This document discusses noise addition and filtering in images. It begins by introducing different types of digital images like binary, grayscale, and color images. It then discusses various sources of image noise like sensor heat, ISO settings, and memory failures. The main types of noise covered are salt and pepper noise, Gaussian noise, speckle noise, and uniform noise. Linear and non-linear filtering techniques are described for removing each noise type, including median filtering, Wiener filtering, and mean/Gaussian filtering. Performance of filters is evaluated using measures like mean squared error and peak signal-to-noise ratio. Matlab is mentioned for implementing noise addition and filtering.

1. Noise Addition and Filtering
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Presented By : Sara El-Masri
Alaa Sababbah
Amna El-Sheikh Ali
Supervised By : Dr. Samy Salamah

2. Outline

3. 1. Introduction
• It is generally desirable for image brightness to be
uniform except where it changes to form an image.
• There are factors, however, that tend to produce
variation in the brightness of a displayed image even
when no image detail is present.
• This variation is usually random and has no particular
pattern.

4. 1. Introduction (cont.)
In many cases, it reduces image quality and is especially
significant when the objects being imaged are small and have
relatively low contrast.
This random variation in image brightness is
designated noise.

5. 1. Introduction (cont.)
Image on the right has more noise
than the image on the left

6. Images
• There are two types of images :

Vector images

Digital images

7. Vector Images
• Vector images made up of vectors which lead through
locations called control points.
• Each of these control points has define on the x and y axes
of the work plain .

8. Digital Images
• A digital image is 2-dim array of real numbers
• 2-D image is divided into N rows and M columns
• the intersection of these rows and columns is known as pixels

9. Types of Digital Images
• Binary images (black and white images)
• Gray scale images
• Color images

10. Binary Images
• Each pixel is just black or white
• There is only two possible values for each pixel
i.e. 0 or 1

11. Gray Scale Images
• Each pixel value of gray scale images normally from
0 (black) to 255 (white)

12. Color images
• In color images each pixel has a particular color ; that
color being described by the amount of red , blue and
green in it .
• Each of these components has a rang 0-255

13. 2. Image noise
Noise in image , is any degradation in an image signal ,
caused by external disturbance while an image is
being sent from one place to another place via satellite
, wireless and network cable .
We can model a noisy image as follows:

14. Source of Image Noise
• Error occurs in image signal while an image is being sent
electronically from one place to another .
• Sensor heat while clicking an image
• ISO factor ISO number indicates how quickly a camera’s sensor
absorbs , light , higher ISO used mare chance of noticeable noise
• By memory cell failure.

15. Types of Image Noise
1) Salt and pepper noise
2) Gaussian noise
3) Speckle noise
4) Uniform noise

16. Salt and pepper noise
• It known as shot noise, impulse noise or Spike noise .
• Its appearance is randomly scattered white or black or
both pixel over the image .
• there are only two possible values exists that is a and b
and the probability of each is less than 0.2 .

17. Salt and pepper noise (cont.)
Reasons for Salt and Pepper Noise:
1)
2)
3)
By memory cell failure.
By malfunctioning of camera’s sensor cells.
By synchronization errors in image digitizing or transmission.
Where: pa, pb are the Probabilities Density Function (PDF), p(z) is distribution
salt and pepper noise in image and A, B are the arrays size image.

18. Salt and pepper noise (cont.)

19. Image with Salt and
Pepper
Original Image

20. Salt and pepper noise (cont.)
• filtering techniques :
 mean filtering .
 Median filtering
 Gaussian filtering

21. Gaussian Noise
Gaussian noise is caused by random fluctuations in the
signal , its modeled by random values add to an image
This noise has a probability density function [pdf] of the
normal distribution. It is also known as Gaussian
distribution.

23. Gaussian Noise (cont.)
Without Noise
With Gaussian Noise

24. Image with Gaussian Noise

25. Sources of Gaussian Noise
• In digital images arise during acquisition .
e.g. Sensor noise caused by poor illumination and/or high
temperature
• Transmission
e.g. Electronic circuit noise .

26. Gaussian Noise (cont.)
• filtering techniques :
mean (convolution) filtering
Median filtering
Gaussian filtering

27. Speckle Noise
• Speckle noise can be modeled by random values multiplied
by pixel values of an image
• results from random fluctuations in the return signal from
an object that is no bigger than a single image-processing
element.
It increases the mean grey level of a local area.

28. Speckle Noise
The distribution noise can be expressed by:
Where g(n,m), is the observed image , u(n,m) is the multiplicative
component . and &(n,m) is the additive component of the speckle noise.

