EE4206/EE5806 Digital Image Processing

EE4206/EE5806 Digital Image Processing

Chapter 4 main points

Filtering in the Frequency Domain

4.1 -Foutier Series and Transform

4.2 - Complex Numbers
- Fourier Series
- Impulses and their Sifting Property
- The Fourier Transform of Functions of one continuous variable
- Convolution

4.3 Sampling and the Fourier transform of Sampled functions
- Sampling
- The Fourier Transform of Sampled Functions
- The Sampling Theorem
- Aliasing
- Function Reconstruction (recovery) from Sampled Data

4.4 The Discrete Fourier Transform (DFT) of one variable
- Obtaining the DFT from the Continuous transform of a Sampled function
- Relationship between the Sampling and Frequency Intervals

4.5 Extension to functions of Two Variables
-The 2D Impulse and its Sifting Property
-The 2D Continuous Fourier Transform pair
-Two-Dimensional Sampling and the 2-D Sampling Theorem
- Aliasing in images
- The 2-D Discrete Fourier Transform and its Inverse

4.6 Some Properties of the 2D Discrete Fourier Transform
- Relations between Spatial and Frequency Intervals
- Translation and Rotation
- Periodicity
- Symmetry Properties
- Fourier Spectrum and Phase Angle
- The 2-D Convolution Theorem

4.7 Filtering in the Frequency Domain
- steps
- Correspondence between filtering in the Spatial and Frequency Domain

4.8 Image Smoothing using Frequency Domain filters
- Ideal Lowpass Filters
- Butterworth Lowpass Filters
- Gaussian Lowpass Filters

4.9 Image Sharpening using Frequency domain filters
- Ideal Highpass Filters
- Butterworth Highpass Filters
- Gaussian Highpass Filters
- The Laplacian in the Frequency domain
- Unsharp masking, highboost Filtering, and High-Frequency-Emphasis Filtering
- Homomorphic Filtering

4.10 Selective Filtering
- Bandreject and Bandpass Filters
- Notch Filters

4.11 Implementation
- Separability ofthe 2-D DFT
- computing the IDFT using a DFT algorithm
- FFT