Image Processing: Filtering in Frequency Domain
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Questions and Answers

What is the value of F 0,1 in the given table?

  • 2
  • 0
  • 3
  • 1 (correct)
  • What is the value of F 2,2 in the given table?

  • 8 (correct)
  • 10
  • 12
  • 6
  • What is the largest frequency in the given table?

  • 3.2
  • 2.8
  • 3.6
  • 4.2 (correct)
  • What is the power corresponding to the frequency 3.6?

    <p>13</p> Signup and view all the answers

    What percentage of the remaining power is calculated after removing the frequency 4.2?

    <p>96%</p> Signup and view all the answers

    What is the cut-off frequency chosen in the solution?

    <p>4.2</p> Signup and view all the answers

    What is the value of F 1,2 in the given table?

    <p>5</p> Signup and view all the answers

    What is the power calculated by removing the frequency 4.2 and adding the frequencies 3.6?

    <p>338</p> Signup and view all the answers

    What is the value of F 3,2 in the given table?

    <p>13</p> Signup and view all the answers

    What is the percentage of the remaining power calculated after removing the frequency 4.2 and adding the frequencies 3.6?

    <p>84%</p> Signup and view all the answers

    Study Notes

    Filtering in the Frequency Domain

    • Filtering in the frequency domain is possible due to the convolution theorem, which states that a spatial convolution can be performed by element-wise multiplication of the Fourier transform by a suitable filter matrix.

    Ideal Filtering

    • Ideal filtering involves using filters that allow specific frequencies and set other frequencies to zero.
    • Types of ideal filters:
      • Ideal low pass filter: removes noise from the image by filtering out high-frequency components.
      • Ideal high pass filter: highlights fine details in the image by filtering out low-frequency components.

    Ideal Low Pass Filter

    • Expressed by the equation: f(x) = 1 if x ≤ D, 0 if x &gt; D, where D is the cutoff frequency.
    • Only passes frequencies below the cutoff frequency D and replaces all other frequencies with zero.
    • Can be applied by transforming the image from the spatial domain to the frequency domain and then selecting the appropriate cutoff frequency D.
    • Example: A circle with a diameter of 15 can be used as the required matrix for ideal low pass filtering.

    Ideal High Pass Filter

    • Expressed by the equation: f(x) = 1 if x ≥ D, 0 if x &lt; D, where D is the cutoff frequency.
    • Only passes frequencies above the cutoff frequency D and replaces all other frequencies with zero.
    • Can be applied by transforming the image from the spatial domain to the frequency domain and then selecting the appropriate cutoff frequency D.
    • Example: A circle with a diameter of 5 can be used as the required matrix for ideal high pass filtering.

    Example Solutions

    • Solution (1):
      • Calculate the frequency matrix using the equation: f = u^2 + v^2, where u and v are the indices of the elements in the matrix.
      • Apply the ideal low pass filter with a cutoff frequency of 1.99.
      • Resultant matrix: F(0,0) = 1, F(0,1) = 0, F(0,2) = 0, ...
    • Solution (2):
      • Calculate the frequency matrix using the equation: f = u^2 + v^2, where u and v are the indices of the elements in the matrix.
      • Choose the cutoff frequency to be 4.2, which corresponds to a power of 18.
      • The remaining power is 96% after removing the frequency 4.2.

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    Description

    This quiz covers filtering in the frequency domain, including the convolution theorem, types of filtering such as ideal and Butterworth filtering, and their applications in image processing.

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