image enhancement in spatial domain

5/28/2018 image enhancement in spatial domain

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Image Enhancement

(Spatial Domain Methods)


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What Is Image Enhancement?

Image enhancement is the process of making

images more useful

The reasons for doing this include:

Highlighting interesting detail in images

Removing noise from images

Making images more visually appealing


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Image Enhancement

Enhance otherwise hidden information Filter important image features

Discard unimportant image features Emphasize, sharpen or smoothen image

features


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Classification of Image enhancement

Spatial Domain

Process intensity of pixels

Two types- intensity transformation and spatialfiltering

Transform Domain

Transform image, process it and then find inversetransform to get image in spatial domain


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Basic of Spatial Domain Filtering

Origin y

x Image f (x, y)

(x, y)

g (x, y) = T[ f (x, y)]

f (x, y)is the

input image

g (x, y)is

the processed image

and Tis operator definedover some neighbourhood

of (x, y)


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Point Processing

Point processing operations take the form

s = T ( r )

srefers to the processed image pixel value and rrefers to the original image pixel value

Tis referred to as agrey level transformation function

or apoint processing operationf(x,y) g(x,y)


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Spatial Domain

The operator T can be defined over

The set of pixels (x,y) of the image

The set of neighborhoods, N(x,y) ofeach pixel


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Point operation

Mask operation

Global operation

Classification of spatial domain


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Brightness modification

Contrast manipulation

Histogram manipulation

Point operation


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Operation on the set of image-pixels

6 8 2 0

12 200 20 10

3 4 1 0

6 100 10 5

Spatial Domain

(Operator: Div. by 2)


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Operation on the set of neighborhood

6 8 2 0

12 200 20 10

226

Spatial Domain

6 8

12 200

(Operator: sum)


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Global Operation

6 8 2 0

12 200 20 10

Spatial Domain

5 5 1 0

2 20 3 4

11 13 3 0

14 220 23 14

(Operator: sum)


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Gray Level/Intensity Transformations

Brightness modification

Image negatives Piecewise-Linear transformationFunctions

Log transformations Power Law transformations

Transformations


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Intensity Level Transformations

Linear

Negative/Identity

Logarithmic

Log/Inverse log

Power law

nth

power/nth

root


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Suited for enhancing white or grey detail embedded indark region and black area predominates

Image Negative

Input gray level

O

utputgraylev

el g(x,y)= 255- f(x,y)


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Logarithmic Transformations

The log transformation maps a narrow range of low

input grey level values into a wider range of output

values

The inverse log transformation performs theopposite transformation

g(x,y) = c * log (1+ f(x,y))


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Log Transformations

InvLog Log

Input grey level values has large range of values

T f i


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Log Transformations

Logarithm of FT reveals more details

Range, 0 to 106becomes 0 to 6.2

P L T f ti


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Power Law Transformations

T(f) = c*f

f


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> 1

Compresses dark values Expands bright values

< 1 Expands dark values Compresses bright values

Transformations


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Power Law Transformations

s = c * r

Map a narrow range of dark input values into awider range of output values or vice versa

Varying gives a whole family of curves


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Application of gamma correction

A cathode ray tube (CRT) converts a video signal

to light in a nonlinear way.

The light intensityIis proportional to a power ()

of the source voltage V, (I=V)

For a computer CRT, is about 2.2

To view image on monitors -correction is required

Application of gamma correction


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Application of gamma-correction


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Power Law Example

Magnetic Resonance

(MR) image of a

fractured human

spine


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Power Law Example ( = 0.6)

= 0.6

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.2 0.4 0.6 0.8 1

Old Intensities

TransformedInte

nsities

l ( )


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= 0.4

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.2 0.4 0.6 0.8 1

Original Intensities

TransformedIntensities


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= 0.3

0

0.1

0.2

0.3

0.4

0.5

0.60.7

0.8

0.9

1

0 0.2 0.4 0.6 0.8 1


TransformedInten

sities

P L E l ( )


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Power Law Example (cont)

s = r 0.6

s=

r0.4

Power Law Example


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Power Law Example

(Image with washed out appearance)

An aerial view

of a runway


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Image after gamma correction (> 1)

