Image Enhancement in the

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Chapter 4 Image Enhancement in the Frequency
Domain
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Chapter 4 Image Enhancement in the Frequency
Domain
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Chapter 4 Image Enhancement in the Frequency
Domain
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Chapter 4 Image Enhancement in the Frequency
Domain
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Chapter 4 Image Enhancement in the Frequency
Domain
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Chapter 4 Image Enhancement in the Frequency
Domain
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Chapter 4 Image Enhancement in the Frequency
Domain
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Chapter 4 Image Enhancement in the Frequency
Domain
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Chapter 4 Image Enhancement in the Frequency
Domain
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Chapter 4 Image Enhancement in the Frequency
Domain
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Chapter 4 Image Enhancement in the Frequency
Domain
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Chapter 4 Image Enhancement in the Frequency
Domain
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Chapter 4 Image Enhancement in the Frequency
Domain
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Chapter 4 Image Enhancement in the Frequency
Domain
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Chapter 4 Image Enhancement in the Frequency
Domain
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Chapter 4 Image Enhancement in the Frequency
Domain
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Chapter 4 Image Enhancement in the Frequency
Domain
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Chapter 4 Image Enhancement in the Frequency
Domain
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DFT in Matlab
Compute DFT gtgt f imread(center_bump.tif) gtgt
F fft2(f) gtgt S abs(F) gtgtimshow(S,)
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Centering DFT

• gtgt Fcfftshift(F)
• gtgt imshow(abs(Fc),)

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Sharpening by Log Transform

• gtgt S2log(1abs(Fc))
• gtgt imshow(S2,)

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From DFT back to signal

• gtgt Fifftshift(Fc)
• gtgt fifft2(F)
• gtgt freal(ifft2(F))

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Basic Frequency Filtering

• gtgt fimread(square_original.tif)
• gtgt M,Nsize(f)
• gtgt Ffft2(f)
• gtgt sig10
• gtgt Hlpfilter(gaussian,M,N,sig)
• gtgt GH.F
• gtgt greal(ifft2(G))
• gtgt imshow(g,)

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Chapter 4 Frequency Domain (the need for padding)
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Chapter 4 Frequency Domain (the need for padding)
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Chapter 4 Frequency Domain (why padding)
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Chapter 4 Image Enhancement in the Frequency
Domain
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Chapter 4 Image Enhancement in the Frequency
Domain
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Chapter 4 Image Enhancement in the Frequency
Domain
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Chapter 4 Frequency Domain Processing
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Chapter 4 Frequency Domain Processing
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Chapter 4 Frequency Domain Processing
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Chapter 4 Frequency Domain Processing
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Padding in Practice

• Assume images f(x,y) h(x,y) of sizes A B and
  C D
• Form two padded functions of size P Q by
  appending zeros to f and g. You can show that
  wraparound error is avoided by
• choosing
• P ? A C - 1
• and
• Y ? B D - 1
• For special case of f(x,y) h(x,y) of the same
  size, M N, we pad with
• P ? 2M - 1 and Q ? 2N - 1

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Padding in Practice

• gtgt PQpaddedsize(size(f))
• Compute the FFT with padding.
• gtgt Fpfft2(f,PQ(1),PQ(2))
• gtgt Hplpfilter(gaussian,PQ(1),PQ(2),2sig)
• gtgt GpHp.Fp
• gtgt gpreal(ifft2(Gp))
• gtgt gpcgp(1size(f,1),1size(f,2))
• gtgt imshow(gp,)
• gtgt imshow(gpc,)

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Chapter 4 Image Enhancement in the Frequency
Domain
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Chapter 4 Image Enhancement in the Frequency
Domain
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Chapter 4 Image Enhancement in the Frequency
Domain
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Chapter 4 Image Enhancement in the Frequency
Domain
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Chapter 4 Image Enhancement in the Frequency
Domain
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Chapter 4 Image Enhancement in the Frequency
Domain
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Chapter 4 Image Enhancement in the Frequency
Domain
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Chapter 4 Image Enhancement in the Frequency
Domain
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Chapter 4 Image Enhancement in the Frequency
Domain
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Chapter 4 Image Enhancement in the Frequency
Domain
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Chapter 4 Image Enhancement in the Frequency
Domain
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Chapter 4 Image Enhancement in the Frequency
Domain
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Chapter 4 Image Enhancement in the Frequency
Domain
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Chapter 4 Image Enhancement in the Frequency
Domain
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Chapter 4 Image Enhancement in the Frequency
Domain
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Chapter 4 Image Enhancement in the Frequency
Domain
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Chapter 4 Image Enhancement in the Frequency
Domain
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Chapter 4 Image Enhancement in the Frequency
Domain
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Chapter 4 Image Enhancement in the Frequency
Domain
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Chapter 4 Image Enhancement in the Frequency
Domain
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Chapter 4 Image Enhancement in the Frequency
Domain
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Chapter 4 Image Enhancement in the Frequency
Domain
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Chapter 4 Image Enhancement in the Frequency
Domain
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Chapter 4 Image Enhancement in the Frequency
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Chapter 4 Image Enhancement in the Frequency
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Chapter 4 Image Enhancement in the Frequency
Domain