data in one of these formats that can
be raster zed for use on a computer display or printer. An image file format may
store data in uncompressed, compressed, or vector formats. Once raster zed, an
image becomes a grid of pixels, each of which has a number of bits to designate its
colour equal to the colour depth of the device displaying it.
1. JPEG/JFIF: Joint Photographic Experts Group / JPEG File Interchange Format.
2. JPEG 2000: It’s the higher version of JPEG.
3. EXIF: Exchangeable Image File Format.
4. TIFF: Tagged Image File Format.
5. RIF: Raw Image Format.
6. GIF: Graphics Interchange Format.
7 BMP: Bitmap File Format.
8. PNG: Portable Network Graphic Format.
9. PPN: Portable Pixmap Format.
10. PGM: Portable Gray map Format.
11. PBM: Portable Bit map Format.

The principal sources of noise in a digital image arise during acquisition and during
transmission. No matter how much care one takes, some amount of noise always
creeps in. Based on the shapes (Probability Density Functions) of the noise.
Image noise is random (not present in the object imaged) variation of brightness
or colour information in images, and is usually an aspect of electronic noise. It can
be produced by the sensor and circuitry of a scanner or digital camera. Image noise
can also originate in film grain and in the unavoidable shot noise of an ideal photon
detector. Image noise is an undesirable by-product of image capture that adds
spurious and extraneous information.
The original meaning of "noise" was and remains "unwanted signal"; unwanted
electrical fluctuations in signals received by AM radios caused audible acoustic
noise ("static"). By analogy unwanted electrical fluctuations themselves came to be
known as "noise". Image noise is, of course, inaudible.
The magnitude of image noise can range from almost imperceptible specks on a
digital photograph taken in good light, to optical and radio astronomical images
that are almost entirely noise, from which a small amount of information can be
derived by sophisticated processing (a noise level that would be totally unacceptable
in a photograph since it would be impossible to determine even what the subject
was).

Degradation
Function
h( x , y )
Restoration
Function+f( x , y )
n(x , y)
g(x , y)
f(x , y)
Image degradation is said to occur when a certain image under goes loss of stored
information either due to digitization or conversion (i.e. algorithmic operations),
decreasing visual quality.
The initial image (source, f(x , y)) undergoes degradation due to various
operations, conversions and losses. This introduces Noise. This Noisy image is
further restored via restoration filters to make it visually acceptable for user.
Degraded Image=Degradation Function*Source + Noise
g(x , y) = h(x , y) * f(x , y) + n(x , y)

Image noise is random (not present in the object imaged) variation of brightness
or colour information in images, and is usually an aspect of electronic noise. It can
be produced by the sensor and circuitry of a scanner or digital camera. Image
noise can also originate in film grain and in the unavoidable shot noise of an ideal
photon detector.
1.Gaussian Noise.
2.Salt and pepper (Impulse) Noise.
3.Poisson Noise.
4.Erlang (Gamma) Noise.
5.Exponential Noise.
6.Uniform Noise.

Principal sources of Gaussian noise in digital images arise during acquisition e.g.
sensor noise caused by poor illumination and/or high temperature, and/or
transmission e.g. electronic circuit noise.
A typical model of image noise is Gaussian, additive, independent at eachpixel,
and independent of the signal intensity, caused primarily by Johnson–Nyquist
noise (thermal noise), including that which comes from the reset noise of
capacitors (“KTC noise").Amplifier noise is a major part of the "read noise" of an
image sensor, that is, of the constant noise level in dark areas of theimage.In color
cameras where more amplification is used in the blue colour channel than in the
green or red channel, there can be more noise in the bluechannel.At higher
exposures, however, image sensor noise is dominated by shot noise, which is not
Gaussian and not independent of signal intensity.

The probability density function (PDF) of Gaussian Noise is given by the expression.


