Noise filtering

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

2. Outline Introduction . Image . Image noise . Source of image noise . Types of image noise . Filtering Filtering Techniques . Filters types . Conclusion . 2

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. 3

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. 4

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

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

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 . 7

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 8

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

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

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

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 12

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 : 13

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. 14

15. Types of Image Noise Salt and pepper noise Gaussian noise Speckle noise Uniform noise 15

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 . 16

17. Salt and pepper noise (cont.) Reasons for Salt and Pepper Noise : By memory cell failure. By malfunctioning of camera’s sensor cells. By synchronization errors in image digitizing or transmission . 17 Where: p a , p b 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.) 18

19. Original Image Image with Salt and Pepper 19

20. filtering techniques : 20 Salt and pepper noise (cont.) 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. 21

22. 22

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

24. Image with Gaussian Noise 24

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

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

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. 27

28. 28 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. Speckle Noise

29. Image with Noise Original Image 29

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

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 : 31 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 32

33. 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 . 34

35. Filtering Techniques Linear Filtering Non- Linear Filtering 35

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 . 36

37. Linear Filters – Example F iltered Gaussian noise . 37

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. 38

39. Non-linear Filter vs. linear Filter 39

40. Filters Types Median filter . Wiener Filter . Mean filter . Gaussian filter 40

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. 41

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 %. 42

43. Example : 3x3 Median 43

44. 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 . 45

46. 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 46 Wiener Filter

47. Wiener filter Example 47

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. 48

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

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

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

52. 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. 52 Gaussian filter

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

54. For comparing original image and filtered image , we calculate following parameters: 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 . 54 Performance Parameters

55. 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. 55 Performance Parameters  

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

57. Implementation in Matlab 57

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. 58

59. QUESTIONS ? Be nice ... 59

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