29. Original Image
Image with Noise

30. Speckle Noise (cont.)
• filtering techniques :
mean (convolution) filtering
Median filtering

31. Uniform Noise
• The uniform noise cause by quantizing the pixels of image
to a number of distinct levels is known as quantization
noise.
• Uniform noise can be analytically described by :
• The gray level values of the noise are evenly distributed across
a specific range

32. Uniform Noise (cont.)
• Quantization noise has an approximately uniform
distribution

33. Uniform Noise (cont.)

34. 3. Filtering
• Filtering image data is a standard process used in
almost all image processing systems.
• Filters are used to remove noise from digital image
while keeping the details of image preserved.
• The choice of filter is determined by
 the nature of the task performed by filter .
 Filter behavior .
 type of the data .

35. Filtering Techniques
Linear Filtering
Non-Linear Filtering

36. Linear Filter
• Linear filters are used to remove certain type of noise.
• The linear filters work best with salt and pepper noise, and
Gaussian noise.
• Gaussian and mean filters.
• Simple to design .
• These filters also
 tend to blur the sharp edges .
 destroy the lines and other fine details of image .

37. Linear Filters – Example
Filtered Gaussian
noise.

38. Non-Linear Filters
• Can preserve edges .
• Very effective at removing impulsive noise .
• They are more powerful than linear filters because they
are able to reduce noise levels without blurring edges.
• Can be difficult to design.
• Median Filter.

39. Non-linear Filter vs. linear Filter

40. Filters Types
1)
Median filter .
2)
Wiener Filter .
3)
Mean filter .
4)
Gaussian filter

41. Median Filter
• Median Filter is a simple and powerful non-linear filter .
• It is used for reducing the amount of intensity variation
between one pixel and the other pixel.
• In this filter, we replaces pixel value with the median value .
• 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
• Salt and pepper noise.

42. Median Filter
• Advantage:
 It is easy to implement.
 Used for de-noising different types of noises.
• Disadvantage:
 Median Filter tends to remove image details when the impulse
noise percentage is more than 0.4 %.

43. Example : 3x3 Median

44. Original
Salt & pepper
%20
De-noising by
Median filter
Original
Salt & pepper
%60
De-noising by
Median filter

45. Wiener Filter
• The purpose of the Wiener filter is to filter out the
noise that has corrupted a signal.
• This filter is based on a statistical approach.
• The goal of wiener filter is reduced the mean square
error (MSE) as much as possible.
• Poisson noise , speckle noise .

46. Wiener Filter
• One method that we assume we have knowledge of the
spectral property of the noise and original signal.
•
•
•
•
•
The Fourier domain of the Wiener filter is Where :
H*(u, v) = Complex conjugate of degradation function
Pn (u, v) = Power Spectral Density of Noise
Ps (u, v) = Power Spectral Density of non-degraded image
H (u, v) = Degradation function

47. Wiener filter Example

48. Mean Filter
• Mean Filter (average filter) is a simple linear filter .
• Replace each pixel value in an image with the mean value of its
neighbors, including itself.
• Gaussian noise .
• Advantage:
 Easy to implement
 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.

49. Mean Filtering Example
Average filtering example using a 3 x 3 sampling window:
Keeping border values unchanged

50. Mean Filtering - Boundaries
• Average filtering example using a 3 x 3 sampling
window:
Extending border values outside with values at boundary

51. Mean Filter Example
• (a) Original Image
• (b) Image corrupted by %12
Gaussian noise .
• (c)De –noising by mean filter

52. Gaussian filter
Gaussian noise
• Gaussian is smoothing filter in the 2D convolution
operation that is used to remove noise and blur from
image.
• Probably the most useful filter (although not the
fastest).
• Gaussian filtering is done by convolution each point
in the input array with a Gaussian kernel and then
summing them all to produce the output array.

53. Gaussian filter Example
(a) Original
(b)Noisy
(c) Gaussian filter
Image corrupted by %60 salt & Pepper Noise

54. Performance Parameters
• For comparing original image and filtered image, we calculate
following parameters:
1) Mean Square Error (MSE): The MSE is the cumulative square error
between the encoded and the original image defined by:
Where, f is the original image and g is the filtered image. The dimension of
the images is m x n. Thus MSE should be as low as possible for effective
filtering .

55. Performance Parameters
2) Signal to Noise Ratio is defined by the power ratio between a signal
and the background noise.
Where P is average power. Both noise and power must be measured at
the same points in a system, and within system with same bandwidth.

56. Performance Parameters
3) Peak signal to Noise ratio (PSNR):
– It is defined by:
PSNR = 10 log (255^2/mse)

57. Implementation in Matlab

58. Conclusion
• Enhancement of an noisy image is necessary task in
image processing.
• Filters are used best for removing noise from the images.
• 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.

59. QUESTIONS ?
Be nice ...