Lecture - Image Enhancement (frequency domain)

Lecture - Image Enhancement (frequency domain) - Bahadir K...

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EE 4780 Image Enhancement (Frequency Domain)
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Bahadir K. Gunturk 2 Frequency-Domain Filtering Compute the Fourier Transform of the image Multiply the result by filter transfer function Take the inverse transform
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Bahadir K. Gunturk 3 Frequency-Domain Filtering
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Bahadir K. Gunturk 4 Frequency-Domain Filtering Ideal Lowpass Filters 1, for and ( , ) 0, otherwise u v u D v D H u v = >> [f1,f2] = freqspace(256,'meshgrid'); >> H = zeros(256,256); d = sqrt(f1.^2 + f2.^2) < 0.5; >> H(d) = 1; >> figure; imshow(H); Separable Non-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); 2 2 0 1, for ( , ) 0, otherwise u v D H u v + =
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Bahadir K. Gunturk 5 Frequency-Domain Filtering Butterworth Lowpass Filter 2 2 2 0 1 ( , ) 1 n H u v u v D = + + As order increases the frequency response approaches ideal LPF
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Bahadir K. Gunturk 6 Frequency-Domain Filtering Butterworth Lowpass Filter Approach to a sinc function.
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Bahadir K. Gunturk 7 Frequency-Domain Filtering Gaussian Lowpass Filter 2 2 0 ( , ) u v D H u v e + - =
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Bahadir K. Gunturk 8 Frequency-Domain Filtering Ideal LPF Butterworth LPF Gaussian LPF
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Unformatted text preview: Bahadir K. Gunturk 9 Example Bahadir K. Gunturk 10 Highpass Filters 2 2 2 1 ( , ) 1 n H u v u v D-= + + 2 2 ( , ) 1 u v D H u v e +-= -2 2 0, for ( , ) 1, otherwise u v D H u v + ≤ = Bahadir K. Gunturk 11 Example Bahadir K. Gunturk 12 Homomorphic Filtering Consider the illumination and reflectance components of an image ( , ) ( , )* ( , ) f x y i x y r x y = Illumination Reflectance [ ] [ ] [ ] ln ( , ) ln ( , ) ln ( , ) f x y i x y r x y = + Take the ln of the image In the frequency domain ( , ) ( , ) ( , ) i r F u v F u v F u v = + Bahadir K. Gunturk 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. Bahadir K. Gunturk 14 Homomorphic Filtering 0.5 2.0 L H γ = =...
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Lecture - Image Enhancement (frequency domain) - Bahadir K...

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