Research of properties of digital noise in contrast images

Vladimir A. Surin, Alexander N. Tyrsin

South-Ural State University (national research university), Chelyabinsk, Russia

Ural Federal University named after the first President of Russia B.N.Yeltsin, Yekaterinburg, Russia

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Yekaterinburg, AIST 2016

Noise in digital images

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Depends from:Production technologies of a

photosensitive matrixPhysical size of a sensor and density

of placement a separate photosensitive elements

Photosensitivity parameter ISO (100, 200, 400, 800, 1600, 3200…)

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Examples of noise at various ISO

ISO 100 ISO 400 ISO 1600 ISO 6400 ISO 12800

Noise in digital images

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Additive Impulse Multiplicative

The analysis showed that in digital images the additive noise prevails. Therefore in a consequence we will consider only the additive noise.

Types of noise

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Noise assessment on images a complex and uncommon task

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100200300400500600700800

Dispersion = 46,66

Signal/noise ratio

Signal/noise = -5 dB

Dispersion of brightness

Noise characteristics

Existing methods of smoothing

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Linear filtering algorithms

Nonparametric methods

Non-Linear filtering algorithms

L = 2m +1 – is moving filter apertureMoving average:

Median filter:

Generalized method of least absolute values (GMLAV) (1,2) :

is a monotone increasing function on the positive half-line

, where

1. Tyrsin A.N. Robust construction of regression models based on the generalized least absolute deviations method // Journal of Mathematical Sciences, 2006, Volume 139, Issue 3, pp. 6634-6642.

2. Tyrsin A. N., Surin V. A. Non-Linear Filtering of Images on the Basis of Generalized Method of Least Absolute Values. CEUR-WS.org. 2014. Vol. 1197. pp. 41-47.

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Experiment

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Noise formation model

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Distribution of noise for various areas of the image on:

Conclusion : For areas near limit of black and white color digital noise has not Gaussian, asymmetric character.

Black border White borderGray scale

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Experimental dataNoise formation model

The schedule of dispersion of noise on areas with various brightness

Areas of the image with various brightness

2.58 25.4 60.69 91.52 127.76 161.91 193.55 225.72 254.640

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Noise model operation

The diagram of brightness for the ideal image

The ideal image of sharp transition from black to white is used in the form of the reference image

Filters:1. Moving average2. Median filter3. GMLAV filterAperture for all filters(B)

Types of apertures :

Let’s investigate effectiveness of three various digital filters when smoothing the image with contrast overfall in the form of sharp transition from black to white by Monte-Carlo method of statistical tests

A B C D I

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Noise model operation

The diagram of brightness for the simulated samples

from the M simulated samples for one sample

Let's simulate M = 1000 samples of n = 50 values (pixels) imitating to jump in brightness from dark to light.

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Filtering

Filter : Moving average Aperture = 5

The diagram of brightness after a filtration by means of averaging

from the M simulated samples for one sample

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Filtering

Filter : Median filter Aperture = 5

The diagram of brightness after a median filtration

from the M simulated samples for one sample

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Filtering

Filter: GMLAV filter Aperture = 5

The diagram of brightness after smoothing on the basis of GMLAV

from the M simulated samples for one sample

)arctg()( xx

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Effectiveness of filters

We build 95% a confidence interval for the M selective dispersions for the received results

n

k

imim kyky

nS

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2)(2, ))(ˆ)((1

where M = 1000, n = 50, i – a type of smoothing ( i=0 – the initial noisy image, i=1 – the image after the linear averaging, i=2 – the image after a median filtration, i=3 – the image after smoothing on the basis of GMLAV), – k-th pixel of the ideal image (contrast overfall without noise), – k-th pixel after a filtration)(ˆ )( ky i

m

)(ky

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Conclusion

1. Process of emergence of the additive noise in digital contrast images has non-linear character.

2. Non-linear nature of noise emergence leads to a spreading of contrast boundaries at images. Besides the distribution law of noise near limits of contrast images becomes not Gaussian even in a case when the additive noise had a normal distribution.

3. Smoothing on the basis of GMLAV of noisy contrast images has essential advantages in comparison with averaging and a median filtration.