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Image Restoration

Image Restoration. Digital Image Processing. Content. Introduction Image degradation/restoration model Noise models Restoration by spatial filtering Estimation of degradation functions Inverse filtering Wiener filtering Geometric transformation. Introduction.

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Image Restoration

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  1. Image Restoration Digital Image Processing

  2. Content • Introduction • Image degradation/restoration model • Noise models • Restoration by spatial filtering • Estimation of degradation functions • Inverse filtering • Wiener filtering • Geometric transformation

  3. Introduction • Objective of image restoration • to recover a distorted imageto the original formbased on idealized models. • The distortion is due to • Image degradation in sensing environmente.g. random atmospheric turbulence • Noisy degradation from sensor noise. • Blurring degradation due to sensors • e.g. camera motion or out-of-focus • Geometric distortion • e.g. earth photos taken by a camera in a satellite

  4. Enhancement Concerning the extraction of image features Difficult to quantify performance Subjective; making an image “look better” Restoration Concerning the restoration of degradation Performance can be quantified Objective; recovering the original image Introduction

  5. Image degradation / restoration model

  6. Noise models • Assuming degradation only due to additive noise (H = 1) • Noise from sensors • Electronic circuits • Light level • Sensor temperature • Noise from environment • Lightening • Atmospheric disturbance • Other strong electric/magnetic signals

  7. Noise models • Assuming that noise is • independent of spatial coordinates, and • uncorrelated with respect to the image content

  8. Noise models

  9. Noise models

  10. Noise models • Other common noise models • Rayleigh noise • Gamma noise • Exponential noise • Uniform noise

  11. Noise Models • Rayleigh Noise • Gamma(Erlang) Noise • Exponential Noise

  12. paper salt -3-levels -simple constant areas (spans from black to white) Noise models

  13. Additive Noise Histograms

  14. Additive Noise Histograms

  15. Noise components Periodic noise can be reduced in via frequency domain Are generated due to electrical or electromechanical interference during image acquisition Periodic Noise

  16. Restoration by spatial filtering Noise is unknown Spatial filtering is appropriate when only additive noise is present

  17. Restoration by spatial filtering

  18. Restoration by spatial filtering

  19. Restoration by spatial filtering

  20. Restoration by spatial filtering Qis the order of filter

  21. Restoration by spatial filtering Noise level is Mean =0 Variance = 400

  22. Restoration by spatial filtering • Mean filters (noise reduced by blurring) • Arithmetic mean filter and geometric mean filter are well suited for random noise such as Gaussian noise • Contraharmonic mean filter is well suited for impulse noise • Disadvantage: must know pepper noise or salt noise in advance

  23. Restoration by spatial filtering

  24. Restoration by spatial filtering wrong

  25. Restoration by spatial filtering -- Repeated passes of median filter tend to blur the image. -- Keep the number of passes as low as possible.

  26. Restoration by spatial filtering Fig. 8 next page

  27. Restoration by spatial filtering Pepper noise Salt noise

  28. High level of noise  large filter • Median and alpha-trimmed filter performed better • Alpha-trimmed did better than median filter

  29. Restoration by spatial filtering • Filters discussed so far • Do not consider image characteristics • Adaptive filters to be discussed • Behaviors based on statistical characteristics of the subimage under a filter window • Better performance • More complicated • Adaptive, local noise reduction filter • Adaptive median filter

  30. Restoration by spatial filtering

  31. Restoration by spatial filtering

  32. Restoration by spatial filtering

  33. Restoration by spatial filtering Adaptive filtering

  34. Restoration by spatial filtering

  35. Restoration by spatial filtering Is Z_med impulse? Is Z_xy impulse?

  36. Restoration by spatial filtering

  37. Periodic Noise Reduction(Frequency Domain Filtering) • Band-Reject Filters • Ideal Band-reject Filter -D(u,v) =distance from the origin of the centered freq. rectangle -W=width of the band -D0=Radial center of the band.

  38. Periodic Noise Reduction(Frequency Domain Filtering) • Butterworth Band-Reject Filter of order n • Gaussian Band-Reject Filter

  39. Periodic Noise Reduction(Frequency Domain Filtering)

  40. Periodic Noise Reduction(Frequency Domain Filtering) • Band-Pass Filters • Opposite operation of a band-reject fiter

  41. Periodic Noise Reduction(Frequency Domain Filtering) • Notch Filters • Rejects (or passes) frequencies in predefined neighborhoods about a center frequency Ideal Must appear in symmetric pairs about the origin. Butterworth Gaussian

  42. Center frequency components Shift with respect to the center Periodic Noise Reduction(Frequency Domain Filtering) • Notch Filters • Ideal

  43. Notch pass filter Horizontal lines of the noise pattern I can be seen

  44. Optimum Notch Filtering Several pairs of components are present  more than just one sinusoidal component

  45. Optimum Notch Filtering

  46. Estimation of degradation functions

  47. Estimation of degradation functions

  48. Estimation of degradation functions

  49. Estimation of degradation functions

  50. Estimation of degradation functions

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