2
.1
)(
22
2/)( 

z
e
zp
2
1
2
607.0
   
z




2



z Gray Level
Mean of average value of z
Standard Deviation
Variance

If we plot this function, we notice that
70% of its value lies in the range and
95% of its value lies in the range
Gaussian noise has a maximum value at μ and then it starts falling off.
Let us consider the image shown in figure.
)](),[(  
)]2(),2[(  
a
b
a b Gray Level
Noofpixels
a b
Noofpixels
(a) (b) Histogram of the image
(c) Gaussian occur Histogram modified
Note: Gaussian
noise occur due to
circuit noise,
sensor noise, poor
illumination, high
temperature.

Fat-tail distributed or "impulsive" noise is sometimes called salt-and-pepper noise
or spike noise. An image containing salt-and-pepper noise will have dark pixels in
bright regions and bright pixels in dark regions. This type of noise can be caused
by analogy-to-digital converter errors, bit errors in transmission, etc. It can be
mostly eliminated by using dark frame subtraction, median filtering and
interpolating around dark/bright pixels.
Dead pixels in an LCD monitor produce a similar, but non-random, display.
The salt-and-pepper noise are also called shot noise, impulse noise or spike noise
that is usually caused by faulty memory locations ,malfunctioning pixel elements
in the camera sensors, or there can be timing errors in the process of digitization
.In the salt and pepper noise there are only two possible values exists that is a and
b and the probability of each is less than 0.2.If the numbers greater than this
numbers the noise will swamp out image. For 8-bit image the typical value for 255
for salt-noise and pepper noise is 0 Reasons for Salt and Pepper Noise: a. By
memory cell failure. b. By malfunctioning of camera’s sensor cells. c. By
synchronization errors in image digitizing or transmission.

Fig . Salt and Pepper noise
The PDF of the salt and pepper noise (bipolar noise) is:
;0
;
;
)( b
a
p
p
zp 
For z=a
For z=b
elsewhere
If or is zero, this noise is called unipolar noise. The PDF of salt and pepper is
shown in figure in the next page.
ap bp

ap
bp
a b Gray Level
Generally, a and b are black and white gray levels respectively. Hence, for a 8-bit image,
a=0, b=255 because of which the noise is called salt (white) and pepper (black).
Sometimes, it is called as speckle noise.
Now take some images to understand it properly.

Let us take the same image as the one taken for the Gaussian example.
a b
When salt anf pepper creeps in, the image looks like
a b

Photon noise, also known as Poisson noise, is a basic form of uncertainty
associated with the measurement of light, inherent to the quantized nature of light
and the independence of photon detections. Its expected magnitude is signal
dependent and constitutes the dominant source of image noise except in low-light
conditions.
Image sensors measure scene irradiance by counting the number of discrete
photons incident on the sensor over a given time interval. In digital sensors, the
photoelectric effect is used to convert photons into electrons, whereas film based
sensors rely on photo-sensitive chemical reactions. In both cases, the
independence of random individual photon arrivals leads to photon noise, a signal
dependent form of uncertainty that is a property of the underlying signal itself

The dominant noise in the darker parts of an image from an image sensor is
typically that caused by statistical quantum fluctuations, that is, variation in the
number of photons sensed at a given exposure level. This noise is known as
photon shot noise. Shot noise has a root-mean-square value proportional to the
square root of the image intensity, and the noises at different pixels are
independent of one another. Shot noise follows a Poisson distribution, which
except at very low intensity levels approximates a Gaussian distribution.
In addition to photon shot noise, there can be additional shot noise from the dark
leakage current in the image sensor; this noise is sometimes known as "dark shot
noise "or "dark-current shot noise". Dark current is greatest at "hot pixels" within
the image sensor. The variable dark charge of normal and hot pixels can be
subtracted off (using "dark frame subtraction"), leaving only the shot noise, or
random component, of the leakage. If dark-frame subtraction is not done, or if the
exposure time is long enough that the hot pixel charge exceeds the linear charge
capacity, the noise will be more than just shot noise, and hot pixels appear as salt-
and-pepper noise.
Individual photon detections can be treated as independent events that follow a
random temporal distribution. As a result, photon counting is a classic Poisson
process, and the number of photons N measured by a given sensor element over a
time interval t is described by the discrete probability distribution .
!
)(
)(
k
te
KNp
kt
r

