Image Denoising using Spatial Domain Filters: A Quantitative StudyAnmol Sharma Dr. Jagroop Singh Undergraduate Engineering Student Associate Professor, ECE DepartmentDAV Institute of Engineering & Technology DAV Institute of Engineering & TechnologyJalandhar, Punjab, India. Jalandhar, Punjab, India.
Problem•Number of Filters available to remove noise. •Performance and correct use of any particular filter for any situation is still a matter of ongoing research.•Knowledge of toolset at hand is essential.
Introduction• Image DenoisingLiterature• Noise Models• Spatial Domain FiltersMethodology• Addition of Noise• Similarity Measures• PSNR• 2D Cross Correlation
ResultsConclusion
Image Denoising•An operation to estimate clean image from a degraded noise affected image.•Noise may be caused due to pixel corruption during acquisition, transmission or compression process. Also due to faulty hardware, poor lighting and motion blur. •Degradation and Restoration problem can be denoted mathematically as –
IntroductionLiteratureMethodologyResultsConclusion
Noise Filters•Essentially inverse degradation models. •When applied to a corrupted image, can estimate the original image. •Divided into two types – Spatial Domain and Transform Domain.•Spatial Domain Filters fairly developed at the moment.•Mathematically,
IntroductionLiteratureMethodologyResultsConclusion
Noise Models Covered•Gaussian Noise or Additive White Gaussian Noise (AWGN)•Salt & Pepper Noise or Impulse Noise•Uniform Noise•Rayleigh Noise•Gamma Noise•Exponential Noise•Poisson Noise
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Spatial Domain FiltersMean Filters•Arithmetic Mean Filter•Geometric Mean Filter•Harmonic Filter•Contra harmonic Filter
Order Statistics or Rank Filters•Median Filter•Minimum and Maximum Filters•Midpoint Filter•Alpha Trimmed Filter
IntroductionLiteratureMethodologyResultsConclusion
Methodology•Noise was added to a grayscale image in a controlled fashion. •Corrupted image was obtained.•The corrupted image was subjected to all the available filters. •The best performing filter was decided according to the similarity measures used. •Process was repeated for all covered noise models.
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Original Image
Add Noise to the image
Corrupted Noisy Image
Apply Filter Get Estimated Original Image
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Original Image (Barbara Test Image
512x512)
Addition of Noise
Noise Affected Image
(Corrupted Image)
Estimated Original Image
after Filter Application
Apply Filter
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Similarity Measures Peak Signal to Noise Ratio
PSNR =
2D Cross Correlation
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Results•The simulations were performed in MATLAB. •Data was recorded in the form of tables and represented using graphs. •The filters scoring the highest value of PSNR as well as 2D Cross Correlation value was declared to be the best filter for that noise model.
IntroductionLiteratureMethodologyResultsConclusion
Filter Analysis using PSNR for Gaussian Noise
IntroductionLiteratureMethodologyResultsConclusion
Arithmeti
c
Geometr
ic
Harmonic
Contraharm
oic
Median Min
Max
Midpoint
Alpha Trim
med
24.87 24.84 24.48 24.53 25.06
17.6 18.05
23.88 23.07
Gaussian
Filter Analysis using 2D Cross Correlation for Gaussian Noise
IntroductionLiteratureMethodologyResultsConclusion
Arithmeti
c
Geometr
ic
Harmonic
Contraharm
oic
Median Min
Max
Midpoint
Alpha Trim
med
0.9639 0.9639 0.9622 0.96260.9654
0.922 0.922
0.9544
0.9447
Gaussian
IntroductionLiteratureMethodologyResultsConclusion
Arithmeti
c
Geometr
ic
Harmonic
Contraharm
onic
Median Min
Max
Midpoint
Alpha Trim
med
23.75 24.47
14.41
21.04
25.25
19.32
0
17.44
23.07
Salt & Pepper
Filter Analysis using PSNR for Salt & Pepper Noise
IntroductionLiteratureMethodologyResultsConclusion
