Research of properties of digital noise in contrast images

1. 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

2. Noise in digital images
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Depends from:
Production technologies of a
photosensitive matrix
Physical size of a sensor and density
of placement a separate
photosensitive elements
Photosensitivity parameter ISO (100, 200, 400, 800, 1600, 3200…)

3. 3
Examples of noise at various ISO
ISO 100 ISO 400 ISO 1600 ISO 6400 ISO 12800
Noise in digital images

4. 4
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

5. 5
Noise assessment on images a complex and uncommon task
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Dispersion = 46,66
Signal/noise ratio
Signal/noise = -5 dB
Dispersion of brightness
Noise characteristics

6. 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.

7. 7
Experiment

8. 8
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

9. 9
Experimental data
Noise formation model
The schedule of dispersion
of noise on areas with
various brightness
Areas of the image with various brightness
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2.58 25.4 60.69 91.52 127.76 161.91 193.55 225.72 254.64

10. 10
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 average
2. Median filter
3. GMLAV filter
Aperture 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

11. 11
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.

12. 12
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

13. 13
Filtering
Filter : Median filter Aperture = 5
The diagram of brightness after a median filtration
from the M simulated samples for one sample

14. 14
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 

15. 15
Effectiveness of filters
We build 95% a confidence interval for the M selective
dispersions for the received results


n
k
i
mim kyky
n
S
1
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

16. 16
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.