chapter 2-part3- enhancement by mask

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Chapter 2 :Enhancement

Part : Enhancement by Mask

Dr. Hojeij youssef

Digital image processing

1

Convolution : each pixel is replaced by the weight values of its neighborhoodpixels . that is :

Whereu &v aretheweight of theusing mask(filter)

Filtering by convolution

Dr. Hojeij youssef 2

u v

'

'

)v ,u( filter )v j ,ui( I ) j ,i( I

) j ,i( filtre) j ,i( I ) j ,i( I



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Smoothing filter : Here each pixel is replaced by the weight averaging of its

neighborhood pixels

Only the low frequency range past

Thereis many size of averaging filter :3×3, 5×5, 7×7, …

Averaging filtering


0 0 0

0 0.11 0

0 0 0

1 1 1

1 1 1

1 1 1

TF1/9×

S.F :3×3 S.F : 5×5OrigineImage

Gaussian filter :

σ Small then limited smoothing σ large then more smoothing

Averaging filtering


222

22 / y xexp

2

1) y , x( filter

1 2 2 2 1

2 7 11 7 2

3 11 17 1 1 3

2 7 11 7 2

1 2 3 2 1

1 1 1 2 2 2 2 2 1 1 1

1 2 2 3 4 4 4 3 2 2 1

1 2 4 5 6 7 6 5 4 2 1

2 3 5 7 8 9 8 7 5 3 2

2 4 6 8 10 11 10 8 6 4 2

2 4 7 9 11 12 11 9 7 4 2

2 4 6 8 10 11 10 8 6 4 2

2 3 5 7 8 9 8 7 5 3 2

1 1 4 5 6 7 6 5 4 2 1

1 2 2 3 4 4 4 3 2 2 1

1 1 1 2 2 2 2 2 1 1 1

σ=0.625 (5×5) σ=1.6 (11×11)



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Exponential filter:

σ Small then limited smoothing σ large then more smoothing

Averaging filtering


) y x(exp4

) y , x( filter 2

Directional smoothing : to protect the edges fromblurring while smoothing.A directional filter can be useful. Spatial averagefilter(i,j: ө ) are calculateinserval direction as :

Averaging filtering


)v ,u( W

)v j ,ui( I N

1): j ,i( I ˆ

u

v

ө

0W



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Median filtering : Here the input pixel is replaced by the median of the pixels

contained in the windows around the pixel that is :

WhereW is thesuitablychosenwindowsthealgorithmformedianfilteringrequiresarrangingthepixel valuesin thewindowsfor increasingordecreasingorder andpickingthemiddlevalue. Generallythewindowssizeischoosingsowthat N w isodd. if N w is eventhenthemedian is takenastheaverageof thetwo values in themiddle

Median Filtering


W )v ,u(),v j ,ui( I median) j ,i( I ̂

Low degreeof intensitynoise

3×3 median filtering 5×5 median filtering

Examples :


Noisy Image 3×3 median filter 3×3 averaging filter

Noisy Image 3×3 Gaussian filter 3×3 median filter 3×3 averaging



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Zero interlace→ Convolve

Zoom


6 54

231

000000

06 0504

000000

020301

6 6 5544

6 6 5544

223311

223311

ZeroInterlace

Convolve

Zero interlace→ Rows and columns interpolate

Zoom


54

31

0000

0504

0000

0301

0000

5.255.34

0000

5.1321

ZeroInterlace

Interpolaterows

25.15.275.12

5.255.34

2475.25.2

5.1321

InterpolateColumns



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Inadditionto therequirementof monochromeimageenhancement,color

imageenhancement manyrequireimprovement of color balanceor colorcontract in acolor image. Enhancement of color imagesbecomesamoredifficult task not only becauseof added dimensionsof thedatabut alsodueto theaddedcomplexity of color perception. A practical approachtodevelopingcolor imageenhancementalgorithmsisshownbelow

Color image enhancement


An ideal high-pass filter is1in which its frequency response is given by :

• r(u,v) is theradial f requency thedistancefromtheorigin to thepoint(u,v)

Gaussian Filtering


else0

B)v ,u(r 1)v ,u( H

22 vu)v ,u(r

tetancons positiveais B

022

022

Rvu0

Rvu1)v ,u( H

chapter 2-part3- enhancement by mask

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