1. Image Restoration - Focus on Noise
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2. References
Gonzales and Wood second edition
Jain
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3. Enhancement - Restoration
Subjective
Objective
Goodness Test
Visual – meet the psychophysical aspects of HVS
Objective measures
Masks
Small. Spatial or Frequency domain
Large. More frequently driven by freq domain analysis
Noise only
Smoothing filters
Similar to Enhancement approaches
Degradation model
Intuitive/heuristic analysis
Math model. This model is often an approx.
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4. Overview
Measured
From [1]
Unknown
Approximation
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5. Noise sources Device noise (often thermal) Digitization process
Sampling and quantization
Transmission
Environment
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6. Noise models White noise: autocorrelation is an impulse Colored noise
Usually assume that noise is uncorrelated with the image
Gaussian: circuit noise, illumination, environment (thermal)
Rayleigh: range imaging
Uniform: easy to model
Others: exponential, impulse (salt and pepper)
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7. Sample pdfs
From [1]
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8. Test image
3 distinct gray levels
From [1]
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9. Additive Noise From [1] 12/3/2018
Noise is added to the respective gray levels. Hence the multiple lobe histograms
From [1]
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10. Additive Noise
From [1]
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11. Estimation of Noise Parameters – Periodic Noise
Periodic noise – filter in frequency domain. Appears as pair of impulses. The removal can be automated when the impulses are more pronounced.
From [1]
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12. Noise Parameter Estimation – Known Model
Noise parameters can be computed by focusing on small sub-image (patch).
From [1]
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13. Mean and S.D. estimation
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14. Image Restoration – Noise Only Degradation
Use Filters: Spatial Filter
n(x,y) is unknown.
For periodic noise, N(u,v) can be estimated from G(u,v) – spikes at predominant noise frequencies.
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15. Noise Reduction Filters
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16. Applying Arithmetic and Geometric Filters
From [1]
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17. More Noise Reduction Filters
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18. Comparisons of Filters
Arithmetic: Smoothing reduces noise. Blurring.
Geometric: Smoothing. Less loss of image detail than Arithmetic.
Harmonic: Reduces salt noise. No impact on pepper noise.
Contraharmonic: Reduces salt and pepper noise. Q>0 reduces pepper noise. Q<0 reduces salt noise. Cannot reduce salt and pepper noise in the same pass.
Q = 0 yields Arithmetic
Q = -1 yields Harmonic
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19. Order Statistics Filters
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20. Multiple applications of the Median Filter
From [1]
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21. Order Statistics Filters - 2
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22. Adaptive Filter – Reduce Local Noise
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23. Arithmetic, Geometric and Adaptive Filters
From [1]
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24. Adaptive Median Filter
Preserve detail.
Smooth non-impulse noise {different from tradition median filter}.
Like Adaptive Filter use a window Sxy.
The center of the window is replaced by the result
Unlike Adaptive Filter, the size of the window is increased.
Notation
zmin = min gray level in Sxy.
zmax = max gray level in Sxy.
zmed = median gray level in Sxy.
zxy = gray level at coordinate (x,y).
Smax = max allowed size of Sxy.
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25. Adaptive Median Filter
Level A:
{ is zmed an impulse?}
while window size is less than Smax do
if zmed > zmin AND zmed < zmax, then Go To Level B
else increase the window size
end while
output zxy
Level B:
{ is zxy an impulse?}
if zxy > zmin AND zxy < zmax, then output zxy
else output zmed
Algorithm objectives
Remove salt and pepper noise
Smooth other noise
Reduce distortions, e.g. excessive thinning or thickening of boundaries
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26. Adaptive Median Filter
From [1]
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27. Periodic Noise Band reject filters Band pass filters Notch filters
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