Noise Models

Noise Models

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Digital Image Processing Image Restoration
Noise models and additive noise removal

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Image Restoration

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Image Restoration
What is noise (in the context of image processing) and how can it
be modeled?
What are the main types of noise that may affect an image?
What are the possible solutions?
Subjective VsObjective (Enhancement VsRestoration)

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Degradation Model for a Digital Image

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Noise Models

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Noise and Noise Models
Gaussian (normal)
Impulse (salt-and-pepper)
Uniform
Rayleigh
Gamma (Erlang)
Exponential

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Effect of Noise on Images & Histograms
Gaussian
Exponential
Impulse
(salt-and-pepper)

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Effect of Noise on Images & Histograms
Rayleigh
Gamma (Erlang)
Uniform

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Noise Models: Gaussian Noise

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Noise Models: Rayleigh Noise

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Noise Models: Erlang (Gamma) Noise

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Noise Models: Exponential Noise
Where

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Noise Models: Uniform Noise
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Noise Models: Impulse (Salt and Pepper) Noise

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Effect of Noise on Images & Histograms

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Effect of Noise on Images & Histograms

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Effect of Noise on Images & Histograms

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Periodic Noise (Example)
Spatially Dependent Case

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Applicability of various noise models

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Estimation of noise parameters

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Estimation of noise parameters (example)

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Estimation of noise parameters (example)

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Estimation of noise parameters

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Restoration of noise-only degradation
Filters to be considered

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Mean Filters: Arithmetic mean filter
Causes a certain amount of blurring (proportional to the window size) to
the image, thereby reducing the effects of noise.
Can be used to reduce noise of different types, but works best for Gaussian,
uniform, or Erlang noise.

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Mean Filters: Geometric mean filter
–A variation of the arithmetic mean filter
–Primarily used on images with Gaussian noise
–Retains image detail better than the arithmetic mean

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Mean Filters: Harmonic mean filter
–Another variation of the arithmetic mean filter
–Useful for images with Gaussian or salt noise
–Black pixels (pepper noise) are not filtered
Harmonic mean filter

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Arithmetic and geometric mean filters (example)

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Mean Filters: Harmonic mean filter

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Mean Filters: Harmonic mean filter

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Mean Filters: Contra-harmonic mean filter

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Classification of contra-harmonic filter applications

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Contra-harmonic mean filter (example)

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Contra-harmonic mean filter (example)

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Rank / Order / Order Statistics Filters
– Known as Rank filters, Order filtersOR Order Statistics filters
– Operate on a neighborhood around a reference pixel by
ordering (ranking) the pixel values and then performing an
operationon those ordered values to obtain the new value for
the reference pixel
– They perform very well in the presence of salt and pepper noise
but are more computationally expensiveas compared to mean
filters

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Rank / Order Statistics Filters: Median filter

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Rank / Order Statistics Filters: Median filter
–Most popular and useful of the rank filters.
–It works by selecting the middle pixel value from the ordered set
of values within the m ×n neighborhood (W) around the
reference pixel.
• If mnis an even number, the arithmetic average of the two
values closest to the middle of the ordered set is used
instead.
–Many variants, extensions, and optimized implementations in
the literature.

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Median filter (Example)

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Rank / Order Statistics Filters: Max and Min filter

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Rank / Order Statistics Filters: Max and Min filter
–Max filter also known as 100
th
percentile filter
–Min filteralso known as zeroth percentile filter
–Maxfilter helps in removing pepper noise
–Minfilter helps in removing salt noise

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Max and Min filter (Example)

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Rank / Order Statistics Filters: Midpoint filter
–Calculates the average of the highest and lowest pixel values
within a window
–What would it do with salt and pepper noise ?

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Midpoint filter (Example)