Image Processing

  1. Frequency Domain Processing
    1. The Fourier Transform
      1. One-Dimensional Fourier Transform
        1. Continuous Fourier Transform
          1. Discrete Fourier Transform
            1. Properties and Interpretation
            2. Two-Dimensional Discrete Fourier Transform
              1. Mathematical Formulation
                1. Forward Transform
                  1. Inverse Transform
                    1. Implementation for Images
                    2. Properties of the 2D DFT
                      1. Periodicity
                        1. Symmetry Properties
                          1. Translation Property
                            1. Rotation Property
                              1. Scaling Property
                                1. Linearity
                                  1. The Convolution Theorem
                                    1. Spatial Convolution as Frequency Multiplication
                                      1. Computational Advantages
                                  2. The Fast Fourier Transform
                                    1. Algorithm Overview
                                      1. Divide-and-Conquer Approach
                                        1. Butterfly Operations
                                        2. Computational Advantages
                                          1. Complexity Reduction
                                            1. Memory Requirements
                                            2. Implementation Considerations
                                              1. Power-of-Two Sizing
                                                1. Zero-padding Strategies
                                              2. Filtering in the Frequency Domain
                                                1. Basic Steps of Frequency Domain Filtering
                                                  1. Image Preprocessing
                                                    1. Forward Fourier Transform
                                                      1. Filter Application
                                                        1. Inverse Fourier Transform
                                                          1. Post-processing
                                                          2. Correspondence Between Spatial and Frequency Filters
                                                            1. Low-pass Filter Equivalence
                                                              1. High-pass Filter Equivalence
                                                                1. Impulse Response Relationship
                                                                  1. Frequency Response Analysis
                                                                2. Frequency Domain Filters
                                                                  1. Low-Pass Filters
                                                                    1. Ideal Low-Pass Filters
                                                                      1. Sharp Cutoff Characteristics
                                                                        1. Ringing Artifacts
                                                                        2. Butterworth Low-Pass Filters
                                                                          1. Order Parameter Effects
                                                                            1. Smooth Transition
                                                                            2. Gaussian Low-Pass Filters
                                                                              1. No Ringing Artifacts
                                                                                1. Separability Properties
                                                                              2. High-Pass Filters
                                                                                1. Ideal High-Pass Filters
                                                                                  1. Sharp Cutoff Characteristics
                                                                                  2. Butterworth High-Pass Filters
                                                                                    1. Order Parameter Effects
                                                                                    2. Gaussian High-Pass Filters
                                                                                      1. Smooth Characteristics
                                                                                    3. Band-Pass and Band-Reject Filters
                                                                                      1. Band-Pass Filter Design
                                                                                        1. Frequency Range Selection
                                                                                        2. Band-Reject Filter Design
                                                                                          1. Notch Filter Implementation
                                                                                          2. Applications in Noise Removal
                                                                                          3. Notch Filters
                                                                                            1. Periodic Noise Removal
                                                                                              1. Multiple Notch Implementation
                                                                                                1. Optimum Notch Filtering
                                                                                              2. Homomorphic Filtering
                                                                                                1. Illumination-Reflectance Model
                                                                                                  1. Multiplicative Model
                                                                                                    1. Logarithmic Transformation
                                                                                                    2. Frequency Domain Separation
                                                                                                      1. Low-frequency Illumination
                                                                                                        1. High-frequency Reflectance
                                                                                                        2. Applications in Image Enhancement
                                                                                                          1. Dynamic Range Compression
                                                                                                            1. Contrast Enhancement

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                                                                                                        3. Spatial Filtering

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                                                                                                        5. Image Restoration and Denoising