Image Enhancement using Frequency Domain · 2010. 12. 6. · IMAGE ENHANCEMENT USING Lab Manual 09...

IMAGE ENHANCEMENT USING

Lab Manual 09 G2

IMAGE ENHANCEMENT USING FREQUENCY DOMAIN

Digital Image Processing Fall 2010 [email protected]

FOURIER TRANSFORM


FOURIER TRANSFORM

1D DISCRETE FOURIER TRANSFORM


1D DISCRETE FOURIER TRANSFORM

,.......4,3,2,1,0)(1)(1

2 == ∑−

− uforexfuFM

Mxuj π ,.......4,3,2,1,0)()(0∑=

uforexfM

uFx

θθθ sincos je j += j

( ) ( )[ ]M1 1

∑−

( ) ( )[ ]MuxjMuxxfM

uFx

ππ 2sin2cos)(1)(0

−= ∑=

EXAMPLE


EXAMPLE

]4732[)( =xf

Apply DFT 43210)(1)(1

2 == ∑−

− uforexfuFM

Mxuj πApply DFT ,.......4,3,2,1,0)()(0∑=

uforexfM

uFx

We get

( )( ) ( )( ) ( )( ) ( )( )( )4302420241024002 )()()()(41)0( ππππ jjjj exfexfexfexfF −−−− +++=

We get

4

00004)0( =F 0000.4)0( =F

EXAMPLE CONTINUE


EXAMPLE CONTINUE

( )( ) ( )( ) ( )( ) ( )( )( )4312421241124012 )()()()(1)1( ππππ jjjj ffffF −−−− ( )( ) ( )( ) ( )( ) ( )( )( )4312421241124012 )()()()(4

)1( ππππ jjjj exfexfexfexfF +++=

iF 2500025001)1( = iF 2500.02500.1)1( −−=( )( ) ( )( ) ( )( ) ( )( )( )4322422241224022 )()()()(1)( ππππ jjjj ffff ( )( ) ( )( ) ( )( ) ( )( )( )4322422241224022 )()()()(

41)2( ππππ jjjj exfexfexfexfF −−−− +++=

50000)2( =F 5000.0)2( =F( )( ) ( )( ) ( )( ) ( )( )( )4332423241324032 )()()()(1)3( ππππ jjjj exfexfexfexfF −−−− +++= ( ))()()()(

4)3( exfexfexfexfF +++=

iF 2500025001)3( +−= iF 2500.02500.1)3( +=

EXAMPLE CONTINUE


EXAMPLE CONTINUE

]0.2500i + 1.2500-0.0000i + 0.5000 0.2500i - 1.2500-4.0000[)( =uF

Real Part ]1.2500-0.50001.2500-4.0000[)( =uR

Imaginary Part ]0.25000.00000.2500-0.0000[)( =uI

FOURIER SPECTRUM


FOURIER SPECTRUM

)()()( ujeuFuF ϕ−= )()( euFuF

Magnitude Spectrum of Fourier Transform

( ) ( )22 )()()( uIuRuF += ( ) ( ))()()( uIuRuF +=

Phase Spectrum of Fourier Transform

⎥⎦

⎤⎢⎣

⎡= −

)()(tan)( 1

uRuIuφ

EXAMPLE 2


EXAMPLE 2

2D DFT


2D DFT

1432101,.......,4,3,2,1,0

),(1),(1

0

)(21

0 −=−=

= ∑∑−

+−−

NvMu

forfor

eyxfM

vuFM

MvyMxujN

π

1,.......,4,3,2,1,00 0= = NvforM x y

),()()( vujevuFvuF ϕ−=


),(),( evuFvuF =


( ) ( )22 ),(),(),( vuIvuRvuF +=

Phase Spectrum of Fourier Transform

⎤⎡ )( vuI⎥⎦

⎤⎢⎣

⎡= −

),(),(tan),( 1

vuRvuIvuφ

2D INVERSE DFT


2D INVERSE DFT

1,.......,4,3,2,1,0)()(

1)(2

1 −==∑∑

−+

− MxforevuFyxf

MMvyMuxj

Nπ

1,.......,4,3,2,1,0),(),(

0 0 −==∑∑

= = NyforevuFyxf

u v

SPATIAL VS FREQUENCY DOMAIN


SPATIAL VS FREQUENCY DOMAIN

),(),(),(*),( vuHvuFyxhyxf ↔

FILTERING IN FREQUENCY DOMAIN


FILTERING IN FREQUENCY DOMAIN

TASK 1


TASK 1

1. Program the Discrete Time Fourier Transform(DFT).

2 Take sample images and Calculate DFT2. Take sample images and Calculate DFT.

3. Calculate Magnitude or Spectrum of Fourier and display.

4 Calculate Phase Spectrum and display4. Calculate Phase Spectrum and display.

5. Calculate the Inverse DFT and display.

6 Ob th Ch6. Observe the Changes

TASK 2


TASK 2

1. Take the sample image of cameraman.tif

2 Calculate the DFT Magnitude Spectrum and Phase2. Calculate the DFT, Magnitude Spectrum and Phase.

3. Keep the magnitude same and Change the Phase to zero.

4 Calculate the inverse DFT4. Calculate the inverse DFT.

5. Note the Changes in image.

TASK 3


TASK 3

1. Take the sample image of cameraman.tif

2 Calculate the DFT Magnitude Spectrum and Phase2. Calculate the DFT, Magnitude Spectrum and Phase.

3. Keep the phase same and Change the magnitude unity.

4 Reverse back to the spatial using Inverse DFT4. Reverse back to the spatial using Inverse DFT.

5. Note the Changes in image.

TASK 4


TASK 4

1. Take sample images

2 Take another sample2. Take another sample.

3. Calculate Magnitude or Phase Spectrum of Fourier.

4 Swap the Phase value4. Swap the Phase value

5. Reverse back to the images using Inverse DFT.


TASK 4


TASK 4


2 Take the any smoothing Filter2. Take the any smoothing Filter

3. Calculate DFT of both.

4 Multiple the corresponding values both4. Multiple the corresponding values both.

5. Calculate the inverse DFT of resultant.


TASK 5


TASK 5


2 Take the any Sharpening Filter2. Take the any Sharpening Filter

3. Calculate DFT of both.

4 Multiple the corresponding values both4. Multiple the corresponding values both.



TASK 6


TASK 6

im = zeros(512, 512);im((256-64):(256+64),(256-64):(256+64)) = 1;

1. Calculate DFT of image.

2. Auto correlate the result.


4. Observe the Changes

Image Enhancement using Frequency Domain · 2010. 12. 6. · IMAGE ENHANCEMENT USING Lab Manual 09...

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