computer vision – enhancement(part ii) hanyang university jong-il park

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

Eg.

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AND if),(),( 210

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m E

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

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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

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Spatial LPF, BPF, HPFSpatial LPF, BPF, HPF

Spatialaveraging

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LPF

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

(c) Spatial band-pass filter

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LLBP

LPHP


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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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

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Eg. 1D Median FilteringEg. 1D Median Filtering

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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

Filtered Image

Filter

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

f

)(2)1()1(2

2

xfxfxfx

f


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

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Laplacian OperatorLaplacian Operator

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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)

(2)

(3)

(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

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

Linear Interpolation : first - order hold

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computer vision – enhancement(part ii) hanyang university jong-il park

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hanyang universitydenoising

hanyang universitycf

hanyang universityspatial

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fixed window