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Digital Image Processing

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Digital Image Processing 5 Image Restoration Preview The ultimate goal of image restoration techniques is to improve an image in some predefined sense. – PowerPoint PPT presentation

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Title: Digital Image Processing


1
Digital Image Processing
  • 5 Image Restoration

2
Preview
  • The ultimate goal of image restoration techniques
    is to improve an image in some predefined sense.
  • Restoration attempts to reconstruct or recover an
    image that has been degraded by using a priori
    knowledge of the degradation phenomenon.
  • Restoration techniques are oriented toward
    modeling the degradation and applying the inverse
    process in order to recover the original image.

3
5.1 A model of degradation/Restoration
  • A model of the image degradation/restoration
    process

4
5.2 Noise models
  • Sources of noise
  • Image acquisition
  • Image transmission
  • Spatial and frequency properties of noise
  • Noise parameters
  • Correlation of the noise with the image.
  • Frequency distribution of noise
  • Assumptions
  • Noise is independent of spatial coordinates.
  • Noise is uncorrelated with respect to the image
    itself.

5
5.2 Noise models
  • Some important noise probability density
    functions
  • Gaussian noise
  • Reyleigh noise

6
5.2 Noise models
  • Some important noise probability density
    functions
  • Erlang (Gamma) noise
  • Exponential noise

7
5.2 Noise models
  • Some important noise probability density
    functions
  • Uniform noise
  • Impulse (salt-and-pepper) noise

8
5.2 Noise models
9
5.2 Noise models
  • Test pattern

10
5.2 Noise models
11
5.2 Noise models
12
5.2 Noise models
  • Periodic noise

13
5.2 Noise models
  • Estimation of noise parameters
  • Mean
  • Variance

14
5.2 Noise models
15
5.3 Restoration spatial filtering
  • Mean filters
  • Arithmetic mean filter
  • Geometric mean filter
  • Harmonic mean filter
  • Contraharmonic mean filter
  • Order-statistics filters
  • Median filter
  • Max and min filters
  • Midpoint filter
  • Alpha-trimmed mean filter
  • Adaptive filter
  • Adaptive, local noise reduction filter
  • Adaptive median filter

16
5.3 Restoration spatial filtering
17
5.3 Restoration spatial filtering
18
5.3 Restoration spatial filtering
19
5.3 Restoration spatial filtering
20
5.3 Restoration spatial filtering
21
5.3 Restoration spatial filtering
22
5.4 Periodic noise reduction
  • Bandreject filters
  • Ideal bandreject filter
  • Butterworth bandreject filter
  • Gaussian bandreject filter

23
5.4 Periodic noise reduction
24
5.4 Periodic noise reduction
  • Bandpass filters

25
5.4 Periodic noise reduction
  • Notch filters
  • Ideal notch filter
  • Butterworth notch filter
  • Gaussian notch filter

26
5.4 Periodic noise reduction
27
5.4 Periodic noise reduction
28
5.5 Linear position-invariant systems
  • Linearity
  • Definition assume that
  • H is linear if and only if
  • Additivity
  • Homogeneity

29
5.5 Linear position-invariant systems
  • Position invariant
  • Definition assume that
  • H is position invariant if
  • Image expression in terms of impulses

30
5.5 Linear position-invariant systems
  • Convolution integral
  • Output image
  • If the system is linear
  • If the system is position invariant

31
5.5 Linear position-invariant systems
  • Expression of convolution integral
  • Degradation model
  • Degradation model in frequency domain

32
5.6 Estimating the degradation function
  • Three principal ways
  • Observation
  • Experimentation
  • Mathematical modeling

33
5.6.1 Estimation by image observation
  • Principle
  • Look at a small section of the image containing
    simple structures as the observed subimage,
  • Construct an unblurred subimage of the same size
    and characteristics
  • degradation function of subimage
  • degradation function

34
5.6.2 Estimation by experimentation
  • Principle
  • Use an equipment to imitate the equipment used to
    acquire the degraded image
  • Obtain the impulse response of the degradation
    equipment
  • Due to the fact that the Fourier transform of an
    impulse is a constant, we have

35
5.6.2 Estimation by experimentation
36
5.6.3 Estimation by modeling
  • An instance of modeling atmospheric turbulence

37
5.6.3 Estimation by modeling
  • Another instance uniform linear motion

38
5.6.3 Estimation by modeling
39
5.7 Inverse filtering
  • Inverse filtering
  • In the presence of noise

40
5.7 Inverse filtering
41
5.8 Wiener filtering
  • Mean square error
  • Conditions
  • The noise and image are uncorrelated
  • Zero mean
  • The gray levels in the estimate are a linear
    function of the gray levels in the degraded image

42
5.8 Wiener filtering
  • Wiener filtering

43
5.8 Wiener filtering
44
5.8 Wiener filtering
45
5.9 Constrained least square filtering
  • Degradation expressed in vector-matrix form
  • Suppose that g(x,y) is of size M ? N.
  • So, g, f and ? all have dimension M N ?1, and
    the matrix H has dimension M N ? M N.

46
5.9 Constrained least square filtering
  • Principle

47
5.9 Constrained least square filtering
  • Solution in the frequency domain

48
5.9 Constrained least square filtering
49
5.10 Geometric mean filter
  • Geometric mean filter

50
5.11 Geometric transformation
  • Geometric transformations modify the spatial
    relationships between pixels in an image.
  • Two steps
  • Spatial transformation
  • Gray level interpolation

51
5.11.1 Spatial transformation
  • Principle
  • Suppose that an image f (x, y) undergoes
    geometric distortion to produce an image g (x,
    y).
  • Transformation may be expressed as
  • x r (x, y) and y s (x, y)

52
5.11.2 Gray level interpolation
  • Approaches
  • Nearest neighbor, or zero-order interpolation
  • Cubic convolution interpolation
  • Bilinear interpolation

53
5.11.2 Gray level interpolation
54
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