Digital Image Processing
Chapter 4: Filtering in The Frequency Domain
(4.6 – 4.11)
4.6.1 Relationships Between Spatial and Frequency Intervals
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4.6.2 Translation and Rotation
3
4.6.3 Periodicity
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4.6.3 Periodicity
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4.6.4 Symmetry Properties
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4.6.4 Symmetry Properties
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4.6.4 Symmetry Properties
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4.6.4 Symmetry Properties
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4.6.4 Symmetry Properties
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4.6.4 Symmetry Properties
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4.6.4 Symmetry Properties
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Real & Even
4.6.4 Symmetry Properties
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4.6.4 Symmetry Properties
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4.6.5 Fourier Spectrum and Phase Angle
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4.6.5 Fourier Spectrum and Phase Angle
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4.6.5 Fourier Spectrum and Phase Angle
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4.6.5 Fourier Spectrum and Phase Angle
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4.6.5 Fourier Spectrum and Phase Angle
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4.6.5 Fourier Spectrum and Phase Angle
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4.6.5 Fourier Spectrum and Phase Angle
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4.6.6 The 2-D Convolution Theorem
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4.6.6 The 2-D Convolution Theorem
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4.6.6 The 2-D Convolution Theorem
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4.6.6 The 2-D Convolution Theorem
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4.6.7 Summary of 2-D Discrete Fourier Transform Properties
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4.6.7 Summary of 2-D Discrete Fourier Transform Properties
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4.6.7 Summary of 2-D Discrete Fourier Transform Properties
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4.6.7 Summary of 2-D Discrete Fourier Transform Properties
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4.7.1 Additional Characteristics of the Frequency Domain
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4.7.2 Frequency Domain Filtering Fundamentals
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4.7.2 Frequency Domain Filtering Fundamentals
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4.7.2 Frequency Domain Filtering Fundamentals
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4.7.2 Frequency Domain Filtering Fundamentals
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4.7.2 Frequency Domain Filtering Fundamentals
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4.7.2 Frequency Domain Filtering Fundamentals
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4.7.3 Summary of Steps for Filtering in the Frequency Domain
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4.7.4 Correspondence Between Filtering in the Spatial and Frequency Domains
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4.7.4 Correspondence Between Filtering in the Spatial and Frequency Domains
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4.7.4 Correspondence Between Filtering in the Spatial and Frequency Domains
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4.7.4 Correspondence Between Filtering in the Spatial and Frequency Domains
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4.7.4 Correspondence Between Filtering in the Spatial and Frequency Domains
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4.8.1 Ideal Lowpass Filters
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4.8.1 Ideal Lowpass Filters
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4.8.1 Ideal Lowpass Filters
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4.8.1 Ideal Lowpass Filters
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4.8.1 Ideal Lowpass Filters
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4.8.2 Butterworth Lowpass Filters
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4.8.2 Butterworth Lowpass Filters
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4.8.2
Butterworth
Lowpass Filters
50
4.8.2 Butterworth Lowpass Filters
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4.8.3 Gaussian Lowpass Filters
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4.8.3 Gaussian Lowpass Filters
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4.8.3 Gaussian Lowpass Filters
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4.8.4 Additional Examples of
Lowpass Filtering
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4.8.4 Additional Examples of Lowpass Filtering
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4.8.4 Additional Examples of Lowpass Filtering
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4.9 Image Sharpening Using Frequency Domain Filters
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4.9.1 Ideal Highpass Filters
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4.9.1 Ideal Highpass Filters
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4.9.1 Ideal Highpass Filters
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4.9.2 Butterworth Highpass Filters
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4.9.2 Butterworth Highpass Filters
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4.9.3 Gaussian Highpass Filter
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4.9.4 The Laplacian in the Frequency Domain
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4.9.4 The Laplacian in the Frequency Domain
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4.9.4 The Laplacian in the Frequency Domain
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4.9.4 The Laplacian in the Frequency Domain
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4.9.5 Unsharp Masking Highboost Filtering and High-Frequency-Emphasis Filtering
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4.9.5 Unsharp Masking Highboost Filtering and High-Frequency-Emphasis Filtering
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4.9.6 Homomorphic Filtering
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4.9.6 Homomorphic Filtering
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4.9.6 Homomorphic Filtering
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4.9.6 Homomorphic Filtering
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4.9.6 Homomorphic Filtering
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4.9.6 Homomorphic Filtering
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4.9.6 Homomorphic Filtering
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4.10.1 Bandreject and Bandpass Filters
78
4.10.2 Notch filters
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4.10.2 Notch filters
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4.10.2 Notch filters
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4.10.2 Notch filters
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4.10.2 Notch filters
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4.11.1 Separability of the 2-D DFT
84
4.11.2 Computing the IDFT Using a DFT Algorithm
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4.11.3 The Fast Fourier Transform(FFT)
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4.11.3 The Fast Fourier Transform(FFT)
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4.11.3 The Fast Fourier Transform(FFT)
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4.11.3 The Fast Fourier Transform(FFT)
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4.11.3 The Fast Fourier Transform(FFT)
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4.11.3 The Fast Fourier Transform(FFT)
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