 239/16/2015MD:Reyad Hossain (GNIT)

where λ is the expected number of photons per unit time interval, which is
proportional to the incident scene irradiance. This is a standard Poisson distribution
with a rate parameter λt that corresponds to the expected incident photon count.
The uncertainty described by this distribution is known as photon noise
Centre image Poisson noise occur

Gamma noise often is associated with processes related to waiting times between
random (Poisson-distributed) events. Gamma noise typically is generated as a
pseudorandom pattern of waiting times between events of a unit mean Poisson
process.
The shape of the Gamma noise is very similar to the Rayleigh distribution. The
Gamma noise distribution starts from zero. It is given by the following expression.
0
)!1()(
1


b
za
zp
b
b
az
e for z≥0
For <0

)(zp
k
ab /)1( 
z
Here, a>0 and b is a positive integer. The mean and the variance of this
distribution are given by,
and
22
/
/
ab
ab





Exponential distribution has an exponential shape. It is given by the following
expression.
Here, a>0
The mean and the variance of the exponential noise is given by
0
)(
az
ae
zp


for z≥0
for z<0
2
2 1
1
a
a




)(zp
a
z

The noise caused by quantizing the pixels of a sensed image to a number of
discrete levels is known as quantization noise. It has an approximately uniform
distribution. Though it can be signal dependent, it will be signal independent if
other noise sources are big enough to cause dithering, or if dithering is explicitly
applied.
Quantization, in mathematics and digital signal processing, is the process of
mapping a large set of input values to a (countable) smaller
set. Rounding and truncation are typical examples of quantization processes.
Quantization is involved to some degree in nearly all digital signal processing, as
the process of representing a signal in digital form ordinarily involves rounding.
Quantization also forms the core of essentially all loss compression algorithms.
The difference between an input value and its quantized value (such as round-off
error) is referred to as quantization error. A device or algorithmic function that
performs quantization is called a quantize. An analogy-to-digital converter is an
example of a quantize.

The uniform noise cause by quantizing the pixels of image to a number of
distinct levels is known as quantization noise. It has approximately uniform
distribution. In the uniform noise the level of the gray values of the noise are
uniformly distributed across a specified range. Uniform noise can be used to
generate any different type of noise distribution. This noise is often used to
degrade images for the evaluation of image restoration algorithms. This noise
provides the most neutral or unbiased noise

As the name suggests, this noise is uniform over a certain band of gray levels.
The PDF of uniform noise is given by
if a ≤ z ≤ b
otherwise
The mean of the function is
The variance of this function is given by
0
1
)( abzp 
2
ba 

12
)( 2
2 ab 

)(zp
ap
bp
a b
z
)(zp
ab 
1
a b
z

Filtering in an image processing is a basis function that is used to achieve many
tasks such as noise reduction, interpolation, and re-sampling. Filtering image data
is a standard process used in almost all image processing systems. The choice of
filter is determined by the nature of the task performed by filter and behavior and
type of the data. Filters are used to remove noise from digital image while keeping
the details of image preserved is an necessary part of image processing. Filters can
be described by different categories:
Filtering without Detection: In this filtering there is a window mask which is
moved across the observed image. This mask is usually of the size (2N+1)/2, in
which N is a any positive integer. In this the centre element is the pixel of concern.
When the mask is start moving from left top corner to the right bottom corner of
the image, it perform some arithmetic operations without discriminating any pixel
of image

Detection followed by Filtering: This filtering involves two steps. In the first
step it identify the noisy pixels of image and in second step it filters those pixels of
image which contain noise. In this filtering also there is a mask which is moved
across the image. It performs some arithmetic operations to detect the noisy
pixels of image. Then the filtering operation is performed only on those pixels of
image which are found to be noisy in the first step, keeping the non-noisy pixel of
image intact.
Hybrid Filtering: In hybrid filtering scheme, two or more filters are used to filter
a corrupted location of a noisy image. The decision to apply a particular filter is
based on the noise level of noisy image at the test pixel location and the
performance of the filter which is used on a filtering mask.

