Computer Vision – Enhancement(Part II) Hanyang University Jong-Il Park.

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Computer Vision – Computer Vision – Enhancement(Part II)Enhancement(Part II)

Hanyang University

Jong-Il Park

Department of Computer Science and Engineering, Hanyang University

Local EnhancementLocal Enhancement

Global enhancement The same operation for all pixels

Local enhancement Different operation for each pixel According to the statistics of local support

Local Histogram EqualizationLocal Histogram Equalization

Using a fixed window at each point Computationally expensive

Histogram equalization at each point

Use of statistics of local supportUse of statistics of local support

otherwise ),(

AND if),(),( 210

DkDkMkmyxfEyxg GGG

Enhancedimage

Originalimage

Spatial OperationsSpatial Operations

Spatial averaging and spatial LPF for noise smoothing

Inputimage *

output

Spatial mask( 33, 55, )

Spatial MaskSpatial Mask

Spatial AveragingSpatial Averaging

Mean-filtering

Noise reduction

),(),(),(lk W

lnkmylkanmv

),(),(),( nmnmunmv ),0(~),( 2 Nnm

),(),(1

),(lk Ww

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nmv wN

wNwhereNnm

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1212,1

, :filter weight equal

tscoefficienfilter :,

Spatial Averaging MaskSpatial Averaging Mask

Spatial averaging masks a(k,l)

Disadvantage : blurring

Effect of window sizeEffect of window size

Eg. Spatial Averaging(1)Eg. Spatial Averaging(1)

Eg. Spatial Averaging(2)Eg. Spatial Averaging(2)

Original image Averaging 후의 image

Cf. Multi-imageCf. Multi-image averagingaveraging

Spatial Operations - FilteringSpatial Operations - Filtering

Parametric Low Pass Filter

but to preserve the mean

Spatial LPF, BPF, HPFSpatial LPF, BPF, HPF

Spatialaveraging

),( nmu ),( nmVLP

),( nmVHP),( nmu

+),( nmVBP),( nmu

(a) Spatial low-pass filter (b) Spatial high-pass filter

(c) Spatial band-pass filter

),(),(),(

21nmhnmhnmh

nmhnmnmh

Original image Lowpass Filter 된 후의 image

Eg. Spatial LPFEg. Spatial LPF

Spatial High-Pass FilteringSpatial High-Pass Filtering

Original image Highpass filtered image

Eg. Spatial HPFEg. Spatial HPF

Original image Lowpass Filter(Short Term) =A

Lowpass Filter(Long Term) =B

Bandpass Filter 된 후의 Image =B-A

Spatial Band-Pass FilteringSpatial Band-Pass Filtering

Denoising by LPFDenoising by LPF

Noisy! Blurred! Trade-off?

Directional SmoothingDirectional Smoothing

Directional Smoothing to protect the edges from blurring while smoothing

):,(),(

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lnkmyN

nmvlk W

|):,(),(|min

nmvnmythatsuch

outFind

direction severalin calculated are ,, averages spatial nmv

Original image Lowpass Filter(Long Term)

Direc. Smoothing ( 대각선 ) Direc. Smoothing ( 수 직 )

Eg. Directional SmoothingEg. Directional Smoothing

Median FilteringMedian Filtering

Median Filter

Properties nonlinear filter

Example

( , ) { ( , ), ( , ) }

filter length should be odd number

v m n median y m k n l k l W

)}({)}({)}()({ mymedianmxmedianmymxmedian

scomparisonNoperationsofNumber W 8/)1(3 2

2,3,8,4,2 , 3 1 median filter

0 2 boundary value , 1 2,3,8 3

2 3,8,4 4, 3 8,4,2 4

5 2 boundary value

2,3,4,4,2

v v median

v median v median

Eg. 1D Median FilteringEg. 1D Median Filtering

Discussion – Median filterDiscussion – Median filter

1) median filter preserve discontinuities in a step function

2) smooth a few pixels whose values differ significantly from the surrounding, without affecting the other pixels.

3) pulse function, whose width is less than one half the filter length, are suppressed

2D Median Filtering2D Median Filtering

Original Image

Filtered Image

Filter

Eg. Median FilteringEg. Median Filtering

Original 7x7 Median filtered image

Salt-and-pepper noise(=impulsive noise)

Excellent performance!

Eg. Median Filter – Impulsive NoiseEg. Median Filter – Impulsive Noise

Eg. Median Filter – Gaussian NoiseEg. Median Filter – Gaussian Noise

Moderate performance

Various patterns for median filterVarious patterns for median filter

Neighborhood patterns used for median filtering

Eg. Median filter – Square patternEg. Median filter – Square pattern

Original image 10% black, 10% white

Median filtering using 3 by 3 square region

Median filtering using 5 by 5 square region

Eg. Median filter – Octagon patternEg. Median filter – Octagon pattern

Original image 5 by 5 octagonal median filter

Eg. Median filter – Reconstruction Eg. Median filter – Reconstruction

Original image Median filtering and color compensation

Sharpening ImagesSharpening Images

Emphasis of high-frequency components Usually exploiting 1st order derivative and 2nd order

derivatives

1D derivatives 1st order derivative:

2nd order derivative:

)()1( xfxfx

)(2)1()1(2

xfxfxfx

Eg. 1st & 2nd order derivativesEg. 1st & 2nd order derivatives

Observation on derivativesObservation on derivatives

2nd order derivative Thinner edges Stronger response to fine details Weaker response to a gray-level step Double response at step changes Intensity of response: point > line > step

The 2nd order derivative is better suited than the 1st order derivative for image enhancement.

Laplacian Operator – Derivation Laplacian Operator – Derivation

The simplest isotropic derivative operator

),(2)1,()1,(),(

),(2),1(),1(

)],1(),([)],(),1([

),(),1(),(

jifjifjifjif

jifjifjif

jifjifjifjif

jifjifjif

),(4)]1,()1,(),1(),1([

),(),(),( 222

jifjifjifjifjif

jifjifjif yx

Laplacian OperatorLaplacian Operator

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00010000100

55554321000)

Sharpening by Laplacian operatorSharpening by Laplacian operator

Eg. SharpeningEg. Sharpening

Original SEM image Laplacian operator Subtraction of the Laplacian from the original

Original image Laplacian operator Subtraction of the Laplacian from the original

Composite Laplacian maskComposite Laplacian mask

Signal

Low-pass

High-pass(1)

(1)+(3)

))1,(),1()1,(),1((4

1),(),(

)(:),(

0),,(),(),(

nmunmunmunmunmunmg

filteredpasshighoutputLaplaciannmgwhere

nmgnmunmv

Unsharp masking and CrispeningUnsharp masking and Crispening

Unsharp mask applicationUnsharp mask application

Original image Processed image

High-boost filteringHigh-boost filtering

Let g(n1, n2) = u(n1, n2) - uL(n1, n2)

v(n1, n2) = u(n1, n2) + k g(n1, n2)

k=1: Unsharp Masking Crispening an image

k>1: High-boost filtering edge or line details to be emphasized

Eg. High-boost filteringEg. High-boost filtering

Zoom(1:2 magnification) revisitedZoom(1:2 magnification) revisited

Nearest neighbor=Replication = zero - order hold

column, row zero-padding

Zoom revisited(cont.)Zoom revisited(cont.)

Linear Interpolation : first - order hold

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5.0123

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5.0123

5.3741

Computer Vision – Enhancement(Part II) Hanyang University Jong-Il Park.

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