Unit 2 ppt2

8/13/2019 Unit 2 ppt2

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Noise Models and Filtering

8/13/2019 Unit 2 ppt2


The sources of noise in digital images arise during

image acquisition (digitization) and transmission.

We can consider a noisy image to be modelled asfollows:

g (x,y)= f (x,y)+ ƞ (x,y)

where f(x, y) is the original image pixel, η (x, y) is the

noise term and g(x, y) is the resulting noisy pixel

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There are many different models for the image noise term

η (x, y) :• Gaussian

• Rayleigh• Erlang• Exponential• Uniform• Impulse

Salt and pepper noise

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Created in an image by electronic circuit and sensors as

a result of poor illumination and high temperature.

where g = gray level; m = mean; s= standard deviation ;

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Radar range and velocity images typically contain noise that can be modeled by the Rayleigh distribution

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Original Image Image with Rayleigh noise

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Gamma noise can be obtained by low pass filtering of laser-

based images. The equation for gamma noise is:

z

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Original imageNoise image added with Gamma noise

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It is a special case of Erlang distribution. The PDF of

exponential distribution can be obtained by substituting b=1 in

erlang PDF.p

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Original image Exponential noise

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The PDF of uniform distribution be:

z

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Original image Noisy image

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The salt-and-pepper type noise (also called impulse noise, shot

noise or spike noise) is typically caused by malfunctioning

pixel elements in the camera sensors, faulty memory locations,

or timing errors in the digitization process.

Salt and Pepper noise can be analytically described by:

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For an 8-bit image, the typical value for pepper noise is 0, and

255 for salt-noise

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Many image enhancement techniques are based on spatialoperations performed on local neighborhoods of input pixels.

Often, the image is convolved with a FIR filter called "spatial

mask".Spatial averaging Here each pixel is replaced by a weighted

average of its neighborhood pixels i.e.

where y(m,n) and v(m,n) are i/pr opposite images. is a suitably

chosen window and ɑ (k,l) are the filter weights.

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A common class of spatial averaging filters has all equal weights giving

where is the number of pixels in the window.Another spatial averaging filter used often is given by

ie. each pixel is replaced by its average with the average of its nearest four

pixels.

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In practice, the pixels are not constant. Hence the window size

is limited. Due to this, the output image of spatial averaging is

distorted in the form of BLURRING.

To protect the edges from blurring while smoothing, a

DIRECTIONAL AVERAGING FILTER is needed. Such a

filtering process is called Directional Smoothing.

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To protect edges from blurring while smoothing, a directional

averaging filter is used. Spatial average are calculated

in several directions as

And the direction is found such that |f(x,y)-v(m,n,θ )| is

minimum

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Original Blurred output Filteredoutput

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Recap

◦ Noise models

◦ Spatial Averaging

◦ Directional Smoothing

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Unit 2 ppt2