CAP5415 Computer Vision Spring 2003

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CAP5415 Computer VisionSpring 2003

• Khurram Hassan-Shafique

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Image Filtering

• Modifying the pixels in an image based on some
  function of a local neighborhood of the pixels

p
10 30 10
20 11 20
11 9 1

5.7

N(p)
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Linear Filtering

• The output is the linear combination of the
  neighborhood pixels
• The coefficients of this linear combination
  combine to form the filter-kernel

1 3 0
2 10 2
4 1 1
1 0 -1
1 0.1 -1
1 0 -1

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Kernel
Filter Output
Image
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Convolution
H7 H8 H9
H4 H5 H6
H1 H2 H3
H1 H2 H3
H4 H5 H6
H7 H8 H9
H9 H8 H7
H6 H5 H4
H3 H2 H1
I1 I2 I3
I4 I5 I6
I7 I8 I9
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Linear Filtering
0 0 0
0 1 0
0 0 0
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Linear Filtering
0 0 0
0 0 1
0 0 0
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Linear Filtering
1 1 1
1 1 1
1 1 1
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Linear Filtering
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
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Gaussian Filter
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Linear Filtering(Gaussian Filter)
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Gaussian Vs Average
Smoothing by Averaging
Gaussian Smoothing
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Noise Filtering
After Averaging
Gaussian Noise
After Gaussian Smoothing
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Noise Filtering
After Averaging
Salt Pepper Noise
After Gaussian Smoothing
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Shift Invariant Linear Systems

• Superposition
• Scaling
• Shift Invariance

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Fourier Transform
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Here u v are larger than the previous slide
Larger than the upper example
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Cheetah Image Fourier Magnitude (above) Fourier
Phase (below)
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Zebra Image Fourier Magnitude (above) Fourier
Phase (below)
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Reconstruction with Zebra phase, Cheetah Magnitude
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Reconstruction with Cheetah phase, Zebra Magnitude
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Suggested Reading

• Chapter 7, David A. Forsyth and Jean Ponce,
  "Computer Vision A Modern Approach"