= 5.0

0

0.1

0.2

0.3

0.4

0.5

0.60.7

0.8

0.9

1

0 0.2 0.4 0.6 0.8 1


TransformedInten

sities


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Different

curves

highlight

different

detail

s = r 3.0

s=

r4.0

Brightness/contrast modification


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Brightness/contrast modification

g(m,n) = f(m,n) + k (increase brightness)

g(m,n) = f(m,n)k (decrease brightness)

Piecewise Linear Transformations


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Thresholding Function

g(x,y) = L-1, f(x,y) > t

= 0, f(x,y) < t

t = threshold level

Piecewise Linear Transformations

Input gray level

Outputg

raylevel

Thresholding


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Thresholding

Thresholding transformations are particularly useful

for segmentation in which we want to isolate an

object of interest from a background

s =1.0

0.0 r threshold

Contrast stretching


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Contrast stretching

Gray/Intensity Level Slicing


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Highlight a specific range of gray values

Two approaches:

Display high value for range of interest, lowvalue else (discard background)

Display high value for range of interest,original value else (preserve background)

y y g

Gray Level Slicing, example


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y g, p


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Bit Plane Slicing

Isolate particular bits ofintensity value

Shows contribution of

each bit

Higher-order bits usually

contain most of the

significant visual

informationLower-order bits

contain subtle details

Intensity= (b7b6b5b4b3b2b1b0)


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y 6 5 3 0

BP 7

BP 5

BP 0

Bit Plane Slicing (example)


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Bit Plane Slicing (example)

Intensity= (b7

b6

b5

b4

b3

b2

b1

b0

)


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Bit Plane Slicing (plane 1)

i l Sli i ( l 2)


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Bi Pl Sli i ( l 3)


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Bi Pl Sli i ( l 4)


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Bit Pl Sli i ( l 5)


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Bit Pl Sli i ( l 6)


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Bit Pl Sli i ( l 7)


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Bit Pl Sli i ( l 8)


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Bit Plane Slicing (cont )


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Bit Plane Slicing (cont)

Reconstructed image

using only bit planes 8

and 7

Reconstructed image

using only bit planes 8, 7

and 6

Reconstructed image

using only bit planes 7, 6

and 5

Histogram


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gray level

Number

ofPixels

0 1 2 3

1 3 0 1

4

1 2

5

Plot of number of occurrences of grey levels against

grey level values

Histogram of image


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Histogram Examples


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g p

Histogram Examples (cont)


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g p ( )

Histogram Examples (cont)


54/68Histogram Examples (cont)


55/68Histogram Examples (cont)


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High contrast

image has the mostevenly spaced histogram

Histogram Equalization


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Equal number of pixels for every gray-value Histogram is constant Preprocessing technique to enhance contrast in

natural images

Find gray level transformation function T to transformimage f such that the histogram of T(f) is equalized

Spreading out the frequencies in an image (orequalising the image) improves dark or washed out

images

Equalisation Transformation Function


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rk:input intensity

sk:processed intensity k: the intensity range

nj:the frequency of intensityj

n: the sum of all frequencies

)( kk rTs

k

j

jj rp1

)(

k

j

j

n

n

1

Histogram Equalisation


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Spread out gray levels to evenly distributein the range

Find cumulative frequency distribution Normalize by dividing by total number ofpixels

Multiply by maximum gray value

Map gray levels

Equalisation Transformation Functions


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Histogram Equalization


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Mean value (or average gray level)


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m = irip(ri)

=1*0.3+2*0.1+3*0.2+4*0.1+5*0.2+6*0.1=2.6

Mean value represents overall brightness

P(r)

0.3

0.2

0.1

0.01 2 3 4 5 6 r

Variance


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gives a measure of the distribution of

histogram values around the mean

0.3

0.2

0.1

0.0

0.3

0.2

0.10.0

V1 =3.34 V2=0.24

v = 2= i(ri-m)2p(ri) M=2.6, v1=(1-2.6)2x0.3+

Standard Deviation

A l th l l i h i


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A value on the gray level axis, showing average

distance of all pixels to the mean

0.3

0.2

0.1

0.0

0.3

0.2

0.1

0.0

D1 > D2

= sqrt(v)

Histograms

V i d St d d D i ti f th


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Variance and Standard Deviation of the

histogram represent average contrast of the

image

The higher the Variance (=the higher the

Standard Deviation), the higher the imagescontrast

Histograms

Hi t ith d St d d d i ti


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Histograms with mean and Standard deviation

M=0.73 D=0.32 M=0.71 D=0.27

image enhancement in spatial domain

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