Linear Filters: Linear filters are used to remove certain type of noise. Gaussian or
Averaging filters are suitable for this purpose. These filters also tend to blur the
sharp edges, destroy the lines and other fine details of image, and perform badly in
the presence of signal dependent noise.
Non-Linear Filters: In recent years, a variety of non-linear median type filters such
as rank conditioned, weighted median, relaxed median, rank selection have been
developed to overcome the shortcoming of linear filter.
Different Type of Linear and Non-Linear Filters:
Mean Filter: The mean filter is a simple spatial filter .It is a sliding-window filter
that replace the center value in the window. It replaces with the average mean of all
the pixel values in the kernel or window. The window is usually square but it can be
of any shape.

Advantage:
a. Easy to implement
b. b. Used to remove the impulse noise.
Disadvantage:
It does not preserve details of image. Some details are removes of image with
using the mean filter

Median Filter: Median Filter is a simple and powerful non-linear filter which is
based order statistics. It is easy to implement method of smoothing images. Median
filter is used for reducing the amount of intensity variation between one pixel and
the other pixel. In this filter, we do not replace the pixel value of image with the
mean of all neighbouring pixel values, we replaces it with the median value. Then
the median is calculated by first sorting all the pixel values into ascending order and
then replace the pixel being calculated with the middle pixel value. If the
neighbouring pixel of image which is to be consider contain an even numbers of
pixels, than the average of the two middle pixel values is used to replace. The median
filter gives best result when the impulse noise percentage is less than 0.1 %. When
the quantity of impulse noise is increased the median filter not gives best result

Enhancement of an noisy image is necessary task in digital image processing.
Filters are used best for removing noise from the images. In this paper we
describe various type of noise models and filters techniques. Filters
techniques are divided into two parts linear and non-linear techniques. After
studying linear and non-linear filter each of have limitations and advantages.
In the hybrid filtering schemes, there are two or more filters are
recommended to filter a corrupted location .The decision to apply a which
particular filter is based on the different noise level at the different test pixel
location or performance of the filter scheme on a filtering mask.

[1]. A. K. Jain, “Fundamentals of Digital Image Processing”, Prentice Hall of India,
First Edition, 1989.
[2]. Rafael C .Gonzalez and Richard E. woods, “Digital Image Processing”, Pearson
Education, Second Edition, 2005
[3]. K. S. Srinivasan and D. Ebenezer, “A New Fast and Efficient Decision-Based
Algorithm for Removal of High-density Impulse Noises,” IEEE Signal Processing
Letters, Vol. 14, No. 3, March 2007.
[4]. H. Hwang and R. A. Haddad”Adaptive Median Filters: New Algorithms and
Results” IEEE Transactions on image processing vol 4. P.no 499-502, Apr 1995.
[5]. Nachtegael, M, Schulte, S, Vander We ken. Kerre, E.E.2005.Fuzzy Filters for
Noise Reduction: The Case of Gaussian Noise. IEEE Explore, 201-206 D, De Witte. V,
206.
[6]. Suresh Kumar, Papendra Kumar, Manoj Gupta, Ashok Kumar Nagawat,
“Performance Comparison of Median and Wiener Filter in Image De-noising”
,International Journal of Computer Applications (0975 – 8887) Volume 12– No.4,
November 2010

Noise recognition in digital image

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