Arithmeti
c
Geometr
ic
Harmonic
Contraharm
onic
Median Min
Max
Midpoint
Alpha Trim
med
0.9531 0.9607
0.7025
0.91390.9669
0.8931
0
0.7994
0.9448
Salt & Pepper
Filter analysis using 2D Cross Correlation for Salt & Pepper Noise
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Arithmeti
c
Geometr
ic
Harmonic
Contraharm
onic
Median Min
Max
Midpoint
Alpha Trim
med
15.97 16.1 16.36 16.05 15.95
18.85
12.07
15.83 15.72
Uniform
Filter analysis using PSNR for Uniform Noise
IntroductionLiteratureMethodologyResultsConclusion
Arithmeti
c
Geometr
ic
Harmonic
Contraharm
onic
Median Min
Max
Midpoint
Alpha Trim
med
0.9624 0.9648 0.9645
0.931
0.9652 0.9655
0.9196
0.9522
0.9425
Uniform
Filter analysis using 2D Cross Correlation for Uniform Noise
IntroductionLiteratureMethodologyResultsConclusion
Arithmeti
c
Geometr
ic
Harmonic
Contraharm
onic
Median Min
Max
Midpoint
Alpha Trim
med
17.21 17.55 18.04 17.57 17.37
20.53
11.34
16.57 17.06
Rayleigh
Filter analysis using PSNR for Rayleigh Noise
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Arithmeti
c
Geometr
ic
Harmonic
Contraharm
onic
Median Min
Max
Midpoint
Alpha Trim
med
0.9585 0.9606 0.9601
0.9308
0.95760.9608
0.9107
0.94650.941
Rayleigh
Filter analysis using 2D Cross Correlation for Rayleigh Noise
IntroductionLiteratureMethodologyResultsConclusion
Arithmeti
c
Geometr
ic
Harmonic
Contraharm
onic
Median Min
Max
Midpoint
Alpha Trim
med
19.86
22.7623.97
22.3
24.74
18.59
9.9
13.12
22.84
Gamma
Filter analysis using PSNR for Gamma Noise
IntroductionLiteratureMethodologyResultsConclusion
Arithmeti
c
Geometr
ic
Harmonic
Contraharm
onic
Median Min
Max
Midpoint
Alpha Trim
med
0.91220.95 0.9575 0.9367 0.9639
0.8962
0.6034
0.6998
0.9432
Gamma
Filter analysis using 2D Cross Correlation for Gamma Noise
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Arithmeti
c
Geometr
ic
Harmonic
Contraharm
onic
Median Min
Max
Midpoint
Alpha Trim
med
18.54 19.2620.07 19.33 19.6 20.07
10.25
16
18.96
Exponential
Filter analysis using PSNR for Exponential Noise
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Arithmeti
c
Geometr
ic
Harmonic
Contraharm
onic
Median Min
Max
Midpoint
Alpha Trim
med
0.9517 0.9561 0.9569
0.9312
0.9519
0.9035
0.8346
0.9165
0.9395
Exponential
Filter analysis using 2D Cross Correlation for Exponential Noise
IntroductionLiteratureMethodologyResultsConclusion
Arithmeti
c
Geometr
ic
Harmonic
Contraharm
onic
Median Min
Max
Midpoint
Alpha Trim
med
22.4424.12 24.53
22.67
25.32
18.41
11.81
14.75
23.1
Poisson
Filter analysis using PSNR for Poisson Noise
IntroductionLiteratureMethodologyResultsConclusion
Arithmeti
c
Geometr
ic
Harmonic
Contraharm
onic
Median Min
Max
Midpoint
Alpha Trim
med
0.9405 0.9574 0.9609 0.9407 0.96740.8943
0.6313
0.7336
0.9451
Poisson
Filter analysis using 2D Cross Correlation for Poisson Noise
Conclusion•Noise parameters were changed and various combinations tested to confirm results.•Number of filter parameters were tested, but the parameter with best results was used. •The procedure and tests were applied to other benchmark images like “Cameraman” and “Pout” to validate results.
IntroductionLiteratureMethodologyResultsConclusion
Noise Model Best Filter
Gaussian Noise Median Filter
Salt & Pepper Median Filter
Uniform Noise Minimum Filter
Rayleigh Noise Minimum Filter
Gamma Noise Median Filter
Exponential Noise Harmonic Mean Filter
Poisson Noise Median Filter
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Future Work•More generalised results are to be evaluated for each noise model, not just for any specific noise density levels. •Filter performance will be evaluated on images corrupted with more than one type of noise model. •A new unsupervised adaptive filter is in works based on median filter which would identify the noise model & density and calibrate it’s parameters accordingly.
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Thank You.