DIP Lecture 7 The 2D Discrete Fourier Transform

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ECSE-4540 Intro to Digital Image Processing • Rich Radke, Rensselaer Polytechnic Institute • Lecture 7: The 2D Discrete Fourier Transform (2/23/15) • 0:00:50 The 1-D Fourier Transform • 0:04:36 The 2-D Fourier Transform • 0:10:54 Interpreting the 2D FT decomposition • 0:14:56 The 2D FT basis functions • 0:19:45 Interpreting the 2D FTs of natural images • 0:24:55 Matlab's fftshift • 0:25:50 Artifacts caused by image boundaries • 0:28:52 A lower-frequency image • 0:34:52 An image with strong edges • 0:37:31 A high-frequency image • 0:39:26 Fourier transform properties • 0:44:35 Circular convolution • 0:52:52 Zero padding • 0:59:20 Edge orientations in spatial vs. frequency domains • 1:05:42 Sudoku image example • Follows Sections 4.5-4.6 of the textbook (Gonzalez and Woods, 3rd ed.).

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