Figures from Gonzalez and Woods, Digital Image Processing, Second Edition, 2002.

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Lecture 10

• Figures from Gonzalez and Woods, Digital Image
  Processing, Second Edition, 2002.

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DFT of Laplacian
3
Chapter 4 Image Enhancement in the Frequency
Domain
4
Chapter 4 Image Enhancement in the Frequency
Domain
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High Boost Filtering
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Chapter 4 Image Enhancement in the Frequency
Domain
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A picture from the news

• Before and after Lapacian filter, picture of
  giant squid by
• Japanese scientists

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The tackiest pictures I could find

• Original After Laplacian Filter

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After High Boost Filter

• A1.7 A1.4

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High Frequency Emphasis
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Chapter 4 Image Enhancement in the Frequency
Domain
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Homomorphic Filtering
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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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Properties of the DFT

• Translation
• Distributivity and scaling
• Rotation
• Periodicity and conjugate symmetry
• Separability
• Simplicity of computing inverse

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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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Need for Padding

• Without padding convolutions will not be properly
  implemented.
• f(x) has period A
• h(x) has period B
• g(x) h(x)f(x) has period PgtAB-1

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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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Convolution and Correlation
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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