Digital Image ProcessingChapter 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

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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

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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

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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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4.10.2 Notch filters

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4.11.1 Separability of the 2-D DFT

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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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