Digital Imaging and Processing

  1. Image Enhancement in the Frequency Domain
    1. Fourier Transform Fundamentals
      1. Mathematical Background
        1. Complex Numbers Review
          1. Euler's Formula
            1. Sinusoids and Complex Exponentials
            2. One-Dimensional Fourier Transform
              1. Continuous Fourier Transform
                1. Discrete Fourier Transform
                  1. Inverse Transforms
                  2. Two-Dimensional Fourier Transform
                    1. 2D Continuous Fourier Transform
                      1. 2D Discrete Fourier Transform
                        1. Mathematical Formulation
                          1. Frequency Domain Representation
                          2. Properties of the 2D DFT
                            1. Periodicity and Symmetry
                              1. Linearity
                                1. Scaling
                                  1. Translation
                                    1. Rotation
                                      1. Convolution Theorem
                                        1. Parseval's Theorem
                                        2. Fast Fourier Transform
                                          1. Algorithm Overview
                                            1. Computational Complexity
                                              1. Implementation Considerations
                                            2. Frequency Domain Filtering Concepts
                                              1. Frequency Domain vs Spatial Domain
                                                1. Advantages and Disadvantages
                                                  1. When to Use Each Approach
                                                  2. The Filtering Process
                                                    1. Steps in Frequency Domain Filtering
                                                      1. Zero-Padding
                                                        1. Centering the Transform
                                                          1. Ringing Effects
                                                        2. Low-Pass Filtering
                                                          1. Ideal Low-Pass Filter
                                                            1. Frequency Response
                                                              1. Ringing Artifacts
                                                              2. Butterworth Low-Pass Filter
                                                                1. Smooth Transition
                                                                  1. Order Effects
                                                                  2. Gaussian Low-Pass Filter
                                                                    1. No Ringing
                                                                      1. Parameter Selection
                                                                      2. Applications and Comparisons
                                                                      3. High-Pass Filtering
                                                                        1. Ideal High-Pass Filter
                                                                          1. Frequency Response
                                                                            1. Edge Enhancement
                                                                            2. Butterworth High-Pass Filter
                                                                              1. Smooth Transition
                                                                                1. Parameter Effects
                                                                                2. Gaussian High-Pass Filter
                                                                                  1. Smooth Response
                                                                                  2. High-Frequency Emphasis
                                                                                  3. Selective Filtering
                                                                                    1. Band-Pass Filters
                                                                                      1. Design and Applications
                                                                                        1. Parameter Selection
                                                                                        2. Band-Reject Filters
                                                                                          1. Notch Filters
                                                                                            1. Periodic Noise Removal
                                                                                            2. Homomorphic Filtering
                                                                                              1. Illumination and Reflectance
                                                                                                1. Implementation Steps

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                                                                                            2. Image Enhancement in the Spatial Domain

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                                                                                            4. Image Restoration