Noise filtering


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Noise filtering

  1. 1. Noise Addition and Filtering ` Presented By : Sara El-Masri Alaa Sababbah Amna El-Sheikh Ali Supervised By : Dr. Samy Salamah
  2. 2. Outline
  3. 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. 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. 5. 1. Introduction (cont.) Image on the right has more noise than the image on the left
  6. 6. Images • There are two types of images :  Vector images  Digital images
  7. 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. 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. 9. Types of Digital Images • Binary images (black and white images) • Gray scale images • Color images
  10. 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. 11. Gray Scale Images • Each pixel value of gray scale images normally from 0 (black) to 255 (white)
  12. 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. 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. 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. 15. Types of Image Noise 1) Salt and pepper noise 2) Gaussian noise 3) Speckle noise 4) Uniform noise
  16. 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. 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. 18. Salt and pepper noise (cont.)
  19. 19. Image with Salt and Pepper Original Image
  20. 20. Salt and pepper noise (cont.) • filtering techniques :  mean filtering .  Median filtering  Gaussian filtering
  21. 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.
  22. 22. Gaussian Noise (cont.) Without Noise With Gaussian Noise
  23. 23. Image with Gaussian Noise
  24. 24. 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 .
  25. 25. Gaussian Noise (cont.) • filtering techniques : mean (convolution) filtering Median filtering Gaussian filtering
  26. 26. 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. 27. 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.
  28. 28. Original Image Image with Noise
  29. 29. Speckle Noise (cont.) • filtering techniques : mean (convolution) filtering Median filtering
  30. 30. 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
  31. 31. Uniform Noise (cont.) • Quantization noise has an approximately uniform distribution
  32. 32. Uniform Noise (cont.)
  33. 33. 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. 34. Filtering Techniques Linear Filtering Non-Linear Filtering
  35. 35. 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. 36. Linear Filters – Example Filtered Gaussian noise.
  37. 37. 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. 38. Non-linear Filter vs. linear Filter
  39. 39. Filters Types 1) Median filter . 2) Wiener Filter . 3) Mean filter . 4) Gaussian filter
  40. 40. 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. 41. 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. 42. Example : 3x3 Median
  43. 43. Original Salt & pepper %20 De-noising by Median filter Original Salt & pepper %60 De-noising by Median filter
  44. 44. 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. 45. 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
  46. 46. Wiener filter Example
  47. 47. 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. 48. Mean Filtering Example Average filtering example using a 3 x 3 sampling window: Keeping border values unchanged
  49. 49. Mean Filtering - Boundaries • Average filtering example using a 3 x 3 sampling window: Extending border values outside with values at boundary
  50. 50. Mean Filter Example • (a) Original Image • (b) Image corrupted by %12 Gaussian noise . • (c)De –noising by mean filter
  51. 51. 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.
  52. 52. Gaussian filter Example (a) Original (b)Noisy (c) Gaussian filter Image corrupted by %60 salt & Pepper Noise
  53. 53. 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 .
  54. 54. 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.
  55. 55. Performance Parameters 3) Peak signal to Noise ratio (PSNR): – It is defined by: PSNR = 10 log (255^2/mse)
  56. 56. Implementation in Matlab
  57. 57. 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. 58. QUESTIONS ? Be nice ...