DIP_quiz_2 - Transform domain processing

Q1 Circular convolution

  • Difference between linear(full) convolution, circular convolution and periodical convolution
    • Linear convolution: the final length will be equal to M+N-1 and directly use the multiplication formula
    • Circular convolution: the final length will be equal to the original length L
        1. use linear convolution to simulate by removing the addition lower bits to the target higher ones
        1. the conv item can be seen as the periodic signal and then we can continualy move it to conv with the conved one to get the final result. Therefore we can simplify this process as a matrix multiplication. And each column is one specific state of the conv item.
    • Periodical convolution: The periodical form of circular convolution.
  • Example
    quiz
  • How to avoid wraparound problem
    • – padding zeros

Q2 Morphological processing

  • dialation and erosion operation

Q3 Image domain transformation

  • Special case – 2D FT of cos function
    • Use Euler formula, and 2D FT definition
  • FB formula
    • radon transform, and differentiation and integration

Q4 White balance

  • Basic calculation about color processing