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EE 7730

EE 7730. Image Enhancement (Frequency Domain). Frequency-Domain Filtering. Compute the Fourier Transform of the image Multiply the result by filter transfer function Take the inverse transform. Frequency-Domain Filtering. Frequency-Domain Filtering. Ideal Lowpass Filters. Non-separable.

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EE 7730

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  1. EE 7730 Image Enhancement (Frequency Domain)

  2. Frequency-Domain Filtering • Compute the Fourier Transform of the image • Multiply the result by filter transfer function • Take the inverse transform EE 7730 - Image Analysis I

  3. Frequency-Domain Filtering EE 7730 - Image Analysis I

  4. Frequency-Domain Filtering • Ideal Lowpass Filters Non-separable >> [f1,f2] = freqspace(256,'meshgrid'); >> H = zeros(256,256); d = sqrt(f1.^2 + f2.^2) < 0.5; >> H(d) = 1; >> figure; imshow(H); Separable >> [f1,f2] = freqspace(256,'meshgrid'); >> H = zeros(256,256); d = abs(f1)<0.5 & abs(f2)<0.5; >> H(d) = 1; >> figure; imshow(H); EE 7730 - Image Analysis I

  5. Frequency-Domain Filtering • Butterworth Lowpass Filter As order increases the frequency response approaches ideal LPF EE 7730 - Image Analysis I

  6. Frequency-Domain Filtering • Butterworth Lowpass Filter EE 7730 - Image Analysis I

  7. Frequency-Domain Filtering • Gaussian Lowpass Filter EE 7730 - Image Analysis I

  8. Frequency-Domain Filtering Ideal LPF Butterworth LPF Gaussian LPF EE 7730 - Image Analysis I

  9. Example EE 7730 - Image Analysis I

  10. Highpass Filters EE 7730 - Image Analysis I

  11. Example EE 7730 - Image Analysis I

  12. Homomorphic Filtering • Consider the illumination and reflectance components of an image Illumination Reflectance • Take the ln of the image • In the frequency domain EE 7730 - Image Analysis I

  13. Homomorphic Filtering • The illumination component of an image shows slow spatial variations. • The reflectance component varies abruptly. • Therefore, we can treat these components somewhat separately in the frequency domain. 1 With this filter, low-frequency components are attenuated, high-frequency components are emphasized. EE 7730 - Image Analysis I

  14. Homomorphic Filtering EE 7730 - Image Analysis I

  15. Summary • Digital Image Fundamentals: Pixel, resolution, bit depth, ... • Linear Systems: Shift invariance, causality, convolution, impulse response, ... • Fourier Transform: 2D Fourier Transform of continuous and discrete signals, 2D FT properties (linearity, shifting, modulation, convolution, multiplication, energy conservation, etc.), Dirac delta function, Kronecker delta function, … • 2D Sampling: Aliasing, anti-aliasing filter, downsampling, interpolation, … • Discrete Fourier Transform: Periodicity, other properties, frequency-domain filtering, … • Discrete Cosine Transform: Properties (real basis functions, good energy compaction), relationship with DFT, matrix representation of DCT, … • Image Enhancement: Image enhancement by point processing (intensity transformation, histogram equalization, histogram specification, etc.), Image enhancement by spatial-domain filtering (lowpass filtering, highpass filtering, median filtering, high-boost filtering, gradient and laplacian operators, etc.), Image enhancement by frequency-domain filtering (lowpass/highpass filters, homomorphic filtering, etc.) EE 7730 - Image Analysis I

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