Notes
Slide Show
Outline
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Image Sampling
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Image Scaling
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Image sub-sampling
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Image sub-sampling
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Even worse for synthetic images
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Sampling and the Nyquist rate
  • Aliasing can arise when you sample a continuous signal or image
    • occurs when your sampling rate is not high enough to capture the amount of detail in your image
    • Can give you the wrong signal/image—an alias
    • formally, the image contains structure at different scales
      • called “frequencies” in the Fourier domain
    • the sampling rate must be high enough to capture the highest frequency in the image
  • To avoid aliasing:
    • sampling rate ≥ 2 * max frequency in the image
      • said another way: ≥ two samples per cycle
    • This minimum sampling rate is called the Nyquist rate
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2D example
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Subsampling with Gaussian pre-filtering
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Subsampling with Gaussian pre-filtering
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Compare with...
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Subsampling with Gaussian pre-filtering
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Some times we want many resolutions
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Gaussian pyramid construction
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Image resampling
  • So far, we considered only power-of-two subsampling
    • What about arbitrary scale reduction?
    • How can we increase the size of the image?
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Image resampling
  • So far, we considered only power-of-two subsampling
    • What about arbitrary scale reduction?
    • How can we increase the size of the image?
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Image resampling
  • So what to do if we don’t know
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Resampling filters
  • What does the 2D version of this hat function look like?
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Bilinear interpolation
  • A simple method for resampling images