Image Denoising using Spatial Domain Filters: A Quantitative Study

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,


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


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


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.


Original Image

Add Noise to the image

Corrupted Noisy Image

Apply Filter Get Estimated Original Image


Original Image (Barbara Test Image

512x512)

Addition of Noise

Noise Affected Image

(Corrupted Image)

Estimated Original Image

after Filter Application

Apply Filter


Similarity Measures Peak Signal to Noise Ratio

PSNR =

2D Cross Correlation


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.


Filter Analysis using PSNR for Gaussian Noise


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


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


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


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


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


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


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


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


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


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


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


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


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


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.


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


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.


Thank You.